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

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

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(d^2y)/(dx^2)=-4y

\frac{d ^{2} y}{d x ^{2}} = - 4 y

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} = - 4 y

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)

\frac{y ^{^{''}}}{8} + 2 y^{^{'}} + 4 y = 0, y (0) = 0, y^{^{'}} (0) = - 5

y^{^{''}} + 9 y = 0, y^{^{'}} (\frac{π}{6}) = - 3, y (0) = 1

\frac{d ^{2} y}{d t ^{2}} - y = 0

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

y^{^{''}} - 7 y^{^{'}} - 8 y = 0, y (0) = 5, y^{^{'}} (0) = - 5

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