What is the solution for (d^2y)/(dt^2)+y=t^2 ?

The solution for (d^2y)/(dt^2)+y=t^2 is y=c_{1}cos(t)+c_{2}sin(t)+t^2-2

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(d^2y)/(dt^2)+y=t^2

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

y = c_{1} cos (t) + c_{2} sin (t) + t^{2} - 2

Solution steps

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

Solve linear ODE:

y = c_{1} cos (t) + c_{2} sin (t) + t^{2} - 2

y = c_{1} cos (t) + c_{2} sin (t) + t^{2} - 2

y^{^{''}} + 2 y^{^{'}} + 2 y = sec (x) e^{- x}

y^{^{''}} + 4 y^{^{'}} + 4 y = \frac{e ^{(- 2 x)}}{x ^{3}}

y + 2 \frac{d ^{2} y}{d x ^{2}} = 1

y^{^{''}} - 5 y = 3 sin (2 \cdot π \cdot x)

y^{^{''}} - 4 y^{^{'}} + 4 y = 6 x^{2}

What is the solution for (d^2y)/(dt^2)+y=t^2 ?
The solution for (d^2y)/(dt^2)+y=t^2 is y=c_{1}cos(t)+c_{2}sin(t)+t^2-2