What is the solution for 2y^{'''}+15y^{''}+24y^'+11y=0 ?

The solution for 2y^{'''}+15y^{''}+24y^'+11y=0 is y=c_{1}e^{-(11t)/2}+c_{2}e^{-t}+c_{3}te^{-t}

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2y^{'''}+15y^{''}+24y^'+11y=0

2 y^{^{'''}} + 15 y^{^{''}} + 24 y^{^{'}} + 11 y = 0

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

Solution steps

2 y^{'''} (t) + 15 y^{''} (t) + 24 y^{'} (t) + 11 y = 0

Solve linear ODE:

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

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

8 \frac{d ^{2} y}{d x ^{2}} - 8 \frac{d y}{d x} + 7 y = 0

324 y^{^{''}} - 396 y^{^{'}} + 121 y = 0

9 y^{^{''}} + 6 y^{^{'}} + y = 0, y (0) = 4, y^{^{'}} (0) = \frac{- 13}{3}

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 0

8 y^{^{''}} - 25 y^{^{'}} + 3 y = 0

What is the solution for 2y^{'''}+15y^{''}+24y^'+11y=0 ?
The solution for 2y^{'''}+15y^{''}+24y^'+11y=0 is y=c_{1}e^{-(11t)/2}+c_{2}e^{-t}+c_{3}te^{-t}