What is the solution for 3e^{5x}(dy)/(dx)=(-25x)/(y^2),y(0)=1 ?

The solution for 3e^{5x}(dy)/(dx)=(-25x)/(y^2),y(0)=1 is y=\sqrt[3]{5xe^{-5x}+e^{-5x}}

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3e^{5x}(dy)/(dx)=(-25x)/(y^2),y(0)=1

3 e^{5 x} \frac{d y}{d x} = \frac{- 25 x}{y ^{2}}, y (0) = 1

Solution steps

3 e^{5 x} \frac{d y}{d x} = \frac{- 25 x}{y ^{2}}

Solve separable ODE:

x \to 2 lim ((x - 1) (x + 1))

(cos (5 x)) y^{^{'}} + 5 (tan (5 x)) y = 2 sec (5 x)

2 x^{2} + 12, [- 5, 0]

\int_{1}^{2} (3 x^{- 2}) d x

\int 2 - 2 x^{2} d x

What is the solution for 3e^{5x}(dy)/(dx)=(-25x)/(y^2),y(0)=1 ?
The solution for 3e^{5x}(dy)/(dx)=(-25x)/(y^2),y(0)=1 is y=\sqrt[3]{5xe^{-5x}+e^{-5x}}