Mathematics: Applications and Interpretation · Topic 5: Calculus

AHL5.18 — Second order differential equations

Mathematics: Applications and Interpretation · SL / HL · syllabus-mapped notes

1. AIAHL5.18.1

   Second order equations as coupled systems

   Rewriting $\tfrac{d^2x}{dt^2}=f(x,\tfrac{dx}{dt},t)$ and using Euler's method.

2. AIAHL5.18.2

   Exact solutions and the phase portrait method

   Damped equations $\tfrac{d^2x}{dt^2}+a\tfrac{dx}{dt}+bx=0$ via eigenvalues.