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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

x^{^{''}} + 6 x = 0

y^{^{''}} + y = 0, y (\frac{π}{3}) = 10, y^{^{'}} (\frac{π}{3}) = - 20

u, \frac{d ^{2} u}{d t ^{2}} = a u (t)

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

y^{^{''''}} - 8 y^{^{'''}} + 17 y^{^{''}} + 2 y^{^{'}} - 24 y = 0

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