Medium Practice — Set 2

Quick Recap — Linear Differential Equations

• Standard form: $\tfrac{dy}{dx}+P(x)y=Q(x)$.
• Integrating factor: $\mathrm{IF}=e^{\int P\,dx}$.
• Solution: $y\cdot\mathrm{IF}=\displaystyle\int Q\cdot\mathrm{IF}\,dx+C$.
• If $Q=0$, the equation reduces to $y=Ce^{-\int P\,dx}$.