2.I.1B

By writing $y(x)=m x$ where $m$ is a constant, solve the differential equation

$\frac{d y}{d x}=\frac{x-2 y}{2 x+y}$

and find the possible values of $m$.

Describe the isoclines of this differential equation and sketch the flow vectors. Use these to sketch at least two characteristically different solution curves.

Now, by making the substitution $y(x)=x u(x)$ or otherwise, find the solution of the differential equation which satisfies $y(0)=1$.

*Typos? Please submit corrections to this page on GitHub.*