DE 1001: general and particular solutions

In this question, we solve for the general and particular solutions of DEs.

Question types

$\displaystyle \frac{\mathrm{d}y}{\mathrm{d}x} = f(x)$ $\frac{d y}{d x} = f (x)$ , where $f(x)$ $f (x)$ is of the form
- $\displaystyle \frac{b}{x^2+a^2}$
- $\displaystyle \frac{b}{x^2-a^2}$
- $\displaystyle \frac{bx}{x^2\pm a^2}$
- $\displaystyle \frac{b}{\cos^2 ax}$
- $\displaystyle \frac{b}{\sin^2 ax}$
$\displaystyle \frac{\mathrm{d}y}{\mathrm{d}x} = f(y)$ $\frac{d y}{d x} = f (y)$ , where $f(y)$ $f (y)$ is of the form
- $a-by$
- $\sqrt{a+by}$
- $\displaystyle \left(a+by\right)^{\frac{2}{3}}$
- $a^2\pm b^2y^2$
- $-b-ay-y^2$
- $e^{ay}$
$\displaystyle \frac{\mathrm{d}^2y}{\mathrm{d}x^2} = f(x)$ $\frac{d ^{2} y}{d x ^{2}} = f (x)$ , where $f(x)$ $f (x)$ is of the form
- $a+bx$
- $e^{ax}$
- $\cos ax$
- $\sin ax$