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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

6 y^{^{''}} + y^{^{'}} - 2 y = 0, y (1) = 2, y^{^{'}} (1) = - \frac{1}{6}

y^{^{''}} - 2 \cdot y^{^{'}} + y = 0

25 y^{^{''}} + 40 y^{^{'}} + 16 y = 0

y^{^{''}} + 3 y^{^{'}} - 10 y = 0, y (0) = 2, y^{^{'}} (0) = 4

y^{^{''}} + 2 y^{^{'}} - 8 y = 0, y (0) = 0, y^{^{'}} (0) = 6

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