Ok, heres the question, have patience with my terrible latex skills... 1. The problem statement, all variables and given/known data The equations of constraint of the rolling disk: dx - asin(theta)d(phi) = 0 -> 1. dy + acos(theta)d(phi) = 0 -> 2. are special cases of general linear diff-eqs of constraint of the form: [tex]\sum[/tex]g_i(x1,...,xn)dxi = 0 -> 3. A constraint condition of this tupe is holonomic only if an integrating function f(x1,...,xn) can be found that turns it into an exact differential. Clearly the fn. must be such that [tex]\delta[/tex](fg_i)/[tex]\delta[/tex]x_j = [tex]\delta[/tex](fg_j)/[tex]\delta[/tex]x_i -> 4. for all i[tex]\neq[/tex]j. Show that no such integrating factor can be found for either of equations 1 or 2. 2. Relevant equations above 3. The attempt at a solution I have found that when I put either equation 1 or 2 into 3, i can cancel the df, and im left with the original equation, but with the sign backwards (ie 1 becomes dx + ..., and 2 becomes dy - ...). I dont know if this actually means anything... I am wondering if I can possibly arrange eq 4. so that i have something to integrate, and show that f diverges...? I dont know how to show that there is no such f...... Anybody have any tips or ideas? Thanks for your time.