What is the solution for sqrt(x)+sqrt(y)(dy)/(dx)=0,y(16)=4 ?

The solution for sqrt(x)+sqrt(y)(dy)/(dx)=0,y(16)=4 is y=\sqrt[3]{x^3-144x^{3/2}+5184}

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sqrt(x)+sqrt(y)(dy)/(dx)=0,y(16)=4

x + y \frac{d y}{d x} = 0, y (16) = 4

y = 3 x^{3} - 144 x^{\frac{3}{2}} + 5184

Solution steps

x + y \frac{d y}{d x} = 0

Solve separable ODE:

y = 3 x^{3} - 144 x^{\frac{3}{2}} + 5184

y = 3 x^{3} - 144 x^{\frac{3}{2}} + 5184

\int \frac{- 8}{x ^{2} + 16} d x

\frac{d}{d x} (arctan (sin (7 x)))

\int o d o

2 y y^{^{'}} + 2 = y^{2} + 2 x, y (0) = 8

\frac{d}{d x} (x arcsec (x^{3}))

What is the solution for sqrt(x)+sqrt(y)(dy)/(dx)=0,y(16)=4 ?
The solution for sqrt(x)+sqrt(y)(dy)/(dx)=0,y(16)=4 is y=\sqrt[3]{x^3-144x^{3/2}+5184}