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)

y^{^{''}} - y = 0, y (0) = 0, y (0) = 1

y^{^{''}} - 6 y = 0, y (0) = - 23, y^{^{'}} (0) = 6

(D^{3} - D^{2}) y = 0

6 y^{^{''}} - y^{^{'}} - 35 y = 0

4 y^{^{'''}} + 5 y^{^{''}} - 23 y^{^{'}} - 6 y = 0

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)