This a Cauchy-Euler Equation
which is
so your auxiliary equation is
so
and your answer is
Hi,
I just need to know where to start in solving this ODE. I know it has something to do with the Method of Undetermined Coefficients, but I'm really stuck. The question is as follows:
Find the general solution of:
where A and B are constants.
Thanks a lot!
You "understanding" is completely wrong. Ay"+ By+ C= 0 is a special case of the "constant coefficients" equation with Ay"+ 0y'+ By= -C. The general Cauchy-Euler equation of the 2nd order is ".
You can solve the homogeneous equation as Super Member (and he certainly is!) indicates and then try a "specific solution" of the form y= ux^2+ vx+ w for u, v, and w constants to be determined.
More generally, the substitution t= ln(x) converts a "Cauchy-Euler" equation to an equation with constant coefficients.