Question #3d111

1 Answer
Feb 5, 2017

y(x) = root(3)((3x^4)/2 +C)

Explanation:

This is a separable differential equation, so we can solve it by separating the variables on the two sides and then integrating:

dy/dx = (2x^3)/y^2

y^2dy = 2x^3dx

int y^2dy = 2int x^3dx

These are standard integrals we can solve using the power rule:

y^3/3 = 2x^4/4 +C

y^3 = (3x^4)/2 +C

and finally:

y = root(3)((3x^4)/2 +C)