What is the solution for y^{''''}+18y^{''}+81y=0 ?

The solution for y^{''''}+18y^{''}+81y=0 is y=c_{1}cos(3t)+c_{2}sin(3t)+t(c_{3}cos(3t)+c_{4}sin(3t))

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y^{''''}+18y^{''}+81y=0

y^{^{''''}} + 18 y^{^{''}} + 81 y = 0

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

Solution steps

y^{(4)} (t) + 18 y^{''} (t) + 81 y = 0

Solve linear ODE:

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

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

x \to 1 lim (x^{2} + 2)

\frac{d}{d x} (\frac{2 x}{( 1 + x ) ^{2}})

\int \frac{ln ( 3 x )}{x} d x

- \frac{18}{t ^{3}} + \frac{3}{t ^{2}}

\int x x + 2 d x

What is the solution for y^{''''}+18y^{''}+81y=0 ?
The solution for y^{''''}+18y^{''}+81y=0 is y=c_{1}cos(3t)+c_{2}sin(3t)+t(c_{3}cos(3t)+c_{4}sin(3t))