What is the solution for ((dy))/((dx))=e^{(3y-x)} ?

The solution for ((dy))/((dx))=e^{(3y-x)} is y=-(ln(3e^{-x}-c_{1}))/3

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((dy))/((dx))=e^{(3y-x)}

\frac{( d y )}{( d x )} = e^{(3 y - x)}

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

Solution steps

\frac{( d y )}{( d x )} = e^{(3 y - x)}

Solve separable ODE:

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

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

\frac{d y}{d t} - 0.5 y + 2 = 0

2 y^{^{'}} = 3 y^{\frac{1}{3}}

(t^{2} - 24 t + 95) y^{^{'}} = y

\frac{d}{d x} (x^{4} + y^{4}) = \frac{d}{d x} (16)

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

What is the solution for ((dy))/((dx))=e^{(3y-x)} ?
The solution for ((dy))/((dx))=e^{(3y-x)} is y=-(ln(3e^{-x}-c_{1}))/3