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

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

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

\frac{d y}{d t} = 2 y - t^{2}

y = \frac{t ^{2}}{2} + \frac{t}{2} + \frac{1}{4} + c_{1} e^{2 t}

Solution steps

\frac{d y}{d t} = 2 y - t^{2}

Solve linear ODE:

y = \frac{t ^{2}}{2} + \frac{t}{2} + \frac{1}{4} + c_{1} e^{2 t}

y = \frac{t ^{2}}{2} + \frac{t}{2} + \frac{1}{4} + c_{1} e^{2 t}

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