What is the solution for 7x^2(dy)/(dx)=(dy)/(dx)+7xe^{-y} ?

The solution for 7x^2(dy)/(dx)=(dy)/(dx)+7xe^{-y} is y=ln(1/2 ln(7x^2-1)+c_{1})

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7x^2(dy)/(dx)=(dy)/(dx)+7xe^{-y}

7 x^{2} \frac{d y}{d x} = \frac{d y}{d x} + 7 x e^{- y}

y = ln (\frac{1}{2} ln (7 x^{2} - 1) + c_{1})

Solution steps

7 x^{2} \frac{d y}{d x} = \frac{d y}{d x} + 7 x e^{- y}

Solve separable ODE:

y = ln (\frac{1}{2} ln (7 x^{2} - 1) + c_{1})

y = ln (\frac{1}{2} ln (7 x^{2} - 1) + c_{1})

\int sin (\frac{x}{2}) \cdot cos (x) d x

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

\frac{1}{x ^{2}}, 3

t^{2} y^{^{''}} + 4 t y^{^{'}} - 18 y = 0

\frac{\partial}{\partial x} (- 2 x e^{- 3 x y})

What is the solution for 7x^2(dy)/(dx)=(dy)/(dx)+7xe^{-y} ?
The solution for 7x^2(dy)/(dx)=(dy)/(dx)+7xe^{-y} is y=ln(1/2 ln(7x^2-1)+c_{1})