What is the solution for (xy^2+3y^2)dy-9ydx=0 ?

The solution for (xy^2+3y^2)dy-9ydx=0 is y=sqrt(18ln(x+3)+c_{1)},y=-sqrt(18ln(x+3)+c_{1)}

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(xy^2+3y^2)dy-9ydx=0

(x y^{2} + 3 y^{2}) d y - 9 y d x = 0

y = 18 ln (x + 3) + c_{1}, y = - 18 ln (x + 3) + c_{1}

Solution steps

(x y^{2} + 3 y^{2}) d y - 9 y d x = 0

Solve separable ODE:

y = 18 ln (x + 3) + c_{1}, y = - 18 ln (x + 3) + c_{1}

y = 18 ln (x + 3) + c_{1}, y = - 18 ln (x + 3) + c_{1}

\frac{d y}{d x} = \frac{2 x}{y}, y (1) = 1

x d y = (\frac{1}{y ^{2}} - y) d x

\frac{d y}{d x} = \frac{3 x ^{2} - e ^{x}}{2 y - 5}, y (0) = 1

y^{^{'}} = y^{2} \cdot x

x y^{2} + y y^{^{'}} = x^{2} y y^{^{'}}

What is the solution for (xy^2+3y^2)dy-9ydx=0 ?
The solution for (xy^2+3y^2)dy-9ydx=0 is y=sqrt(18ln(x+3)+c_{1)},y=-sqrt(18ln(x+3)+c_{1)}