In the discussion of the Riccati equation dy/dt =
Chapter , Problem 31(choose chapter or problem)
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 u(t) = 1 y(t) y1(t) yields a linear equation for du/dt.
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