What is the solution for 5y^'-y=e^{-t}+3t ?

The solution for 5y^'-y=e^{-t}+3t is y=-1/(6e^t)-3(t+5)+c_{1}e^{t/5}

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5y^'-y=e^{-t}+3t

5 y^{^{'}} - y = e^{- t} + 3 t

y = - \frac{1}{6 e ^{t}} - 3 (t + 5) + c_{1} e^{\frac{t}{5}}

Solution steps

5 y^{'} (t) - y = e^{- t} + 3 t

Solve linear ODE:

y = - \frac{1}{6 e ^{t}} - 3 (t + 5) + c_{1} e^{\frac{t}{5}}

y = - \frac{1}{6 e ^{t}} - 3 (t + 5) + c_{1} e^{\frac{t}{5}}

\int \frac{( 9 sin ^{3} ( x ) )}{cos ( x )} d x

x \to \infty lim (\frac{1}{5 x})

\int (x \cdot sin (x^{2} + 1)) d x

\frac{d}{d x} (e^{\frac{- x ^{2}}{2}})

2 x + \frac{4 x}{3 x - 1}

What is the solution for 5y^'-y=e^{-t}+3t ?
The solution for 5y^'-y=e^{-t}+3t is y=-1/(6e^t)-3(t+5)+c_{1}e^{t/5}