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

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

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y^{''}+by=0

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} = 0, y^{^{'}} (0) = 3, y (0) = 0

y^{^{''}} - y^{^{'}} - 2 y = 0, y (0) = a, y^{^{'}} (0) = 2

y^{^{''}} + 4 y^{^{'}} + 3 y = 0, y (0) = 1, y^{^{'}} (0) = 0

2 y^{^{''}} + 6 y^{^{'}} + 8 y = 0, y (0) = 5, y^{^{'}} (0) = 0

x^{^{''}} + x^{^{'}} + 2 x = 0

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