What is the solution for ((y^'-e^{-t}+6))/y =-6 ?

The solution for ((y^'-e^{-t}+6))/y =-6 is y= 1/(5e^t)-1+(c_{1})/(e^{6t)}

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((y^'-e^{-t}+6))/y =-6

\frac{( y ^{^{'}} - e ^{- t} + 6 )}{y} = - 6

y = \frac{1}{5 e ^{t}} - 1 + \frac{c _{1}}{e ^{6 t}}

Solution steps

\frac{( y ^{'} ( t ) - e ^{- t} + 6 )}{y} = - 6

Solve linear ODE:

y = \frac{1}{5 e ^{t}} - 1 + \frac{c _{1}}{e ^{6 t}}

y = \frac{1}{5 e ^{t}} - 1 + \frac{c _{1}}{e ^{6 t}}

\int ∣ 2 x - 6 ∣ d x

d er i v a t i v e f (x) = - \frac{5}{x ^{5}}

f (u) = e^{u}

x \to 6 lim (7 x + ∣ x - 6 ∣)

d er i v a t i v e sin (cos (7 x))

What is the solution for ((y^'-e^{-t}+6))/y =-6 ?
The solution for ((y^'-e^{-t}+6))/y =-6 is y= 1/(5e^t)-1+(c_{1})/(e^{6t)}