What is the solution for y^'=6x^2(1-7e^{-y}) ?

The solution for y^'=6x^2(1-7e^{-y}) is y=-ln(-1/(7(-1+e^{2x^3+c_{1)})})

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y^'=6x^2(1-7e^{-y})

y^{^{'}} = 6 x^{2} (1 - 7 e^{- y})

y = - ln (- \frac{1}{7 ( - 1 + e ^{2 x^{3} + c_{1}} )})

Solution steps

y^{'} (x) = 6 x^{2} (1 - 7 e^{- y})

Solve separable ODE:

y = - ln (- \frac{1}{7 ( - 1 + e ^{2 x^{3} + c_{1}} )})

y = - ln (- \frac{1}{7 ( - 1 + e ^{2 x^{3} + c_{1}} )})

e^{x + y} sin (x) d x + (2 y + 1) e^{- y^{2}} d y = 0

\frac{d y}{d x} = \frac{4 x y}{( ln ( y ) ) ^{2}}

y^{^{'}} = - y + 7

\frac{d}{d x} (\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}}) = 1

2 y t^{3} d y + 3 y^{2} t^{2} d t = 0

What is the solution for y^'=6x^2(1-7e^{-y}) ?
The solution for y^'=6x^2(1-7e^{-y}) is y=-ln(-1/(7(-1+e^{2x^3+c_{1)})})