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

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

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(dy)/(dt)(t)-2y=3e^t

\frac{d y}{d t} (t) - 2 y = 3 e^{t}

y = - \frac{3 e ^{t}}{2} - \frac{3 e ^{t} t}{2} + \frac{3}{2} Ei (t) t^{2} + c_{1} t^{2}

Solution steps

\frac{d y}{d t} (t) - 2 y = 3 e^{t}

Solve linear ODE:

y = - \frac{3 e ^{t}}{2} - \frac{3 e ^{t} t}{2} + \frac{3}{2} Ei (t) t^{2} + c_{1} t^{2}

y = - \frac{3 e ^{t}}{2} - \frac{3 e ^{t} t}{2} + \frac{3}{2} Ei (t) t^{2} + c_{1} t^{2}

\int \frac{4 x + 2}{( x + 1 ) ( x ^{2} + 1 )} d x

\frac{d}{d x} (1000 (1 - \frac{x}{500})^{2})

\frac{d y}{d x} = 4 + 9 x + 32 y + 72 x y

\int_{0}^{t} e^{s} sin (t - s) d s

f (s) = - \frac{12}{s ^{5}}

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