MATH 210 Fall 2005
Differential Equations
Study Guide for Final Examination
For those topics, where the practice problems are not specified, please consult the homework
problems assigned for the corresponding sections in the text.
1. First-order equations:
a separable ODEs,
b homogeneous ODEs,
c exact ODEs,
d linear ODEs.
2. Qualitative methods: finding equilibria, determining stability, plotting phase line
3. Existence and uniqueness of solutions:
Theorem on existence and uniqueness of solutions of initial value problems, domain of exis-
tence, examples showing nonuniqueness.
4. Second-order homogeneous differential equations:
Fundamental solution, linear independence, Wronskian.
Problems: 17-21, 23, 26, 27( p.145);
Problems: 1-7, 9-15, 17-23( p.156)
5. Second-order inhomogeneous differential equations:
method of undermined coefficients.
Problems: 1, 3,5,7, 15, 17, 19, 21, 23, 31, 33, 35 ( p.173)
6. Linear systems with constant coefficients:
Planar systems, general solution and phase portraits for systems of equations whose matrices
have real distinct and multiple and complex conjugate eigenvalues, exponential of a matrix;
initial-value problems; higher-order linear differential equations, variation of parameters for
inhomogeneous systems of linear equations.
Problems assigned in HW6, HW7, and HW8.
7. Nonlinear systems:
Linearization.
Problems assigned in HW8.