Mathematics - Differential Equation Question with Solution | TestHub

$\left(x+2\right)\frac{dy}{dx}=x^2+4x+4-13$

$\frac{dy}{dx}= \frac{{\left(x+2\right)}^2}{\left(x+2\right)}- \frac{13}{(x+2)}$

$dy= \left(\left(x+2\right)-\frac{13}{x+2}\right)dx$

$y=\frac{x^2}{2}+2x-13{\log }_e\left|\left(x+2\right)\right|+C$

If$x=0$then$y=0$

$0= 0+0-13 log\left|2\right|+C$

$C =13\log \left(2\right)$

If$x= -4,$then$y$

$y=\frac{16}{2}-8-13\log \left|-2\right|+13\log \left|2\right|$

$y=0$

Hence, answer is$0$.