Question

non homogenous ODE and Rules for methods of undetermined coefficients :-
Find general solution
1) y”+ 3y’ +2y = 30 е²x
2) y”+ 9y= cos x + 1/3 cos 3x
3) y”+ 4y’+ 4y = е-²x sin2x
4) y”+ 4y’+ 6.25y = 3.125 (x+1)2
solve IVP
1) y”- 3y’+ 2.25y = 27 (x2+x) , y(0) =20 , y’(0) =30
2) y”+2y’+ 10y = 17 sin x- 37 sin 3x , y(0) =6.6 , y’(0) = - 2.2