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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

1296 y^{^{''}} + 72 y^{^{'}} + y = 0, y (0) = 7, y^{^{'}} (0) = 5

y^{^{''}} - 16 y = 0, y (0) = 13, y^{^{'}} (0) = 20

y^{^{''}} + 6 y^{^{'}} + 5 y = 0, y (0) = 0, y^{^{'}} (0) = 0

2 y^{^{'''}} + 7 y^{^{''}} - 17 y^{^{'}} - 10 y = 0

1 y^{^{''}} + 3 y^{^{'}} + 2 y = 0

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