# How do you use the differential equation dy/dx=-48/(3x+5)^3 to find the equation of the function given point (-1,3)?

$y = \frac{8}{3 x + 5} ^ 2 + 1$
Either by sight or by substituting $u = 3 x + 5$ youfind that $y = \frac{8}{3 x + 5} ^ 2 + c$
To make this curve pass through the point $\left(- 1 , 3\right)$, insert the co-ordinates and solve for $c$:
$3 = \frac{8}{3 \left(- 1\right) + 5} ^ 2 + c$
So $c = 1$.