What is the solution for (dy}{dx}=\frac{2x)/y ,y(1)=1 ?

The solution for (dy}{dx}=\frac{2x)/y ,y(1)=1 is y=sqrt(2x^2-1)

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(dy}{dx}=\frac{2x)/y ,y(1)=1

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

y = 2 x^{2} - 1

Solution steps

\frac{d y}{d x} = \frac{2 x}{y}

Solve separable ODE:

y = 2 x^{2} - 1

y = 2 x^{2} - 1

x d y = (\frac{1}{y ^{2}} - y) d x

\frac{d y}{d x} = \frac{3 x ^{2} - e ^{x}}{2 y - 5}, y (0) = 1

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

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

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

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