# Thread: 1st order ODE?

1. ## 1st order ODE?

Dear friends,
Please suggest any method for the solution of the following equation:
$A(sin(at)+\frac{1}{2}sin(2at))+B(cos(at)+cos(2at)) =Dy(t)+\frac{dy}{dt}$
$y(t_1)=y_s$
$t\in(0,t_1)$

A,B,D,a=const
Thank you in advance.

2. Have you tried to find an integrating factor?

$I = e^{\int D~dt}$

3. Thank you for your reply.
It is interesting that i got different results from the method of integrating factor and from the method of variation of constant. Is there any criteria for the equations, which can be solved with the integrating factor? Maybe, this equation can't be solved applying this method, or I just made a mistake solving.