In the discussion of the Riccati equation dy/dt = r (t)+a(t)y+b(t)y2 given in this appen...

In the discussion of the Riccati equation dy/dt = r (t)+a(t)y+b(t)y² given in this appendix, we did one change of variables to convert to a Bernoulli equation and then another change of variables to obtain a linear equation. It is possible to combine the two into a single change of variables. If y₁(t) is a particular solution of the Riccati equation above, show that changing to the new dependent variable

yields a linear equation for du/dt.