What is the solution for 3e^{4x}(dy)/(dx)=-16 x/(y^2),y(0)=1 ?

The solution for 3e^{4x}(dy)/(dx)=-16 x/(y^2),y(0)=1 is y=\sqrt[3]{4xe^{-4x}+e^{-4x}}

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3e^{4x}(dy)/(dx)=-16 x/(y^2),y(0)=1

3 e^{4 x} \frac{d y}{d x} = - 16 \frac{x}{y ^{2}}, y (0) = 1

Solution steps

3 e^{4 x} \frac{d y}{d x} = - 16 \frac{x}{y ^{2}}

Solve separable ODE:

\frac{d x}{d t} = 100 - \frac{x}{100}, x = 2000, t = 0

(\frac{y}{2}) y^{^{'}} = e^{- x}, y (0) = 4

\frac{d}{d x} (y^{2}) = 4 x^{2} + 2 x - 5

y^{2} sec (6 x) \frac{d y}{d x} = 1, y (0) = 0

y d y + x d x = 0

What is the solution for 3e^{4x}(dy)/(dx)=-16 x/(y^2),y(0)=1 ?
The solution for 3e^{4x}(dy)/(dx)=-16 x/(y^2),y(0)=1 is y=\sqrt[3]{4xe^{-4x}+e^{-4x}}