What is the solution for y^{''}-7y=t^2 ?

The solution for y^{''}-7y=t^2 is y=c_{1}e^{sqrt(7)t}+c_{2}e^{-sqrt(7)t}-(t^2)/7-2/49

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y^{''}-7y=t^2

y^{^{''}} - 7 y = t^{2}

y = c_{1} e^{7 t} + c_{2} e^{- 7 t} - \frac{t ^{2}}{7} - \frac{2}{49}

Solution steps

y^{''} (t) - 7 y = t^{2}

Solve linear ODE:

y = c_{1} e^{7 t} + c_{2} e^{- 7 t} - \frac{t ^{2}}{7} - \frac{2}{49}

y = c_{1} e^{7 t} + c_{2} e^{- 7 t} - \frac{t ^{2}}{7} - \frac{2}{49}

(y^{^{''}} + 2 y^{^{'}} + 5) = e^{x}

y^{^{'''}} + y^{^{'}} = x + sin (x) + cos (x)

y^{^{''}} + y^{^{'}} - 2 y = 3 e^{- 2 x} - 2 x

y^{^{''}} + y^{^{'}} - 2 y = 2 t, y (0) = 0

y^{^{''}} - 3 y^{^{'}} + y = 2 e^{x} + e^{- x}

What is the solution for y^{''}-7y=t^2 ?
The solution for y^{''}-7y=t^2 is y=c_{1}e^{sqrt(7)t}+c_{2}e^{-sqrt(7)t}-(t^2)/7-2/49