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differential equation Lecture#7

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This lecture will improve your knowledge in differential equation lecture is by Lecturer AZEEM INAAM of SMI university.

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DIFFERENTIAL EQUATION (MT-202) SYED AZEEM INAM DIFFERENTIAL EQUATION (MT-202) LECTURE #7 LINEAR DIFFERENTIAL EQUATION: A first order differential equation is linear if it has the form 𝑦′(π‘₯) + 𝑃(π‘₯)𝑦 = 𝑄(π‘₯) EXAMPLE#1: 𝑑𝑦 𝑑π‘₯ + 𝑦 = 𝑠𝑖𝑛π‘₯ EXAMPLE#2: Solve 𝑑𝑦 𝑑π‘₯ = 3π‘₯2 βˆ’ 𝑦 π‘₯ EXAMPLE#3: Suppose a tank contain 200 gallons of brine (salt mixed with water), in which 100 pounds of salt is dissolved. A mixture consisting of 1/8 pounds of salt per gallon is flowing into the tank at a rate of 3 gallon per minute, and the mixture is continuously stirred. Meanwhile brine is allowed to empty out of the tank at the same rate of 3 gallons per minute. How much salt is in the tank at any time?

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differential equation Lecture#7

  • 1. DIFFERENTIAL EQUATION (MT-202) SYED AZEEM INAM DIFFERENTIAL EQUATION (MT-202) LECTURE #7 LINEAR DIFFERENTIAL EQUATION: A first order differential equation is linear if it has the form 𝑦′(π‘₯) + 𝑃(π‘₯)𝑦 = 𝑄(π‘₯) EXAMPLE#1: 𝑑𝑦 𝑑π‘₯ + 𝑦 = 𝑠𝑖𝑛π‘₯ EXAMPLE#2: Solve 𝑑𝑦 𝑑π‘₯ = 3π‘₯2 βˆ’ 𝑦 π‘₯ EXAMPLE#3: Suppose a tank contain 200 gallons of brine (salt mixed with water), in which 100 pounds of salt is dissolved. A mixture consisting of 1/8 pounds of salt per gallon is flowing into the tank at a rate of 3 gallon per minute, and the mixture is continuously stirred. Meanwhile brine is allowed to empty out of the tank at the same rate of 3 gallons per minute. How much salt is in the tank at any time?