Exclusive to AA HL and AI HL, differential equations are approached quite differently across the two courses. In AA HL, students solve first order differential equations analytically using separation of variables, the integrating factor method for equations of the form y' + P(x)y = Q(x), and homogeneous equations via the substitution y = vx; Euler's method is also covered for numerical approximation. In AI HL the emphasis is on modelling and numerical methods: students set up differential equations from context, solve separable equations, interpret slope fields, apply Euler's method using spreadsheets, and analyse systems of coupled differential equations through phase portraits — identifying equilibrium points and long-term behaviour using eigenvalue analysis.
Start here
Start by downloading the cheat sheet and the vocabulary below. After that, move to the video lessons with their respective exercise lists.
Video lessons
Learn the content with the videos provided and reinforce your comprehension by practicing with the exercise list above.
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