What is the solution for y^{''}+ay^'-2a^2y=1 ?

The solution for y^{''}+ay^'-2a^2y=1 is y=c_{1}e^{at}+c_{2}e^{-2at}-1/(2a^2)

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y^{''}+ay^'-2a^2y=1

y^{^{''}} + a y^{^{'}} - 2 a^{2} y = 1

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

Solution steps

y^{''} (t) + a y^{'} (t) - 2 a^{2} y = 1

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} + y = e^{- x}, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 6 y^{^{'}} + 9 y = 2 e^{(- 3 x)} \frac{1}{x ^{2} + 1}

y^{^{''}} + 4 y^{^{'}} - 5 y = (- 4 x^{2} - 8 x - 3) e^{3 x}

y^{^{''}} - 4 y^{^{'}} + 5 = 4 sin (x) - \frac{25}{8} x

y^{^{'''}} - y^{^{'}} = 4 e^{- x} + 3 e^{x}

What is the solution for y^{''}+ay^'-2a^2y=1 ?
The solution for y^{''}+ay^'-2a^2y=1 is y=c_{1}e^{at}+c_{2}e^{-2at}-1/(2a^2)