$\displaystyle y=ax^2+bx$
Find the solution for the constants a & b.
$\displaystyle \frac{d^2y}{dx^2}+6\frac{dy}{dx}+36x=0$
I got as far as:
$\displaystyle y'=2ax+b$
$\displaystyle y''=2a$
And don't know what to do next.
$\displaystyle y=ax^2+bx$
Find the solution for the constants a & b.
$\displaystyle \frac{d^2y}{dx^2}+6\frac{dy}{dx}+36x=0$
I got as far as:
$\displaystyle y'=2ax+b$
$\displaystyle y''=2a$
And don't know what to do next.
If you were supposed to solve for $\displaystyle x$ then $\displaystyle x=\frac{-b \pm \sqrt{b^2+4ay}}{2a}$ (using quadratic formula), else the question doesn't make any sense.
If you were supposed to find $\displaystyle a$ and $\displaystyle b$ ,there would be 2 equations.