Question

How do you solve the differential `dy/dx=(10x^2)/sqrt(1+x^3)`?

Answer 1

`y = 20/3 sqrt(1+x^3)+C`

Explanation:

We know that

`d/dx(sqrt(1+x^3))=3/2 x^2/sqrt(1+x^3)`

so, grouping variables

`dy =20/3d/dx(sqrt(1+x^3))dx` integrating

`y = 20/3 sqrt(1+x^3)+C`