What is the solution for y^{''}+(1/2)y=0 ?

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

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y^{''}+(1/2)y=0

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

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

Solution steps

y^{''} (t) + (\frac{1}{2}) y = 0

Solve linear ODE:

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

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

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = e^{5 x}

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

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = 8, y^{^{'}} (0) = 7

y^{^{''}} - 6 y^{^{'}} - 7 y = 0, y (0) = 4, y^{^{'}} (0) = 4

y^{^{''}} - 6 y^{^{'}} + 25 y = 0, y (0) = 2, y^{^{'}} (0) = - 2

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