What is the solution for y^{''}-8y^'-33y=0 ?

The solution for y^{''}-8y^'-33y=0 is y=c_{1}e^{11t}+c_{2}e^{-3t}

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y^{''}-8y^'-33y=0

y^{^{''}} - 8 y^{^{'}} - 33 y = 0

y = c_{1} e^{11 t} + c_{2} e^{- 3 t}

Solution steps

y^{''} (t) - 8 y^{'} (t) - 33 y = 0

Solve linear ODE:

y = c_{1} e^{11 t} + c_{2} e^{- 3 t}

y = c_{1} e^{11 t} + c_{2} e^{- 3 t}

y^{^{''}} - \frac{5}{2} y^{^{'}} + y = 0

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

y^{^{''}} + 2 y^{^{'}} + 5 y = 0, y (0) = 0, y^{^{'}} (0) = 1

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} + 2 y = 0

y^{^{''}} + 5 y^{^{'}} + 6 y = 0, y (0) = 1, y^{^{'}} (0) = 2

What is the solution for y^{''}-8y^'-33y=0 ?
The solution for y^{''}-8y^'-33y=0 is y=c_{1}e^{11t}+c_{2}e^{-3t}