What is the solution for x^{''}+11x+20x=0 ?

The solution for x^{''}+11x+20x=0 is x=c_{1}cos(sqrt(31)t)+c_{2}sin(sqrt(31)t)

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x^{''}+11x+20x=0

x^{^{''}} + 11 x + 20 x = 0

x = c_{1} cos (31 t) + c_{2} sin (31 t)

Solution steps

x^{''} (t) + 11 x + 20 x = 0

Solve linear ODE:

x = c_{1} cos (31 t) + c_{2} sin (31 t)

x = c_{1} cos (31 t) + c_{2} sin (31 t)

y^{^{''}} + 4 y^{^{'}} + cy = 0, y (0) = 0, y^{^{'}} (0) = - 3

2 y^{^{''}} + 16 y^{^{'}} + 8 y = 0, y (0) = 5, y^{^{'}} (0) = 0

(2 D^{2} - 5 D - 3) y = 0

y^{^{''}} + 1960 y = 0

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

What is the solution for x^{''}+11x+20x=0 ?
The solution for x^{''}+11x+20x=0 is x=c_{1}cos(sqrt(31)t)+c_{2}sin(sqrt(31)t)