5. Equations of the form y’ = P(x)*y^2 + Q(x)*y + R(x) arecalled Riccati equations.
i) If we know a solution y = φ(x) of this equation, then anyother solution
can be written in the form y(x) = φ(x)+ 1/v(x), where v(x) is anunknown
function which satisfies a certain linear equation. Using thefact that
φ and y both solve the above Riccati equation, find thedifferential
equation that v satisfies.
ii) Consider the equation 3y’ + y^2 +2/(x^2) = 0. Find onesolution of this equation by inspection.
iii) Use the method of part(i) to find the general solution ofthe equation
in (ii).
