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

The solution for (dy)/(dt)+2y=3t^2+2t-1 is y=(3t^2)/2-t/2-1/4+(c_{1})/(e^{2t)}

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(dy)/(dt)+2y=3t^2+2t-1

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

y = \frac{3 t ^{2}}{2} - \frac{t}{2} - \frac{1}{4} + \frac{c _{1}}{e ^{2 t}}

Solution steps

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

Solve linear ODE:

y = \frac{3 t ^{2}}{2} - \frac{t}{2} - \frac{1}{4} + \frac{c _{1}}{e ^{2 t}}

y = \frac{3 t ^{2}}{2} - \frac{t}{2} - \frac{1}{4} + \frac{c _{1}}{e ^{2 t}}

What is the solution for (dy)/(dt)+2y=3t^2+2t-1 ?
The solution for (dy)/(dt)+2y=3t^2+2t-1 is y=(3t^2)/2-t/2-1/4+(c_{1})/(e^{2t)}