The equation is the following:
[math]cosx*y'=cosx + 2sinx*y[/math]
Here is how I tried to solve it (attached image of blank paper with the problem solved on it).
The official solution, however, is:
[math]y=1/(cos^2x)*(x/2 + sin2x/4)[/math]
I don't understand why my solution is not correct, when I successfully identified P(x) and Q(x) (according to the differential equation solver website), and plugged them in the formula for y(x) for linear DE. For clarification, the last formula I was talking about was this one:
[math]y(x) = e^(-\int P(x) \,dx) * (C + \int Q(x)*e^(\int P(x) \,dx))[/math]
I would appreciate any help given.
[math]cosx*y'=cosx + 2sinx*y[/math]
Here is how I tried to solve it (attached image of blank paper with the problem solved on it).
The official solution, however, is:
[math]y=1/(cos^2x)*(x/2 + sin2x/4)[/math]
I don't understand why my solution is not correct, when I successfully identified P(x) and Q(x) (according to the differential equation solver website), and plugged them in the formula for y(x) for linear DE. For clarification, the last formula I was talking about was this one:
[math]y(x) = e^(-\int P(x) \,dx) * (C + \int Q(x)*e^(\int P(x) \,dx))[/math]
I would appreciate any help given.