What is the solution for 4(d^2y)/(dx^2)+y=0 ?

The solution for 4(d^2y)/(dx^2)+y=0 is y=c_{1}cos(x/2)+c_{2}sin(x/2)

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4(d^2y)/(dx^2)+y=0

4 \frac{d ^{2} y}{d x ^{2}} + y = 0

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

Solution steps

4 \frac{d ^{2} y}{d x ^{2}} + y = 0

Solve linear ODE:

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

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

y^{^{''}} + 3 y^{^{'}} + 5 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''''}} + 3 y^{^{'''}} + y^{^{''}} = 0

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

16 y^{^{''}} + 8 y^{^{'}} + 145 y = 0, y (0) = - 2, y^{^{'}} (0) = 1

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

What is the solution for 4(d^2y)/(dx^2)+y=0 ?
The solution for 4(d^2y)/(dx^2)+y=0 is y=c_{1}cos(x/2)+c_{2}sin(x/2)