What is the solution for 3x-4ysqrt(x^2+1)(dy)/(dx)=0,y(0)=-8 ?

The solution for 3x-4ysqrt(x^2+1)(dy)/(dx)=0,y(0)=-8 is y=-sqrt((3\sqrt{x^2+1)+125)/2}

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3x-4ysqrt(x^2+1)(dy)/(dx)=0,y(0)=-8

3 x - 4 y x^{2} + 1 \frac{d y}{d x} = 0, y (0) = - 8

y = - \frac{3 x ^{2} + 1 + 125}{2}

Solution steps

3 x - 4 y x^{2} + 1 \frac{d y}{d x} = 0

Solve separable ODE:

y = - \frac{3 x ^{2} + 1 + 125}{2}

y = - \frac{3 x ^{2} + 1 + 125}{2}

3 \frac{d y}{d x} - 7 \frac{d y}{d x} + 3 y = 0

\frac{d y}{d x} = \frac{x}{y ^{2}}, y (2) = 3

(2 - x^{3}) y^{^{'}} - 3 x^{2} y = 0

\frac{d y}{d x} = (\frac{y}{x})

u^{^{'}} = 2 e^{7 x - H (x)}

What is the solution for 3x-4ysqrt(x^2+1)(dy)/(dx)=0,y(0)=-8 ?
The solution for 3x-4ysqrt(x^2+1)(dy)/(dx)=0,y(0)=-8 is y=-sqrt((3\sqrt{x^2+1)+125)/2}