What is the solution for sqrt(y)(dy)/(dx)+sqrt(y^3)=1,y(4)=0 ?

The solution for sqrt(y)(dy)/(dx)+sqrt(y^3)=1,y(4)=0 is y=\sqrt[3]{e^{-3x+12}-2e^{-(3x)/2+6}+1}

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sqrt(y)(dy)/(dx)+sqrt(y^3)=1,y(4)=0

y \frac{d y}{d x} + y^{3} = 1, y (4) = 0

Solution steps

y \frac{d y}{d x} + y^{3} = 1

Solve separable ODE:

(x^{2} + 25) y^{^{'}} = x y

x^{2} \frac{d y}{d x} + \frac{1}{x} y = \frac{2}{x} y^{- 3}

\frac{d x}{d y} = 1 - 0.4 x

y^{^{'}} - x^{2} cos (y) = x^{2}

y^{^{'}} = y^{2} x^{2}

What is the solution for sqrt(y)(dy)/(dx)+sqrt(y^3)=1,y(4)=0 ?
The solution for sqrt(y)(dy)/(dx)+sqrt(y^3)=1,y(4)=0 is y=\sqrt[3]{e^{-3x+12}-2e^{-(3x)/2+6}+1}