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

The solution for (d^2f)/(dx^2)+4f(x)=0 is f(x)=c_{1}cos(2x)+c_{2}sin(2x)

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(d^2f)/(dx^2)+4f(x)=0

\frac{d ^{2} f}{d x ^{2}} + 4 f (x) = 0

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} = - 16 y^{^{'}}

7 y^{^{''}} + 5 y^{^{'}} - 6 y = 0

4 y^{^{''}} - 72 y^{^{'}} + 324 y = 0

y^{^{''}} + 7 y^{^{'}} + 12 y = 0, y (0) = 1, y^{^{'}} (0) = - 9

y^{^{''}} - 9 y^{^{'}} - 3 y = 0

What is the solution for (d^2f)/(dx^2)+4f(x)=0 ?
The solution for (d^2f)/(dx^2)+4f(x)=0 is f(x)=c_{1}cos(2x)+c_{2}sin(2x)