Ricatti Equation The first-order nonlinear DEis known as the Ricatti equation.5(a) Show th...

Ricatti Equation The first-order nonlinear DE

is known as the Ricatti equation.5

(a) Show that if one solution y1(t) of the Ricatti equation is known, then a more general solution containing an arbitrary constant can be found by substituting y = y1(t) + 1/ν(t) into the DE and requiring ν(t) to satisfy ν′ = − [q(t) + 2r(t)y1(t)]ν − r(t), which is a linear equation.

(b) Verify that y1(t) = 1 satisfies the Ricatti equation