Ordinary Differential Equations

dx 3. Given d't = (x - 1)(1 - 2r) (a) Verify that 2r - 1 log r-1 is an implicit solution of the given differential equation (b) Find one explicit solution, that is, solve for r in part (a) 4. A Riccati equation is of the form dy dr P(x)y' + Q(x)y + R(I) (*) (a) If a solution m is known, show that the substitution y = 1 + = reduces (#) to a linear equation in v dy 2 cos'(x) - sin (x) + y (b) Solve dar 2 cos(a) given that y1 = sin(x) is a solution