
Section 14: General remarks on solutions, families of curves,
orthogonal trajectories 

Section 5: Motion problems 

Section 6: The brachistochrone, treated without calculus of
variations 

Section 711: Homogenous and exact equations, integrating
factors, linear first order equations, reduction of order 

Section 12: The catenary, assign 13 as reading (review of
RLC circuits) 

Section 1416: Second order linear equations, homogeneous
equations, the use of a known solution to find another 

Section 17: Homogeneous equations with constant coefficients 

Section 18: The method of undetermined coefficients 

Section 19: The method of variation of parameters 

Section 20: Vibrations in mechanical and electrical systems 

Section 21: Newton's law of gravitation and the motion of
the planets 

Section 22: Higher order linear equations, coupled harmonic
oscillators 

Section 23: Operators methods for finding particular
solutions 

Section 2425: Oscillations and the Sturm separation
theorem, Sturm comparison theorem 

Section 2731: Review of power series, series solutions of
first order equations, second order equations, ordinary points, regular
singular points, Gauss's hypergeometric equation. 