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^{^{'''}} + 3 y^{^{''}} - 8 y^{^{'}} - 30 y = 0

y^{^{'''}} - 7 y^{^{''}} - 8 y^{^{'}} + 16 y = 0

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

y^{^{''}} - 12 y^{^{'}} + 36 y = 0, y (0) = 3, y^{^{'}} (0) = \frac{39}{2}

y^{^{''}} + 18 y^{^{'}} + 80 y = 0, y (0) = 9, y^{^{'}} (0) = - 76

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}