What is the solution for (d^3+d^2-9d-9)y=0 ?

The solution for (d^3+d^2-9d-9)y=0 is y=c_{1}e^{-x}+c_{2}e^{-3x}+c_{3}e^{3x}

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(d^3+d^2-9d-9)y=0

(d^{3} + d^{2} - 9 d - 9) y = 0

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

Solution steps

(d^{3} + d^{2} - 9 d - 9) y = 0

Solve linear ODE:

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

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

x^{^{''}} + 9 x = 0

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

x, \frac{d ^{2} x}{d y ^{2}} = a^{2} x

\frac{d ^{3} y}{d x ^{3}} - 2 y^{^{''}} + 1 y = 0

\frac{1}{16} y^{^{''}} + 4 y = 0

What is the solution for (d^3+d^2-9d-9)y=0 ?
The solution for (d^3+d^2-9d-9)y=0 is y=c_{1}e^{-x}+c_{2}e^{-3x}+c_{3}e^{3x}