What is the solution for 2y^{'''}+7y^{''}-17y^'-10y=0 ?

The solution for 2y^{'''}+7y^{''}-17y^'-10y=0 is y=c_{1}e^{2t}+c_{2}e^{-t/2}+c_{3}e^{-5t}

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2y^{'''}+7y^{''}-17y^'-10y=0

2 y^{^{'''}} + 7 y^{^{''}} - 17 y^{^{'}} - 10 y = 0

y = c_{1} e^{2 t} + c_{2} e^{- \frac{t}{2}} + c_{3} e^{- 5 t}

Solution steps

2 y^{'''} (t) + 7 y^{''} (t) - 17 y^{'} (t) - 10 y = 0

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- \frac{t}{2}} + c_{3} e^{- 5 t}

y = c_{1} e^{2 t} + c_{2} e^{- \frac{t}{2}} + c_{3} e^{- 5 t}

1 y^{^{''}} + 3 y^{^{'}} + 2 y = 0

2 y^{^{''''}} + 4 y^{^{''}} + 2 y = 0

121 y^{^{''}} + 64 y^{^{'}} = 0

y^{^{''}} + 8 y^{^{'}} + 52 y = 0, y (0) = 6, y^{^{'}} (0) = 7

\frac{d ^{2} x}{d t ^{2}} = - π^{2} x

What is the solution for 2y^{'''}+7y^{''}-17y^'-10y=0 ?
The solution for 2y^{'''}+7y^{''}-17y^'-10y=0 is y=c_{1}e^{2t}+c_{2}e^{-t/2}+c_{3}e^{-5t}