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

The solution for (dy)/(dt)+1/2 y= 1/2 e^{t/3} is y=(3e^{t/3})/5+(c_{1})/(e^{t/2)}

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(dy)/(dt)+1/2 y= 1/2 e^{t/3}

\frac{d y}{d t} + \frac{1}{2} y = \frac{1}{2} e^{\frac{t}{3}}

y = \frac{3 e ^{\frac{t}{3}}}{5} + \frac{c _{1}}{e ^{\frac{t}{2}}}

Solution steps

\frac{d y}{d t} + \frac{1}{2} y = \frac{1}{2} e^{\frac{t}{3}}

Solve linear ODE:

y = \frac{3 e ^{\frac{t}{3}}}{5} + \frac{c _{1}}{e ^{\frac{t}{2}}}

y = \frac{3 e ^{\frac{t}{3}}}{5} + \frac{c _{1}}{e ^{\frac{t}{2}}}

n = 0 \sum \infty 5 (- \frac{10}{11})^{n}

x \to 0 - lim (arctan (x))

\int (3 x^{2} + 1)^{6} d x

f (x) = (\frac{x ^{2}}{8 - 6 x})

x \to 5 lim (4 x - 20)

What is the solution for (dy)/(dt)+1/2 y= 1/2 e^{t/3} ?
The solution for (dy)/(dt)+1/2 y= 1/2 e^{t/3} is y=(3e^{t/3})/5+(c_{1})/(e^{t/2)}