Using Frobenius method for solving the ODE
$$x^2y''+(x^2-x)y'+2y=0$$
I am getting roots of inicial equation as $1 + i$ and $1 - i$ so I am not getting to solve when the roots are complex.
Any help is appreciated.
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Welcome to [math.se] SE. Take a [tour]. You'll find that simple "Here's the statement of my question, solve it for me" posts will be poorly received. What is better is for you to add context (with an [edit]): What you understand about the problem, what you've tried so far, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance. – Another User Mar 17 '23 at 19:43
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3The method works just as well for complex roots as for real ones, you just have to do arithmetic using complex numbers. You might note that $$ x^{a + b i} = x^a x^{bi} = x^a \exp(b i \ln(x)) = x^a (\cos(b \ln(x)) + i \sin(b \ln(x))$$ – Robert Israel Mar 17 '23 at 19:59