DIFFERENTIAL EQUATIONS

At the end of this section, students should be able to:

1. solve first order linear differential equations \(y'-ky=f(x)\) using an integrating factor, given that \(k\) is a real constant or a function of \(x\), and \(f\) is a function;
2. solve first order linear differential equations given boundary conditions;
3. solve second order ordinary differential equations with constant coefficients of the form \(ay''+by'+cy=0=f(x)\), where \(a, b, c\in \mathbb{R}\) and \(f(x)\) is:
(a) a polynomial,
(b) an exponential function,
(c) a trigonometric function;
and the complementary function may consist of
(a) real and distinct root,
(b) 2 equal roots,
(c) 2 complex roots;
4. solve second order ordinary differential equation given boundary conditions;
5. use substitution to reduce a second order ordinary differential equation to a suitable form.