What is the solution for (d^3y)/(dx^3)-5(dy)/(dx)=0 ?

The solution for (d^3y)/(dx^3)-5(dy)/(dx)=0 is y=c_{1}+c_{2}e^{-sqrt(5)x}+c_{3}e^{sqrt(5)x}

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(d^3y)/(dx^3)-5(dy)/(dx)=0

\frac{d ^{3} y}{d x ^{3}} - 5 \frac{d y}{d x} = 0

y = c_{1} + c_{2} e^{- 5 x} + c_{3} e^{5 x}

Solution steps

\frac{d ^{3} y}{d x ^{3}} - 5 \frac{d y}{d x} = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{- 5 x} + c_{3} e^{5 x}

y = c_{1} + c_{2} e^{- 5 x} + c_{3} e^{5 x}

u^{^{''}} + (a^{2} + b) H (t) = 0

y^{^{''}} + 13 y^{^{'}} + 36 y = 0

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 7 y = 0

y^{^{''}} + 2 y^{^{'}} - 3 y = 0, y (0) = 2, y^{^{'}} (0) = 10

\frac{d ^{4} y}{d x ^{4}} + 6 \frac{d ^{2} y}{d x ^{2}} + 9 y = 0

What is the solution for (d^3y)/(dx^3)-5(dy)/(dx)=0 ?
The solution for (d^3y)/(dx^3)-5(dy)/(dx)=0 is y=c_{1}+c_{2}e^{-sqrt(5)x}+c_{3}e^{sqrt(5)x}