Question

Differential Equations: Given that y1(t) = t^4 is a known solution of the second order linear differential equation t^2y'' - 4ty' + 4y = 0, t > 0, find the general solution of the equation.

Answer 1

let y=x^m,
y'=mx^(m-1)
y"=m(m-1)x^(m-2)
plug in the values in the eqn,
m^2-m-4m+4=0
(m-4)(m-1)=0
m=1,4
y=Ax+Bx^4