If y(x) solves (x+2)dydx=x^2+4x-9, x-2, y(0)=0, then y(-4) is:

Question

If $y(x)$ solves $(x+2)\dfrac{dy}{dx}=x^2+4x-9$, $x
e-2$, $y(0)=0$, then $y(-4)$ is:

Accepted Answer

$$y = \int\left(x+2-\frac{13}{x+2}\right)dx = \frac{x^2}{2}+2x-13\ln|x+2|+c.$$

Using $y(0)=0$: $c=-13\ln2$. At $x=-4$: $y=8-8-13\ln2+13\ln2=0$.

Solutions · 1