Power series method of solving ODE

femi
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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.
 
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I did not check it but did you try plugging in

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

and expand your series again?
 
Very nice suggestion.
 
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?
 
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!
 

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