What is the solution for y^{''}=ky-c ?

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

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y^{''}=ky-c

y^{^{''}} = k y - c

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

Solution steps

y^{''} (t) = k y (t) - c

Solve linear ODE:

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

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

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

y^{^{''}} - y^{^{'}} - 2 y = \frac{e ^{2 t} + e ^{- 2 t}}{2}

y^{^{'''}} + 144 y^{^{'}} = tan (12 x)

y^{^{''}} - 4 y^{^{'}} + 3 y = e^{4 x} (- 8 + 29 x + 12 x^{2})

y^{^{''}} + 4 y = 32 sin (2 x) + 16 cos (2 x)

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