Question

Solve the differential equation by separation of variables. dx/dy= dy/dx=x^2*cuberoot(y+1)

Answer 1

Answer:

$\dfrac{2}{3}(1+y)^{\dfrac{2}{3}}+ \dfrac{x^3}{3}=c$

Step-by-step explanation:

variable separable form:

$\dfrac{\mathrm{d} y}{\mathrm{d} x}=x^2\sqrt[3] {1+y}\\\dfrac{dy}{\sqrt{1+y}} = x^2dx\\\int\dfrac{dy}{\sqrt[3] {1+y}} = \int x^2dx\\\dfrac{2}{3}(1+y)^{\dfrac{2}{3}}= \dfrac{x^3}{3}+c\\\dfrac{2}{3}(1+y)^{\dfrac{2}{3}}+ \dfrac{x^3}{3}=c$

hence the solution comes out be

$\dfrac{2}{3}(1+y)^{\dfrac{2}{3}}+ \dfrac{x^3}{3}=c$