What is the solution for 2x-6ysqrt(x^2+1)(dy)/(dx)=0,y(0)=-1 ?

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

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2x-6ysqrt(x^2+1)(dy)/(dx)=0,y(0)=-1

2 x - 6 y x^{2} + 1 \frac{d y}{d x} = 0, y (0) = - 1

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

Solution steps

2 x - 6 y x^{2} + 1 \frac{d y}{d x} = 0

Solve separable ODE:

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

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

\frac{d x}{d t} = - x^{2} + 4 x

\frac{d x}{d t} + cos (t) x - cos (t) = 0

y^{^{'}} = y (1 - \frac{y}{2000})

\frac{d x}{d t} = 12 - \frac{36 x}{100}

\frac{d y}{d t} = - \frac{1}{50} (y - 17)

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