The differential equation dy dx = P(x) + Q(x)y + R(x)y2 dP - = P(a - bP) dt ' is known
Chapter 2, Problem 35(choose chapter or problem)
The differential equation dy dx = P(x) + Q(x)y + R(x)y2 dP - = P(a - bP) dt ' is known as Riccati's equation. (a) A Riccati equation can be solved by a succession of two substitutions provided we know a particular solution y1 of the equation. Show that the substitution y = y1 + u reduces Riccati's equation to a Bernoulli equation (4) with n = 2. The Bernoulli equation can then be reduced to a linear equation by the substitution w = u-1 (b) Find a one-parameter family of solutions for the differential equation dy dx -- - -y + y'
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