You should get : .
so that the two solutions are : & .
Hence, the general solution is .
ok i wanted to know if someone could check my work and let me know if they got the same thing.
im supposed to find the values of m so that the function y = x^m is a solution to,
x^2y'' - 3xy' - y = 0.
i got m = 0. i just took the first and 2nd derivative of the function and plugged it into the equation and solved.
thanks in advance.
In case we don't know there are solutions of the form and considering that we have an Euler equation, the subtitution with independent variable, transforms the given equation into a linear homogeneous differential equation with constant coefficients.