Differential Equation

Question

Find solution of the indicated form

t^2(d^2y/dt^2) + t(dy/dt) - 4y=0. y=t^r

I took derivatives and plugged in and tried to get down to quadratic formula but got stuck.

Answer 1

y = t^r; y' = rt^r-1; y'' = r(r - 1)t^r-2;

[r(r - 1) + r - 4]r^t = 0; r²- 4 = 0; r = ±2

y = C₁t² + C₂t^-2.