Q2. The differential equation +p(x)y+q(x)y² = r(x) is known as Riccati's equation. If one particular solution, say y1 (x), of the Riccati's equation is known, then its solution y = y(x) can be obtained by two consecutive substitutions. (i). Show that the substitution y = y1 + u reduces Riccati's equation to a Bernoulli equation, and specify n. (ii). Transform the Bernoulli equation obtained in (i) to linear equation.

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