What is the solution for (d^3y)/(dx^3)=(dy)/(dx) ?

The solution for (d^3y)/(dx^3)=(dy)/(dx) is y=c_{1}+c_{2}e^{-x}+c_{3}e^x

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(d^3y)/(dx^3)=(dy)/(dx)

\frac{d ^{3} y}{d x ^{3}} = \frac{d y}{d x}

y = c_{1} + c_{2} e^{- x} + c_{3} e^{x}

Solution steps

\frac{d ^{3} y}{d x ^{3}} = \frac{d y}{d x}

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} + c_{3} e^{x}

y = c_{1} + c_{2} e^{- x} + c_{3} e^{x}

16 y^{^{''''}} = 625 y

y^{^{''}} + 64 y = 0, y (0) = \frac{2}{3}, y^{^{'}} (0) = - \frac{4}{3}

(4 D^{3} + 4 D^{2} + D) y = 0

y^{^{''}} + 2 y - 3 y = 0

y^{^{''}} + 4 y^{^{'}} + 29 y = 0, y (0) = 0, y^{^{'}} (0) = 5

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