What is the solution for (dy)/(dt)=7te^{-y},y(0)=3 ?

The solution for (dy)/(dt)=7te^{-y},y(0)=3 is y=ln((7t^2)/2+e^3)

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(dy)/(dt)=7te^{-y},y(0)=3

\frac{d y}{d t} = 7 t e^{- y}, y (0) = 3

y = ln (\frac{7 t ^{2}}{2} + e^{3})

Solution steps

\frac{d y}{d t} = 7 t e^{- y}

Solve separable ODE:

y = ln (\frac{7 t ^{2}}{2} + e^{3})

y = ln (\frac{7 t ^{2}}{2} + e^{3})

\frac{d}{d y} (7 y)

\int \frac{( ln ( x ) ) ^{8}}{x} d x

\int (x^{2} + x + 1) sin (x) d x

x \to - 1 lim (1 + x)

\frac{d}{d x} (\frac{- 12 x}{( x ^{2} + 3 ) ^{2}})

What is the solution for (dy)/(dt)=7te^{-y},y(0)=3 ?
The solution for (dy)/(dt)=7te^{-y},y(0)=3 is y=ln((7t^2)/2+e^3)