A differential equation of the form y' + p(x)y + q(x)y = r(r) is called a Riccati equations. a) If y = Y(r) is a known solution to the Riccati equation, show that the substitution y = Y(z) + v-(x) reduces it to the linear equation v'- [p(x) + 2Y(x)q(x)]v=q(x) b) Find the general solution to the Riccati equation xy - xy - xy = 1, x > 0, given that y = - is a solution.