## 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.