What is the solution for (D^3-3D^2-10D)y=0 ?

The solution for (D^3-3D^2-10D)y=0 is y=c_{1}+c_{2}e^{-2x}+c_{3}e^{5x}

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(D^3-3D^2-10D)y=0

(D^{3} - 3 D^{2} - 10 D) y = 0

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

Solution steps

(D^{3} - 3 D^{2} - 10 D) y = 0

Solve linear ODE:

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

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

y^{^{''}} + 25 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - 36 y = 0, y (\frac{π}{4}) = 1, y^{^{'}} (\frac{π}{4}) = - 2

y^{^{''}} + 3 y^{^{'}} - y = 0, y (1) = 2, y^{^{'}} (1) = 0

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (1) = 1, y^{^{'}} (1) = 4

y^{^{'''}} + 2 y^{^{''}} - 4 y^{^{'}} - 8 y = 0

What is the solution for (D^3-3D^2-10D)y=0 ?
The solution for (D^3-3D^2-10D)y=0 is y=c_{1}+c_{2}e^{-2x}+c_{3}e^{5x}