1. **State the problem:** Solve the differential equation $$y'' = -y$$. 2. **Recall the formula and rules:** This is a second-order linear differential equation with constant coefficients. The characteristic equation is $$r^2 = -1$$. 3. **Solve the characteristic equation:** $$r^2 = -1 \implies r = \pm i$$ where $$i$$ is the imaginary unit. 4. **Write the general solution:** For complex roots $$\alpha \pm \beta i$$, the solution is $$y = C_1 \cos x + C_2 \sin x$$. 5. **Interpretation:** The solution represents sinusoidal oscillations, consistent with the graph showing a wave oscillating between -1 and 1. **Final answer:** $$y = C_1 \cos x + C_2 \sin x$$ where $$C_1$$ and $$C_2$$ are constants determined by initial conditions.