What is the solution for (d^3y)/(dx^3)-8y=0 ?

The solution for (d^3y)/(dx^3)-8y=0 is y=c_{1}e^{2x}+e^{-x}(c_{2}cos(sqrt(3)x)+c_{3}sin(sqrt(3)x))

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(d^3y)/(dx^3)-8y=0

\frac{d ^{3} y}{d x ^{3}} - 8 y = 0

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

Solution steps

\frac{d ^{3} y}{d x ^{3}} - 8 y = 0

Solve linear ODE:

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

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

What is the solution for (d^3y)/(dx^3)-8y=0 ?
The solution for (d^3y)/(dx^3)-8y=0 is y=c_{1}e^{2x}+e^{-x}(c_{2}cos(sqrt(3)x)+c_{3}sin(sqrt(3)x))