What is the solution for 3x-2ysqrt(2x+1)(dy)/(dx)=0,y(0)=-4 ?

The solution for 3x-2ysqrt(2x+1)(dy)/(dx)=0,y(0)=-4 is y=-sqrt((x-1)\sqrt{2x+1)+17}

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3x-2ysqrt(2x+1)(dy)/(dx)=0,y(0)=-4

3 x - 2 y 2 x + 1 \frac{d y}{d x} = 0, y (0) = - 4

y = - (x - 1) 2 x + 1 + 17

Solution steps

3 x - 2 y 2 x + 1 \frac{d y}{d x} = 0

Solve separable ODE:

y = - (x - 1) 2 x + 1 + 17

y = - (x - 1) 2 x + 1 + 17

\frac{d x}{d y} = 2 x^{3} y - 10 x^{2} y

\frac{d}{d x} (y^{4} + 5 x) = \frac{d}{d x} (11)

\frac{d y}{d x} = 6 x y - 3 y

\frac{d y}{d x} + 2 x y^{2} = 0, y (1) = 2

\frac{4 y ^{^{'}} + y ^{2} + 4 \cdot 1}{x ^{2}} = 0

What is the solution for 3x-2ysqrt(2x+1)(dy)/(dx)=0,y(0)=-4 ?
The solution for 3x-2ysqrt(2x+1)(dy)/(dx)=0,y(0)=-4 is y=-sqrt((x-1)\sqrt{2x+1)+17}