 Solution

ID: 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/solution

After division by

x > 0

, the equation is linear with coefficient

- 1/ x

y

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

 New to topics? Read the docs here!