What is the solution for (2D^4-3D^3-2D^2)y=0 ?

The solution for (2D^4-3D^3-2D^2)y=0 is y=c_{1}e^{-x/2}+c_{2}e^{2x}+c_{3}+c_{4}x

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(2D^4-3D^3-2D^2)y=0

(2 D^{4} - 3 D^{3} - 2 D^{2}) y = 0

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

Solution steps

(2 D^{4} - 3 D^{3} - 2 D^{2}) y = 0

Solve linear ODE:

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

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

\frac{1}{2} y^{^{''}} + 3 y^{^{'}} + 4 y = 0, y (0) = 0, y^{^{'}} (0) = - \frac{5}{3}

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (0) = 4, y^{^{'}} (0) = 14

y^{^{''}} + y = 0, y (0) = 11, y^{^{'}} (0) = 33

\frac{1}{20} y^{^{''}} + 3 y^{^{'}} + 80 y = 0

y^{^{''}} - 6 y^{^{'}} + 10 y = 0, y (0) = 2, y^{^{'}} (0) = 3

What is the solution for (2D^4-3D^3-2D^2)y=0 ?
The solution for (2D^4-3D^3-2D^2)y=0 is y=c_{1}e^{-x/2}+c_{2}e^{2x}+c_{3}+c_{4}x