Riccati Equations. The equation dy dt = q1(t) + q2(t)y + q3(t)y2 is known as a Riccati23
Chapter 2, Problem 33(choose chapter or problem)
Riccati Equations. The equation dy dt = q1(t) + q2(t)y + q3(t)y2 is known as a Riccati23 equation. Suppose that some particular solution y1 of this equation is known. A more general solution containing one arbitrary constant can be obtained through the substitution y = y1(t) + 1 v(t) . Show that v(t) satisfies the first order linear equation dv dt = (q2 + 2q3y1)v q3. Note that v(t) will contain a single arbitrary constant.
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