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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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