What is the solution for y^{'''}+81y^'=0 ?

The solution for y^{'''}+81y^'=0 is y=c_{1}+c_{2}cos(9t)+c_{3}sin(9t)

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y^{'''}+81y^'=0

y^{^{'''}} + 81 y^{^{'}} = 0

y = c_{1} + c_{2} cos (9 t) + c_{3} sin (9 t)

Solution steps

y^{'''} (t) + 81 y^{'} (t) = 0

Solve linear ODE:

y = c_{1} + c_{2} cos (9 t) + c_{3} sin (9 t)

y = c_{1} + c_{2} cos (9 t) + c_{3} sin (9 t)

y^{^{''}} + 6 y^{^{'}} + 25 y = 0, y (0) = 6, y^{^{'}} (0) = - 17

x^{^{''}} + 36 x = 0

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

\frac{d ^{2} y}{d x ^{2}} - 13 \frac{d y}{d x} + 12 y = 0

- 2 y^{^{''}} - 2 \cdot π^{2} y = 0

What is the solution for y^{'''}+81y^'=0 ?
The solution for y^{'''}+81y^'=0 is y=c_{1}+c_{2}cos(9t)+c_{3}sin(9t)