What is the solution for y^{''}-2y-24=0 ?

The solution for y^{''}-2y-24=0 is y=c_{1}e^{sqrt(2)t}+c_{2}e^{-sqrt(2)t}-12

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y^{''}-2y-24=0

y^{^{''}} - 2 y - 24 = 0

y = c_{1} e^{2 t} + c_{2} e^{- 2 t} - 12

Solution steps

y^{''} (t) - 2 y - 24 = 0

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- 2 t} - 12

y = c_{1} e^{2 t} + c_{2} e^{- 2 t} - 12

y^{^{''}} + 4 y^{^{'}} + 4 y = 3 t

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 3 y = 24 e^{3 x}

y^{^{''}} - y^{^{'}} - 2 y = 8 sin (t) - 2 cos (t)

y^{^{''}} + 6 y^{^{'}} + 13 y = 13 x^{2}

2 y^{^{''}} - y^{^{'}} - y = t + 1, y (0) = 1, y^{^{'}} (0) = 0

What is the solution for y^{''}-2y-24=0 ?
The solution for y^{''}-2y-24=0 is y=c_{1}e^{sqrt(2)t}+c_{2}e^{-sqrt(2)t}-12