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

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

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(dy)/(dx)=(3x)/(2y)

\frac{d y}{d x} = \frac{3 x}{2 y}

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

Solution steps

\frac{d y}{d x} = \frac{3 x}{2 y}

Solve separable ODE:

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

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

\int e^{x} ln (e^{x} + 1) d x

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y^{^{'}} - (\frac{2}{x} y) = (\frac{y ^{3}}{x ^{3}}), y (1) = 1

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