find the general solution of the given differential
equation.
1. y'' + y = tan t, 0 < t < π/2
2. y'' + 4y' + 4y = t-2 e-2t , t >
0
find the solution of the given initial value problem.
3. y'' + y' − 2y = 2t, y(0) = 0, y'(0) = 1
1) find the solution t the non-homogenous DE
y''-16y=3e5x , y(0)=1 , y'(0)=2
2)find the solution to the DE using cauchy-euler method
x2y''+7xy'+9y=0 , y(1)=2 , y'(1)=3
3)find the solution to the DE using Laplace
y''+8y'+16y=0 , y(0)=-1 , y'(0)=8