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

Table of contents
- Solution c

Solution

The homogeneous characteristic equation is

r^{2} - 4 r + 3 = (r - 1) (r - 3) = 0

e^{x}

and

e^{3 x}

. Since the forcing

e^{3 x}

already appears among these solutions, try a particular solution

y_{p} = A x e^{3 x}

. Differentiation and substitution give

y_{p}^{''} - 4 y_{p}^{'} + 3 y_{p} = 2 A e^{3 x},

so

A = 1/2

. The general solution is

y = C_{1} e^{x} + C_{2} e^{3 x} + \frac{x}{2} e^{3 x} .

 Ancestors (11)

 View article source

 Discussion (0) New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version