Differential Equations Lecture Notes ((exclusive)) [ Fully Tested ]

Solve ( \frac{dy}{dx} + 2y = e^{-x} ). Integrating factor : ( \mu(x) = e^{\int 2,dx} = e^{2x} ). Multiply through: ( e^{2x}y' + 2e^{2x}y = e^{x} ) Left side is ( \frac{d}{dx}(e^{2x}y) = e^{x} ) Integrate: ( e^{2x}y = e^{x} + C ) Thus ( y = e^{-x} + Ce^{-2x} ).

A powerful tool for handling difficult initial value problems. differential equations lecture notes