What is the solution for linear y^{''}+5y=0 ?

The solution for linear y^{''}+5y=0 is y=c_{1}cos(sqrt(5)t)+c_{2}sin(sqrt(5)t)

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linear y^{''}+5y=0

linear

y^{^{''}} + 5 y = 0

y = c_{1} cos (5 t) + c_{2} sin (5 t)

Solution steps

y^{''} (t) + 5 y = 0

Solve linear ODE:

y = c_{1} cos (5 t) + c_{2} sin (5 t)

y = c_{1} cos (5 t) + c_{2} sin (5 t)

x^{^{''}} + 4 x^{^{'}} + 16 x = 0

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

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

y^{^{''}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = - 6

y^{^{''}} + 8 y^{^{'}} + 41 y = 0, y (0) = 1, y^{^{'}} (0) = 2

What is the solution for linear y^{''}+5y=0 ?
The solution for linear y^{''}+5y=0 is y=c_{1}cos(sqrt(5)t)+c_{2}sin(sqrt(5)t)