What is the solution for y^{''''}-4y^{'''}+9y^{''}-36y^'=0 ?

The solution for y^{''''}-4y^{'''}+9y^{''}-36y^'=0 is y=c_{1}+c_{2}e^{4t}+c_{3}cos(3t)+c_{4}sin(3t)

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y^{''''}-4y^{'''}+9y^{''}-36y^'=0

y^{^{''''}} - 4 y^{^{'''}} + 9 y^{^{''}} - 36 y^{^{'}} = 0

y = c_{1} + c_{2} e^{4 t} + c_{3} cos (3 t) + c_{4} sin (3 t)

Solution steps

y^{(4)} (t) - 4 y^{'''} (t) + 9 y^{''} (t) - 36 y^{'} (t) = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{4 t} + c_{3} cos (3 t) + c_{4} sin (3 t)

y = c_{1} + c_{2} e^{4 t} + c_{3} cos (3 t) + c_{4} sin (3 t)

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

y^{^{''''''}} - 15 y^{^{'''''}} + 56 y^{^{''''}} = 0

4 y^{^{''}} - y = 0, y (- 9) = 1, y^{^{'}} (- 9) = - 1

\frac{1}{16} y^{^{''}} + y^{^{'}} + 2 y = 0

y^{^{''}} + y^{^{'}} + \frac{1}{3} y = 0

What is the solution for y^{''''}-4y^{'''}+9y^{''}-36y^'=0 ?
The solution for y^{''''}-4y^{'''}+9y^{''}-36y^'=0 is y=c_{1}+c_{2}e^{4t}+c_{3}cos(3t)+c_{4}sin(3t)