What is the solution for y^{''''}+5y^{''}=0 ?

The solution for y^{''''}+5y^{''}=0 is y=c_{1}+c_{2}t+c_{3}cos(sqrt(5)t)+c_{4}sin(sqrt(5)t)

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y^{''''}+5y^{''}=0

y^{^{''''}} + 5 y^{^{''}} = 0

y = c_{1} + c_{2} t + c_{3} cos (5 t) + c_{4} sin (5 t)

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} t + c_{3} cos (5 t) + c_{4} sin (5 t)

y = c_{1} + c_{2} t + c_{3} cos (5 t) + c_{4} sin (5 t)

y^{^{''}} + 25 y = 0, y (π) = 0, y (0) = 0

y^{^{''}} = a y^{^{'}}

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = x e^{5 x}

9 y^{^{''}} - 12 y^{^{'}} + 4 y = 0, y (0) = 2, y^{^{'}} (0) = 1

\frac{d ^{2} y}{d x ^{2}} - 10 \frac{d y}{d x} + 29 y = 0

What is the solution for y^{''''}+5y^{''}=0 ?
The solution for y^{''''}+5y^{''}=0 is y=c_{1}+c_{2}t+c_{3}cos(sqrt(5)t)+c_{4}sin(sqrt(5)t)