find the general solution of the given differential equation
1. 2y''+3y'+y=t^2 +3sint
find the solution of the given initial value problem
1. y''−2y'−3y=3te^2t, y(0) =1, y'(0) =0
2. y''−2y'+y=te^t +4, y(0) =1, y'(0) =1
given the 3rd order differential equation: y''' - 3y'' + 2y' =
ex / (1 + e-x)
i) set u = y' to reduce the order of the equation to order 2
ii) solve the reduced equation using variation of parameters
iii) find the solution of the original differential equation