What is the solution for (d^2y)/(dx^2)+3y=0 ?

The solution for (d^2y)/(dx^2)+3y=0 is y=c_{1}cos(sqrt(3)x)+c_{2}sin(sqrt(3)x)

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(d^2y)/(dx^2)+3y=0

\frac{d ^{2} y}{d x ^{2}} + 3 y = 0

y = c_{1} cos (3 x) + c_{2} sin (3 x)

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 3 y = 0

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x)

y = c_{1} cos (3 x) + c_{2} sin (3 x)

y^{^{'''}} + 6 \cdot y^{^{''}} = 0

y^{^{''}} - 4 y^{^{'}} + 40 y = 0, y (0) = 3, y^{^{'}} (0) = 2

y^{^{''}} - 6 y^{^{'}} + 13 y = 0, y (0) = - 3

5 y^{^{''}} + 45 y = 0, y (0) = - 8, y^{^{'}} (0) = 0

y^{^{''}} + 12 y^{^{'}} + 36 y = 0, y (0) = - 2, y^{^{'}} (0) = 8

What is the solution for (d^2y)/(dx^2)+3y=0 ?
The solution for (d^2y)/(dx^2)+3y=0 is y=c_{1}cos(sqrt(3)x)+c_{2}sin(sqrt(3)x)