What is the solution for (dy)/(dx)=((-3x^2+2y^2))/(4xy) ?

The solution for (dy)/(dx)=((-3x^2+2y^2))/(4xy) is y=sqrt(-3/2 x^2+c_{1)x},y=-sqrt(-3/2 x^2+c_{1)x}

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(dy)/(dx)=((-3x^2+2y^2))/(4xy)

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

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

Solution steps

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

Solve Bernoulli ODE:

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

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

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What is the solution for (dy)/(dx)=((-3x^2+2y^2))/(4xy) ?
The solution for (dy)/(dx)=((-3x^2+2y^2))/(4xy) is y=sqrt(-3/2 x^2+c_{1)x},y=-sqrt(-3/2 x^2+c_{1)x}