What is the solution for 4y^{'''}+5y^{''}-23y^'-6y=0 ?

The solution for 4y^{'''}+5y^{''}-23y^'-6y=0 is y=c_{1}e^{2t}+c_{2}e^{-t/4}+c_{3}e^{-3t}

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4y^{'''}+5y^{''}-23y^'-6y=0

4 y^{^{'''}} + 5 y^{^{''}} - 23 y^{^{'}} - 6 y = 0

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

Solution steps

4 y^{'''} (t) + 5 y^{''} (t) - 23 y^{'} (t) - 6 y = 0

Solve linear ODE:

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

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

x^{^{''}} - 6 x^{^{'}} + 8 x = 0, x (0) = 3

y^{^{''}} + y - 6 y^{^{'}} = 0

y^{^{''}} - 8 y^{^{'}} - 7 y = 0

y^{^{''}} + 2 y^{^{'}} + 2 y = 0, y (\frac{π}{2}) = 0, y (0) = 1

x^{^{''}} + 6 x^{^{'}} + 9 x = 0, x (0) = a, x^{^{'}} (0) = b

What is the solution for 4y^{'''}+5y^{''}-23y^'-6y=0 ?
The solution for 4y^{'''}+5y^{''}-23y^'-6y=0 is y=c_{1}e^{2t}+c_{2}e^{-t/4}+c_{3}e^{-3t}