Question

Use the method for solving equations of the form dy =G(ax + by) to solve the following differential equation. dx dy dx V6x + y - 6 Ignoring lost solutions, if any, an implicit solution in the form F(x,y) = C is = C, where is an arbitrary constant. (Type an expression using x and y as the variables.)

Answer 1

Ans: dy dx = √6xty -6 6x+y=t 6 + dy da dt da seda -6) dy da Now, dt = E-6 - dt = da =) at वर ses -1/2 dt = (on on integrating both sides) =(dx St =x+t (s that to t =x+c 2 t ) 2 (6*+4)2 = x+6 (since t = 6x+4) o is arbitrasy constant. a 2 Sexty = xtc Hence. 2 Sbary = xto is the sequired solution, f(x, y) = 1 2 56x+y where o is an arbitrasy constant,