Past exam of the year 1 of the computer science course of the University of Oxford / 2014 / Discrete mathematics, continuous mathematics and probability / 4 / b

Table of contents
- Solution b

Solution

After division by

x > 0

, the equation is linear with coefficient

- 1/ x

on

y

. Its integrating factor is

1/ x

, and the product rule gives

(\frac{y}{x})^{'} = \frac{x y ^{'} - y}{x ^{2}} = e^{x} sin x .

Using the antiderivative from the preceding part,

y (x) = C x + \frac{x e ^{x}}{2} (sin x - cos x), x > 0.

The arbitrary constant multiplies the homogeneous solution

x

.

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