# Question #54eb5

Dec 18, 2016

$\frac{3}{2} {x}^{2} + 3 x y - 2 {x}^{4} = C$

#### Explanation:

As ${\left(3 x + 3 y\right)}_{y} ' = {\left(3 x - 8 {y}^{3}\right)}_{x} ' = 3$, the given equation is an exact

differential equation. Now I proceed to integrate. The integral is

$3 \int x \mathrm{dx} + 3 \int \left(y \mathrm{dx} + x \mathrm{dy}\right) - 8 \int {y}^{3} \mathrm{dy}$

$= \frac{3}{2} {x}^{2} + 3 \int d \left(x y\right) - 2 {y}^{4}$

$\implies \frac{3}{2} {x}^{2} + 3 x y - 2 {x}^{4} = C$.