This document contains instructions for solving various types of differential equations. It includes:
1) Finding the general solution to given differential equations
2) Finding the particular solution given initial conditions
3) Converting between forms of the general solution for harmonic oscillation equations
4) Solving a differential equation subject to boundary conditions
5) Solving a differential equation subject to initial conditions
Class 10 Maths contains mainly three concepts one is numbers second is geometry and third is trigonometry and Mensuration. NCERT solutions for class 10 maths are really helpful while doing home work and preparing for exams to score good marks in the board exam. https://www.entrancei.com/topics-topics-class-10-mathematics
APEX INSTITUTE was conceptualized in May 2008, keeping in view the dreams of young students by the vision & toil of Er. Shahid Iqbal. We had a very humble beginning as an institute for IIT-JEE / Medical, with a vision to provide an ideal launch pad for serious JEE students . We actually started to make a difference in the way students think and approach problems. We started to develop ways to enhance students IQ. We started to leave an indelible mark on the students who have undergone APEX training. That is why APEX INSTITUTE is very well known of its quality of education
Class 10 Maths contains mainly three concepts one is numbers second is geometry and third is trigonometry and Mensuration. NCERT solutions for class 10 maths are really helpful while doing home work and preparing for exams to score good marks in the board exam. https://www.entrancei.com/topics-topics-class-10-mathematics
APEX INSTITUTE was conceptualized in May 2008, keeping in view the dreams of young students by the vision & toil of Er. Shahid Iqbal. We had a very humble beginning as an institute for IIT-JEE / Medical, with a vision to provide an ideal launch pad for serious JEE students . We actually started to make a difference in the way students think and approach problems. We started to develop ways to enhance students IQ. We started to leave an indelible mark on the students who have undergone APEX training. That is why APEX INSTITUTE is very well known of its quality of education
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2004. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
Maths Assignment Help boasts a team of exceptionally skilled, knowledgeable, and reliable experts in the field of assignment assistance. With a strong commitment to delivering original and impactful assignment solutions within designated deadlines, we ensure utmost customer satisfaction. Each of our solutions undergoes rigorous quality checks to guarantee excellence. Our primary focus lies in delivering assignments of outstanding quality, making it our foremost objective.
Reach out to our team via: - Websitehttps://www.mathsassignmenthelp.com/ Email: info@mathsassignmenthelp.com Call/WhatsApp: +1(315)557–6473
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
1. DEPARTMENT OF MATHEMATICAL SCIENCES
FACULTY OF SCIENCE
UNIVERSITI TEKNOLOGI MALAYSIA
SSCM 1703 DIFFERENTIAL EQUATIONS TUTORIAL 2
1. Find the general solution for each of the following differential equations.
(a) y
′′ 4y
′
+ 3y = 0: (b) y
′′
+ 10y
′
+ 25y = 0:
(c) y
′′
+ 16y = 0: (d) 12y
′′ 5y
′ 2y = 0:
2. Find the particular solution for each of the following differential equations.
(a)
d2y
dx2
12
dy
dx
+ 11y = 0; y(0) = 3; y
′
(0) = 11.
(b) 2
d2y
dx2 + 5
dy
dx
+ 2y = 0; y(0) = 0; y
′
(0) = 1.
(c)
d2y
dx2
4
dy
dx
+ 4y = 0; y(1) = 4; y
′
(0) = 0.
(d)
d2y
dx2
6
dy
dx
+ 13y = 0; y(=2) = 0; y
′
(=2) = 2.
3. The general solution of the equation
d2x
dt2 + !2x = 0;
where ! is a constant, may be written in either of the forms
x = Acos !t + B sin !t = C sin (!t + );
where A;B;C and are constants.
(a) Determine the formula for C and in terms of A and B.
(b) Taking ! = 6, find C and given that x = 9
2
p
3 and
dx
dt
= 27 when t = 0.
4. Find the solution of the differential equation
6
d2y
dx2 +
dy
dx
2y = 0;
which satisfy the conditions y′ = 4 when x = 0 and y ! 0 as x ! 1:
5. Find the solution of the differential equation
d2y
dt2 + 6
dy
dt
16y = 0;
which satisfy the conditions y(0) = 3 and y ! 0 as t ! 1:
