Solving ode with complex numbers

cragar · Mar 25, 2014

I want to solve [itex]y''+y'+y=(sin(x))^2[/itex] and try to use
[itex]y=Ae^{ix}[/itex] but then when I square it I get [itex]A^2 e^{2ix}[/itex]
I found y' and y'' and solved for A and it didn't work I guess I could use the formula for reducing powers but I would like to try and get around that.

lurflurf · Mar 26, 2014

hint
$$(D^3+4D)(\sin(x))^2=0$$
or
(sin(x))^2 is a solution of y'''+4y

chose the particular solution from those solutions

Solving ode with complex numbers

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Solving ode with complex numbers

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