What is the solution for (d^3y)/(dx^3)-21(dy)/(dx)-20y=0 ?

The solution for (d^3y)/(dx^3)-21(dy)/(dx)-20y=0 is y=c_{1}e^{-x}+c_{2}e^{-4x}+c_{3}e^{5x}

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(d^3y)/(dx^3)-21(dy)/(dx)-20y=0

\frac{d ^{3} y}{d x ^{3}} - 21 \frac{d y}{d x} - 20 y = 0

y = c_{1} e^{- x} + c_{2} e^{- 4 x} + c_{3} e^{5 x}

Solution steps

\frac{d ^{3} y}{d x ^{3}} - 21 \frac{d y}{d x} - 20 y = 0

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 4 x} + c_{3} e^{5 x}

y = c_{1} e^{- x} + c_{2} e^{- 4 x} + c_{3} e^{5 x}

10 y^{^{''}} - 3 y^{^{'}} = 0

y^{^{''}} + 3 y^{^{'}} + 8 y = 0

\frac{d ^{2} x}{d t ^{2}} = x

y^{^{''}} - 6 y^{^{'}} + 8 y = 0, y (0) = 2, y^{^{'}} (0) = 2

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

What is the solution for (d^3y)/(dx^3)-21(dy)/(dx)-20y=0 ?
The solution for (d^3y)/(dx^3)-21(dy)/(dx)-20y=0 is y=c_{1}e^{-x}+c_{2}e^{-4x}+c_{3}e^{5x}