What is the solution for y^{''}-10y+24y=0 ?

The solution for y^{''}-10y+24y=0 is y=c_{1}cos(sqrt(14)t)+c_{2}sin(sqrt(14)t)

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y^{''}-10y+24y=0

y^{^{''}} - 10 y + 24 y = 0

y = c_{1} cos (14 t) + c_{2} sin (14 t)

Solution steps

y^{''} (t) - 10 y + 24 y = 0

Solve linear ODE:

y = c_{1} cos (14 t) + c_{2} sin (14 t)

y = c_{1} cos (14 t) + c_{2} sin (14 t)

y^{^{''''}} - 20 y^{^{'''}} + 100 y^{^{''}} = 0

81 y^{^{''}} - 9 y = 0, y (0) = 0, y^{^{'}} (0) = 0

9 y^{^{''}} + 4 y^{^{'}} - 5 y = 0

y^{^{''}} + (3 - a) y^{^{'}} - 2 (a - 1) y = 0

- c x^{^{''}} = b x, x (0) = 0

What is the solution for y^{''}-10y+24y=0 ?
The solution for y^{''}-10y+24y=0 is y=c_{1}cos(sqrt(14)t)+c_{2}sin(sqrt(14)t)