a) Show that the differential equation is $\frac{{dy}}{{dx}} = 2xy$

Separate variables correctly and attempt integration of both sides

Obtain term $ln{\text{ }}y$, or equivalent

Obtain term ${x^2}$, or equivalent

Evaluate a constant, or use limits $x = 1$, $y = 2$, in a solution containing terms $\alpha ln{\text{ }}y$ and $b{x^2}$

Obtain correct solution in any form

Obtain the given answer correctly

b) State that the gradient at $\left( { - 1,{\text{ }}2} \right)$ is $ - 4$

Show the sketch of curve with correct concavity, positive y-intercept and axis of symmetry $x = 0$

[SR: A solution with $k \ne 2$, or not evaluated, can earn B0M1A1A1M1A1A0 in part (a).]

[SR: If given answer is assumed valid, give B1 if $\frac{{dy}}{{dx}}$ is shown correctly to be equal to $2xy$, is stated to be proportional to $xy$, and shown to be equal to 4 at $\left( {1,{\text{ }}2} \right)$.]