8.7 Assessed Exercises 4

Solutions in tutor’s pigeonhole by 17:00 on Tuesday 13th December, please. Feedback is available from the moodle website.

A4.1. For each of the following, sketch the region of integration and evaluate the double integral by calculating a repeated integral with appropriate limits:

where $R$ and $S$ are rectangles.

[4]

A4.2. Find the general solutions to the following differential equations:

a) $\frac{d^{2}y}{dx^{2}}-7\frac{dy}{dx}+12y=0$.

[1]

b) $\frac{dy}{dx}-\frac{y}{x}=\frac{1}{x^{2}}$.

[3]

A4.3. Solve the initial value problem: $\frac{dy}{dx}=\frac{x^{2}-1}{y^{2}}$, $y(0)=1$.

[2]