What is the solution for (dy)/(dx)=(3x^2-1)/(2y) ?

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

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(dy)/(dx)=(3x^2-1)/(2y)

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

y = x^{3} - x + c_{1}, y = - x^{3} - x + c_{1}

Solution steps

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

Solve separable ODE:

y = x^{3} - x + c_{1}, y = - x^{3} - x + c_{1}

y = x^{3} - x + c_{1}, y = - x^{3} - x + c_{1}

\frac{d}{d x} (\frac{1}{2} csc (\frac{x}{4}))

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

ln (x^{2} + 1) + e^{- x^{2}}

\frac{100}{x}

\int \frac{x ^{2}}{( x + 1 ) ^{3}} d x

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