21M.1.AHL.TZ1.15

pestleMathematicsAIHLPaper 121M· ahl-5-15-slope-fieldssource ↗

The diagram shows the slope field for the differential equation

$\frac{d y}{d x} = \sin (x + y), - 4 \leq x \leq 5, 0 \leq y \leq 5$ .

The graphs of the two solutions to the differential equation that pass through points $(0, 1)$ and $(0, 3)$ are shown.

For the two solutions given, the local minimum points lie on the straight line $L_{1}$ .

Find the equation of $L_{1}$ , giving your answer in the form $y = m x + c$ .

[3]

For the two solutions given, the local maximum points lie on the straight line $L_{2}$ .

Find the equation of $L_{2}$ .

[2]

Markscheme / solution

$\sin (x + y) = 0$ A1

$\Rightarrow x + y = 0$ (M1)

(the equation of $L_{1}$ is) $y = - x$ A1

[3 marks]

$x + y = π$ OR $y = - x + π$ (M1)A1

[2 marks]

Examiners’ report

[N/A]