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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

4 y + 9 y^{^{''}} = - 12 y^{^{'}}

9 y^{^{''}} + 12 y^{^{'}} + 4 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} - 7 y^{^{'}} + 12 y = 0, y (0) = 3, y^{^{'}} (0) = 0

\frac{d ^{2}}{d x ^{2}} ((u (x)) e^{2 x}) = 0

y^{^{''}} - 2 y^{^{'}} - 3 y = 0, y^{^{'}} = 13, y (0) = 3

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