# What is a solution to the differential equation y'=-9x^2y^2?

Jul 31, 2016

$y = \frac{1}{3 {x}^{3} + C}$

#### Explanation:

$y ' = - 9 {x}^{2} {y}^{2}$

this is separable

$\frac{1}{y} ^ 2 y ' = - 9 {x}^{2}$

$\int \setminus \frac{1}{y} ^ 2 y ' \setminus \mathrm{dx} = \int \setminus - 9 {x}^{2} \setminus \mathrm{dx}$

$\int \setminus \frac{1}{y} ^ 2 \setminus \mathrm{dy} = - 9 \int \setminus {x}^{2} \setminus \mathrm{dx}$

using power rule

$- \frac{1}{y} = - 3 {x}^{3} + C$

$\frac{1}{y} = 3 {x}^{3} + C$

$y = \frac{1}{3 {x}^{3} + C}$