Solve the initial value problem. dy/dx=x\sqrt{ x^5}, y(0)=0. y=?

Answer 1

dy/dx = x √(x⁵) = x^7/2

y = (2/9)x^9/2 + C

The initial condition y(0) = 0 implies C = 0.

y = (2/9)x^9/2