Solved: The differential equation dydx P(x) Q(x)y R(x)y2 is known as Riccatis equation
Chapter 2, Problem 35(choose chapter or problem)
The differential equation dydx P(x) Q(x)y R(x)y2 is known as Riccatis equation. (a) A Riccati equation can be solved by a succession of two substitutions provided that we know a M particular solution y1 of the equation. Show that the substitution y y1 u reduces Riccatis equation to a Bernoulli equation (4) with n 2. The Bernoulli equation can then be reduced to a linear equation by the substitution w u1 . (b) Find a one-parameter family of solutions for the differential equation where y1 2x is a known solution of the equation.
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