What is the solution for (dy)/(dx)= y/x+(9x^2)/(y^2) ?

The solution for (dy)/(dx)= y/x+(9x^2)/(y^2) is y=x\sqrt[3]{27ln(x)+c_{1}}

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(dy)/(dx)= y/x+(9x^2)/(y^2)

\frac{d y}{d x} = \frac{y}{x} + \frac{9 x ^{2}}{y ^{2}}

y = x 3 27 ln (x) + c_{1}

Solution steps

\frac{d y}{d x} = \frac{y}{x} + \frac{9 x ^{2}}{y ^{2}}

Solve Bernoulli ODE:

y = x 3 27 ln (x) + c_{1}

y = x 3 27 ln (x) + c_{1}

\int \frac{12 x ^{2}}{4 x ^{3} + 1} d x

\int \frac{2 x - 5}{x ^{2} - 5 x + 6} d x

\int_{12}^{\infty} x e^{- x} d x

f (x) = sin (e^{x})

f (x)

What is the solution for (dy)/(dx)= y/x+(9x^2)/(y^2) ?
The solution for (dy)/(dx)= y/x+(9x^2)/(y^2) is y=x\sqrt[3]{27ln(x)+c_{1}}