Find the general solution of CauchyEuler Equation x2y 5xy

Find the general solution of Cauchy-Euler Equation x^2y\" - 5xy\' + 9y = 0, x > 0.

Solution

For Cauchy Euler Equation we assume solution of the form: y=x^k

Substituting gives

k(k-1)-5k+9=0

k^2-6k+9=0

k=3, repeated roots

So,

genreal solution is

y=x^3(A+B ln(x))