Power series method of solving ODE

[femi]

Please can somebody help me with this problem

y" + y' + sin^2(x)y - 2sinx = 0

I used power series method and i used the macclurin expresion for sinx but i was not able to get a recurrence formula.

 

[trambolin]

I did not check it but did you try plugging in

$\sin^2(x) = \frac{1-\cos(2x)}{2}$

and expand your series again?

 

[HallsofIvy]

Very nice suggestion.

 

[femi]

I cann't get it that way. I think i need to use the macclurin series so that sin^2 will be in terms of x. Pls any other suggestion?

 

[HallsofIvy]

I have no idea what you mean by "i need to use the macclurin series so that sin^2 will be in terms of x". Of course $sin^2 x$ is in terms of x- that has nothing to do with a series! And trambolin did not mean that you shouldn't use MacLaurin series but that it is far easier to write a MacLaurin series for cos(2x) than to have a MacLaurin series, for sin(x) squared!