What is the solution for 3e^{3x}(dy)/(dx)=-9 x/(y^2) ?

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

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3e^{3x}(dy)/(dx)=-9 x/(y^2)

3 e^{3 x} \frac{d y}{d x} = - 9 \frac{x}{y ^{2}}

y = 3 3 x e^{- 3 x} + e^{- 3 x} + c_{1}

Solution steps

3 e^{3 x} \frac{d y}{d x} = - 9 \frac{x}{y ^{2}}

Solve separable ODE:

y = 3 3 x e^{- 3 x} + e^{- 3 x} + c_{1}

y = 3 3 x e^{- 3 x} + e^{- 3 x} + c_{1}

x \to \frac{π}{2} lim (7 sec (x) - 7 tan (x))

\frac{d}{d x} (arctan (\frac{x - 1}{x + 1}))

\int_{0}^{x} e^{- x} d x

f (x) = 4 x - 4 e^{x}

x^{2} y^{^{''}} + x y^{^{'}} - y = 1

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