What is the solution for 7x^2y^'=y^'+7xe^{-y} ?

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

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7x^2y^'=y^'+7xe^{-y}

7 x^{2} y^{^{'}} = y^{^{'}} + 7 x e^{- y}

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

Solution steps

7 x^{2} y^{'} (x) = y^{'} (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})

y^{^{'}} + \frac{2}{x} \cdot y = 0

x \to - 4 - lim (\frac{3}{x ^{2} - 16})

\int 3 x^{4} (- x^{5} + 5)^{4} d x

t^{(\frac{3}{2})}

\frac{x ^{2}}{x - 5}

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