What is the solution for (6d^3+5d^2)y=0 ?

The solution for (6d^3+5d^2)y=0 is y=c_{1}e^{-(5x)/6}+c_{2}+c_{3}x

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(6d^3+5d^2)y=0

(6 d^{3} + 5 d^{2}) y = 0

y = c_{1} e^{- \frac{5 x}{6}} + c_{2} + c_{3} x

Solution steps

(6 d^{3} + 5 d^{2}) y = 0

Solve linear ODE:

y = c_{1} e^{- \frac{5 x}{6}} + c_{2} + c_{3} x

y = c_{1} e^{- \frac{5 x}{6}} + c_{2} + c_{3} x

y^{^{'''}} + 7 y^{^{''}} + 14 y^{^{'}} + 8 y = 0

\frac{d ^{4} y}{d t ^{4}} + 2 y^{^{''}} + y = 0

y^{^{''}} - 5 y^{^{'}} + 6 y = 0, y (0) = 1, y^{^{'}} (0) = - 5

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

0.05 y^{^{''}} + 2 y^{^{'}} + \frac{1}{0.01} y = 0

What is the solution for (6d^3+5d^2)y=0 ?
The solution for (6d^3+5d^2)y=0 is y=c_{1}e^{-(5x)/6}+c_{2}+c_{3}x