What is the solution for (d^3-5d^2+4d-20)x=0 ?

The solution for (d^3-5d^2+4d-20)x=0 is x=c_{1}e^{5t}+c_{2}cos(2t)+c_{3}sin(2t)

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(d^3-5d^2+4d-20)x=0

(d^{3} - 5 d^{2} + 4 d - 20) x = 0

x = c_{1} e^{5 t} + c_{2} cos (2 t) + c_{3} sin (2 t)

Solution steps

(d^{3} - 5 d^{2} + 4 d - 20) x = 0

Solve linear ODE:

x = c_{1} e^{5 t} + c_{2} cos (2 t) + c_{3} sin (2 t)

x = c_{1} e^{5 t} + c_{2} cos (2 t) + c_{3} sin (2 t)

\frac{y ^{^{''}}}{y} = - a^{2}

9 y^{^{''}} - 5 y^{^{'}} = 0, y^{1} (0) = e^{- 7 x}

x^{^{''}} + 5 \cdot x = 0, x (1) = 0, x (0) = 0

(D^{4} - 1) y = 0

y^{^{''}} - 4 y^{^{'}} = 0, y (0) = 5 - 5 e^{4}, y (1) = 0

What is the solution for (d^3-5d^2+4d-20)x=0 ?
The solution for (d^3-5d^2+4d-20)x=0 is x=c_{1}e^{5t}+c_{2}cos(2t)+c_{3}sin(2t)