If I have [itex] y''+y'+2y=sin(x)+cos(x) [/itex](adsbygoogle = window.adsbygoogle || []).push({});

can I just say [itex] y=Ae^{ix} [/itex]

and then find y' and y'' and then plug them in and solve for A.

so I get that [itex] A= \frac{1}{1+i} [/itex]

then i multiply and divided by the complex conjugate.

then I back substitute in Eulers formula.

now since I have my original equation has both a real and an imaginary part.

when I multiply out A times Eulers formula, I will take both real and imaginary parts.

and I get that y=sin(x) and tested this and it works.

But is what i did with Eulers formula ok.

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# Solving an ODE with eulers formula.

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