N2008 P1 Q4

Find the general solution of the differential equation \(\frac{\mathrm dy}{\mathrm dx}=\frac{3x}{x^2+1}\).[2]

Find the particular solution of the differential equation for which \(y=2\) when \(x=0\).[1]

What can you say about the gradient of every solution curve as \(x\to\pm\infty\)?[1]

Sketch, on a single diagram, the graph of the solution found in part (ii), together with 2 other members of the family of solution curves.[3]