63. The equation dy/dx = A(x)y² + B(x)y + C(x) is called a Riccati equation. Suppose that one particular solution yı(x) of this equation is known. Show that the substitu- tion у %3D ут + transforms...

Extracted text: 63. The equation dy/dx = A(x)y² + B(x)y + C(x) is called a Riccati equation. Suppose that one particular solution yı(x) of this equation is known. Show that the substitu- tion у %3D ут + transforms the Riccati equation into the linear equation dv + (B +2Ay1)v = -A. dx Use the method of Problem 63 to solve the equations in Prob- given that y1(x) = x is a solution of each. lems 64 dy 64. + y2 = 1 + x² dx