What is the solution for (10D^3+D^2-7D+2)y=0 ?

The solution for (10D^3+D^2-7D+2)y=0 is y=c_{1}e^{-x}+c_{2}e^{(2x)/5}+c_{3}e^{x/2}

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(10D^3+D^2-7D+2)y=0

(10 D^{3} + D^{2} - 7 D + 2) y = 0

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

Solution steps

(10 D^{3} + D^{2} - 7 D + 2) y = 0

Solve linear ODE:

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

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

y^{^{'''}} - 4 y^{^{''}} = 0

y^{^{''}} + 2 y^{^{'}} + 17 y = 0, y (0) = 4, y^{^{'}} (0) = - 3

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

(4 D^{4} + 20 D^{3} + 35 D^{2} + 25 D + 6) y = 0

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

What is the solution for (10D^3+D^2-7D+2)y=0 ?
The solution for (10D^3+D^2-7D+2)y=0 is y=c_{1}e^{-x}+c_{2}e^{(2x)/5}+c_{3}e^{x/2}