| Date | May 2014 | Marks available | 7 | Reference code | 14M.1.hl.TZ0.2 |
| Level | HL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 2 | Adapted from | N/A |
Question
Consider the differential equation \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = {y^3} - {x^3}\) for which \(y = 1\) when \(x = 0\). Use Euler’s method with a step length of \(0.1\) to find an approximation for the value of \(y\) when \(x = 0.4\).
Markscheme
use of \(y \to y + h\frac{{{\text{d}}y}}{{{\text{d}}x}}\) (M1)
| \(x\) | \(y\) | \({\text{d}}y{\text{/d}}x\) | \(h{\text{d}}y{\text{/d}}x\) | |
| 0 | 1 | 1 | 0.1 | (A1) |
| 0.1 | 1.1 | 1.33 | 0.133 | A1 |
| 0.2 | 1.233 | 1.866516337 | 0.1866516337 | A1 |
| 0.3 | 1.419651634 | 2.834181181 | 0.283418118 | A1 |
| 0.4 | 1.703069752 | (A1) |
Note: After the first line, award A1 for each subsequent \(y\) value, provided it is correct to 3sf.
approximate value of \(y(0.4) = 1.70\) A1
Note: Accept \(1.7\) or any answers that round to \(1.70\).
[7 marks]
Examiners report
[N/A]
