What is the solution for 5y^{'''}+45y^'-1350y=0 ?

The solution for 5y^{'''}+45y^'-1350y=0 is y=c_{1}e^{6t}+e^{-3t}(c_{2}cos(6t)+c_{3}sin(6t))

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5y^{'''}+45y^'-1350y=0

5 y^{^{'''}} + 45 y^{^{'}} - 1350 y = 0

y = c_{1} e^{6 t} + e^{- 3 t} (c_{2} cos (6 t) + c_{3} sin (6 t))

Solution steps

5 y^{'''} (t) + 45 y^{'} (t) - 1350 y = 0

Solve linear ODE:

y = c_{1} e^{6 t} + e^{- 3 t} (c_{2} cos (6 t) + c_{3} sin (6 t))

y = c_{1} e^{6 t} + e^{- 3 t} (c_{2} cos (6 t) + c_{3} sin (6 t))

\frac{d ^{2} y}{d t ^{2}} + 4 \cdot y = 0

y^{^{''}} - 2 y^{^{'}} + 5 y = 0, y (0) = 2, y^{^{'}} (0) = 4

\frac{1}{4} x^{^{''}} + 2 x^{^{'}} + 4 x = 0

8 y^{^{''}} + y^{^{'}} + 128 y = 0, y (0) = 5, y^{^{'}} (0) = 8

y^{^{''}} + 5 y^{^{'}} - 8 y = 0

What is the solution for 5y^{'''}+45y^'-1350y=0 ?
The solution for 5y^{'''}+45y^'-1350y=0 is y=c_{1}e^{6t}+e^{-3t}(c_{2}cos(6t)+c_{3}sin(6t))