Chapter 12.2, Problem 23E

To determine

To prove:

The given system $\frac{dx}{dt}=x-2y,$ $\frac{dy}{dt}=3x-4y$ can be transformed to $\frac{du}{dt}=-2u,\frac{d\upsilon }{dt}=-\upsilon$ using change of variables $x=2u+\upsilon .y=3u+\upsilon$.

The $u$-axis maps to the line $y=\frac{3}{2}x$ and $\upsilon$-axis maps to the line $y=x$.