What is the solution for (dy)/(dx)=(5x)/(9y) ?

The solution for (dy)/(dx)=(5x)/(9y) is y=(sqrt(c_{1)+5x^2})/3 ,y=-(sqrt(c_{1)+5x^2})/3

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(dy)/(dx)=(5x)/(9y)

\frac{d y}{d x} = \frac{5 x}{9 y}

y = \frac{c _{1} + 5 x ^{2}}{3}, y = - \frac{c _{1} + 5 x ^{2}}{3}

Solution steps

\frac{d y}{d x} = \frac{5 x}{9 y}

Solve separable ODE:

y = \frac{c _{1} + 5 x ^{2}}{3}, y = - \frac{c _{1} + 5 x ^{2}}{3}

y = \frac{c _{1} + 5 x ^{2}}{3}, y = - \frac{c _{1} + 5 x ^{2}}{3}

What is the solution for (dy)/(dx)=(5x)/(9y) ?
The solution for (dy)/(dx)=(5x)/(9y) is y=(sqrt(c_{1)+5x^2})/3 ,y=-(sqrt(c_{1)+5x^2})/3