Question

Solve the DE (2x+1)^2 y''+8(2x+1) y'+5y=0
Hint: let t=2x+1

Answer 1

Another Euler-Cauchy equation. Assume a solution is of the form \(y=t^r\).

Answer 2

I got the roots as \[\frac{ -7 \pm \sqrt{29}}{2 }\]
Do i set that up using y(x)=c1 cos(ln x) + c2 sin (ln x)

Answer 3

No, you don't have any complex roots, there's no need for Euler's formula here.

Answer 4

Thanks again.

Answer 5

yw