What is the solution for (4D^3-13D-6)y=0 ?

The solution for (4D^3-13D-6)y=0 is y=c_{1}e^{2x}+c_{2}e^{-x/2}+c_{3}e^{-(3x)/2}

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(4D^3-13D-6)y=0

(4 D^{3} - 13 D - 6) y = 0

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

Solution steps

(4 D^{3} - 13 D - 6) y = 0

Solve linear ODE:

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

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

r^{2} x^{^{''}} + r x^{^{'}} - n^{2} x = 0

9 y^{^{''}} + 9 y^{^{'}} + 2 y = 0

y^{^{''}} + y = 0, y (\frac{π}{2}) = 2, y^{^{'}} (\frac{π}{2}) = 1

3 y^{^{'''}} + 2 y^{^{'}} = 0

\frac{d ^{2} x}{d t ^{2}} + 8 \cdot \frac{d x}{d t} + 4 x = 0

What is the solution for (4D^3-13D-6)y=0 ?
The solution for (4D^3-13D-6)y=0 is y=c_{1}e^{2x}+c_{2}e^{-x/2}+c_{3}e^{-(3x)/2}