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

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

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

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

y = c_{2} sin (2 x)

Solution steps

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

Solve linear ODE:

y = c_{2} sin (2 x)

y = c_{2} sin (2 x)

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

y^{^{''}} - \frac{3}{2} y^{^{'}} + y = 0

77 y^{^{''''}} + 39 y^{^{''}} + 4 y = 0

\frac{d ^{2} y}{d t ^{2}} + 2 \frac{d y}{d t} + 10 y = 0

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

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