What is the solution for (dy)/(dx)=(2x-3)/(5y) ?

The solution for (dy)/(dx)=(2x-3)/(5y) is y=sqrt((2x^2-6x+c_{1))/5},y=-sqrt((2x^2-6x+c_{1))/5}

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(dy)/(dx)=(2x-3)/(5y)

\frac{d y}{d x} = \frac{2 x - 3}{5 y}

y = \frac{2 x ^{2} - 6 x + c _{1}}{5}, y = - \frac{2 x ^{2} - 6 x + c _{1}}{5}

Solution steps

\frac{d y}{d x} = \frac{2 x - 3}{5 y}

Solve separable ODE:

y = \frac{2 x ^{2} - 6 x + c _{1}}{5}, y = - \frac{2 x ^{2} - 6 x + c _{1}}{5}

y = \frac{2 x ^{2} - 6 x + c _{1}}{5}, y = - \frac{2 x ^{2} - 6 x + c _{1}}{5}

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

\frac{d ^{2}}{d x ^{2}} (x e^{x})

\frac{d}{d x} (ln (\frac{( 1 - x )}{( x + 5 ) ^{3}}))

\frac{d}{d x} (cos (\frac{π x}{2}))

\frac{\partial}{\partial x} (6 x + 12)

What is the solution for (dy)/(dx)=(2x-3)/(5y) ?
The solution for (dy)/(dx)=(2x-3)/(5y) is y=sqrt((2x^2-6x+c_{1))/5},y=-sqrt((2x^2-6x+c_{1))/5}