Use the integrating factor method to find the general solution of the following differential equations.?

Question

(a) 2y'-3y = 5
(b) y'+ 2ty = 5t
(c) ty'= 4y + t^4

Use the varation of parameters method to nd the general solution of the following differential equation. Then find the particular solution satisfying the given initial condition.
(a) y'-3y = 4; y(0) = 2
(b) y' + y = e^t; y(0) = 1
(c) y' + 2ty = 2t^3; y(0) = -1.

Thank you!!!
(a) 2y'-3y = 5
(b) y'+ 2ty = 5t
(c) ty'= 4y + t^4

Use the varation of parameters method to nd the general solution of the following differential equation. Then find the particular solution satisfying the given initial condition.
(a) y'-3y = 4; y(0) = 2
(b) y' + y = e^t; y(0) = 1
(c) y' + 2ty = 2t^3; y(0) = -1.

Thank you!!!

Explanation / Answer

a) integrating factor= e^int-3/2dt;

  

hence solution is

y( e^int-3/2dt ) = int 5/2 e^int-3/2dt +c

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