What is the solution for y^{''''}-13y^{''}+36y=0 ?

The solution for y^{''''}-13y^{''}+36y=0 is y=c_{1}e^{3t}+c_{2}e^{-3t}+c_{3}e^{2t}+c_{4}e^{-2t}

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y^{''''}-13y^{''}+36y=0

y^{^{''''}} - 13 y^{^{''}} + 36 y = 0

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} + c_{3} e^{2 t} + c_{4} e^{- 2 t}

Solution steps

y^{(4)} (t) - 13 y^{''} (t) + 36 y = 0

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} + c_{3} e^{2 t} + c_{4} e^{- 2 t}

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} + c_{3} e^{2 t} + c_{4} e^{- 2 t}

y^{^{''}} + 6 y^{^{'}} + 13 y = 0, y (0) = 1, y^{^{'}} (0) = 0

9 y^{^{''}} - 16 y = 0

3 \frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + y = 0

y^{^{''}} + y^{^{'}} + 12 y = 0

9 y^{^{''}} + 36 y^{^{'}} + 100 y = 0, y (1) = 4, y^{^{'}} (1) = 9

What is the solution for y^{''''}-13y^{''}+36y=0 ?
The solution for y^{''''}-13y^{''}+36y=0 is y=c_{1}e^{3t}+c_{2}e^{-3t}+c_{3}e^{2t}+c_{4}e^{-2t}