What is the solution for (dy)/(dt)=(e^{-2t+3y}) ?

The solution for (dy)/(dt)=(e^{-2t+3y}) is y=-(ln(3/2 e^{-2t}-c_{1}))/3

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(dy)/(dt)=(e^{-2t+3y})

\frac{d y}{d t} = (e^{- 2 t + 3 y})

y = - \frac{ln ( \frac{3}{2} e ^{- 2 t} - c _{1} )}{3}

Solution steps

\frac{d y}{d t} = (e^{- 2 t + 3 y})

Solve separable ODE:

y = - \frac{ln ( \frac{3}{2} e ^{- 2 t} - c _{1} )}{3}

y = - \frac{ln ( \frac{3}{2} e ^{- 2 t} - c _{1} )}{3}

x \to 6 lim (\frac{x ^{2} - 6}{x + 4})

y = 16 - x^{2}, y = x^{2} - 2

\int \frac{19}{x ( x ^{2} + 4 ) ^{2}} d x

\int_{1}^{7} x^{2} - 4 x - 12 d x

x^{\frac{7}{2}} e^{x}

What is the solution for (dy)/(dt)=(e^{-2t+3y}) ?
The solution for (dy)/(dt)=(e^{-2t+3y}) is y=-(ln(3/2 e^{-2t}-c_{1}))/3