Ordinary Differential Equations

Lists of exercises:

0. Integrals
1. Separable first order ODEs. Homogeneous equations y’=f(y/x).
2. Inhomogeneous linear first order ODEs. Orthogonal trajectories.
3. Second order ODEs.
4. Inhomogeneous linear second order ODEs with constant coefficients.
5. Inhomogeneous linear second order ODEs.
6. Systems of first order ODEs.

Literature available online:

1. Mathematics : a short introduction to ordinary and partial differential equations – chapters: 1,2,3.


Tasks in the test:
1) solve y’+p(x)y=f(x) with variation of constant method,
2) find and draw orthogonal trajcetories for a given family of curves,
3) solve ay”+by’+cy = f(x) with undetermined coefficients method,
4) solve second order equation (F(y”, y’, x)=0 or F(y”, y’,y)=0 or y”+p(x)y’+q(x)y = f(x)),
5) solve given system of equations (nonlinear, with elimination method, or linear homogoneous with constant coefficients, with Euler method).

The grade depends on number of tasks corectly solved in the test in the last lecture (22.01.2019):
3 of 5 tasks solved – is a fair grade (3.0),
4 of 5 tasks solved – is a good grade (4.0),
5 of 5 tasks solved – is a very good grade (5.0).

On 29.01.2019, on the last tutorial you can retake the test.