Originally Posted by

**falconed** Hey everyone!

I have a question:

$\displaystyle 2x^2\frac{d^2y}{dx^2} + 3x\frac{dy}{dx} - 15y = 0$

So I let:

$\displaystyle y = x^k$

$\displaystyle y' = kx^{k-1}$

$\displaystyle y'' = k^2x^{k-2}$

Therefore,

$\displaystyle 2x^2k^2x^{k-2} + 3xkx^{k-1} - 15x^k = 0$

So would I be right in saying:

$\displaystyle x^k(2k(k-1) + 3k - 15) = 0$

$\displaystyle x^k \ne 0$

$\displaystyle 2k(k-1) + 3k - 15 = 0$

Therefore, k = 2.5, k = -3

$\displaystyle y = \frac{A}{x^3} + Bx^{\tfrac{5}{2}}$

Would this solution be right?

Thanks in advance.