What is the solution for ((y^'-e^{-t}+5)/y)=-5,y(0)=-2 ?

The solution for ((y^'-e^{-t}+5)/y)=-5,y(0)=-2 is y= 1/(4e^t)-1-5/(4e^{5t)}

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((y^'-e^{-t}+5)/y)=-5,y(0)=-2

(\frac{y ^{^{'}} - e ^{- t} + 5}{y}) = - 5, y (0) = - 2

y = \frac{1}{4 e ^{t}} - 1 - \frac{5}{4 e ^{5 t}}

Solution steps

(\frac{y ^{'} ( t ) - e ^{- t} + 5}{y}) = - 5

Solve linear ODE:

y = \frac{1}{4 e ^{t}} - 1 - \frac{5}{4 e ^{5 t}}

y = \frac{1}{4 e ^{t}} - 1 - \frac{5}{4 e ^{5 t}}

What is the solution for ((y^'-e^{-t}+5)/y)=-5,y(0)=-2 ?
The solution for ((y^'-e^{-t}+5)/y)=-5,y(0)=-2 is y= 1/(4e^t)-1-5/(4e^{5t)}