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

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

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(d^3y)/(dx^3)+8(dy)/(dx)=0

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

y = c_{1} + c_{2} cos (2^{1 + \frac{1}{2}} x) + c_{3} sin (2^{1 + \frac{1}{2}} x)

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} cos (2^{1 + \frac{1}{2}} x) + c_{3} sin (2^{1 + \frac{1}{2}} x)

y = c_{1} + c_{2} cos (2^{1 + \frac{1}{2}} x) + c_{3} sin (2^{1 + \frac{1}{2}} x)

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = 2, y^{^{'}} (0) = 5

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = 2, y^{^{'}} (0) = 4

y^{^{''}} - y^{^{'}} = 0

x^{^{''}} + 96 x = 0

y^{^{''}} - α y = 0

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