Easy Practice — Set 2

Quick Recap — Variables Separable

• Write as $f(y)\,dy=g(x)\,dx$ and integrate both sides.
• $\tfrac{dy}{dx}=ky\Rightarrow y=Ce^{kx}$ (growth/decay).
• $\tfrac{dy}{dx}=\tfrac{y}{x}\Rightarrow y=Cx$; $\tfrac{dy}{dx}=\tfrac{x}{y}\Rightarrow y^2-x^2=C$.
• Apply initial conditions after integrating to fix $C$.