What is the solution for (dy)/(dt)+2y=e^{t/3} ?

The solution for (dy)/(dt)+2y=e^{t/3} is y=(3e^{t/3})/7+(c_{1})/(e^{2t)}

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(dy)/(dt)+2y=e^{t/3}

\frac{d y}{d t} + 2 y = e^{\frac{t}{3}}

y = \frac{3 e ^{\frac{t}{3}}}{7} + \frac{c _{1}}{e ^{2 t}}

Solution steps

\frac{d y}{d t} + 2 y = e^{\frac{t}{3}}

Solve linear ODE:

y = \frac{3 e ^{\frac{t}{3}}}{7} + \frac{c _{1}}{e ^{2 t}}

y = \frac{3 e ^{\frac{t}{3}}}{7} + \frac{c _{1}}{e ^{2 t}}

\int 17 tan^{2} (x) sec^{3} (x) d x

\frac{d}{d x} (\frac{1 + sec ( x )}{1 - sec ( x )})

ln (t^{3})

y^{^{'}} = \frac{y ^{2} + x ^{2}}{2 x y}

cos (x) y^{^{'}} + sin (x) y = 0

What is the solution for (dy)/(dt)+2y=e^{t/3} ?
The solution for (dy)/(dt)+2y=e^{t/3} is y=(3e^{t/3})/7+(c_{1})/(e^{2t)}