ordinary and partial de

1. Presentation
On
Ordinary and Partial
Differential Equations

2. Submitted to:
Saba Fatema
Submitted by:
MD. Jahid Hasan
ID: 152-15-5588
Sec: ‘E’

3.  Solve the following second order linear
differential equation with constant coefficient:
4 𝑑
2
𝑦
𝑑𝑥
2 -2
𝑑𝑦
𝑑𝑥
+ 5𝑦 = 0
Soln :
4 𝑑2
𝑦
𝑑𝑥2 -2
𝑑𝑦
𝑑𝑥
+ 5𝑦 = 0 …………….(1)
Let, y= 𝒆 𝒎𝒙 be the solution of (1)
The auxiliary equation is;
4 𝑚2 − 2𝑚 + 5 = 0
m=
2± 4−4.4.5
2.4

2± 4−80
8

2± −76
8
1/4 ± i
76
8

4. The general solution is;
Y= 𝑒1/4𝑥[𝐴 𝑐𝑜𝑠
76
8
x + B 𝑠𝑖𝑛
76
8
x (Ans.)

5. THANK YOU