What is the solution for 7x^2y^'=y^'+5xe^{-y} ?

The solution for 7x^2y^'=y^'+5xe^{-y} is y=ln(5/14 ln(7x^2-1)+c_{1})

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7x^2y^'=y^'+5xe^{-y}

7 x^{2} y^{^{'}} = y^{^{'}} + 5 x e^{- y}

y = ln (\frac{5}{14} ln (7 x^{2} - 1) + c_{1})

Solution steps

7 x^{2} y^{'} (x) = y^{'} (x) + 5 x e^{- y}

Solve separable ODE:

y = ln (\frac{5}{14} ln (7 x^{2} - 1) + c_{1})

y = ln (\frac{5}{14} ln (7 x^{2} - 1) + c_{1})

y^{^{''}} - 6 y^{^{'}} + 9 y = t^{- 3} e^{3 t}

\frac{( 2 x y + 1 )}{y} d x + \frac{( y - x )}{y ^{2}} d y = 0

sin (sin (x))

\int (sin (x) cos^{5} (x)) d x

(4 cos (t))^{^{'}}

What is the solution for 7x^2y^'=y^'+5xe^{-y} ?
The solution for 7x^2y^'=y^'+5xe^{-y} is y=ln(5/14 ln(7x^2-1)+c_{1})