Find the general solution:

\fThere is no general rule in choosing an expression or quantity in the substitution. However, the resulting equation must lead to a method that was previously discussed. Example: Find the general solution of y(xtanx + Iny)dx + tanxdy = 0 Let z = Iny and dz = then substitute in the given equation, We get, (xtanx + z)dx + tanxdz = 0 (This is linear in the variable z) The Standard form. + zcotx = x dx Where, P = cotx and Q = x The integrating factor. ( = el cotxdx _ einsinx = sinx The solution is, zo = foQdx + C since z = Iny Iny sinx = [ xsinxax + C using by parts. We get, Iny sinx = sinx - xcosx + C Ans