MATHEMATICS 2 (MA10193) EXAMPLES SHEET 4

I will look at work given to me or left in the folder on my office door (1W3.35). If you do not have a copy of this sheet, you can find one at

http://www.bath.ac.uk/~masgks/MA10193/sheet4.ps (or .dvi or .pdf).

1. Solve the differential equation

\frac{d^{2}y}{dx^{2}} − 8\frac{dy}{dx} + 41y = 0

if y = 1 when x = 0 and y = 0 when x = π/2.

2. Find a solution to

\frac{d^{2}y}{dx^{2}} − 3\frac{dy}{dx} + 10y = 24 sin x

which satisfies y = 0 when x = 0 and y = 1 when x = π/4.

3. Solve the simultaneous equations

\begin{aligned}7\frac{dx}{dt} + 3y & = x \\ 3\frac{dy}{dt} − 4x & = 0. \end{aligned}

4.Solve the simultaneous equations

\begin{aligned}\frac{dx}{dt} + 3\frac{dy}{dt} + 3x − 4y & = 3t^{2} \\ 2\frac{dx}{dt} + \frac{dy}{dt} − 4x + 5y & = −2t + 2 \end{aligned}

GKS, 12/04/05