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 Original Message (ID '207772') By Bill Simpson: Since you have an explicit equation for p[x] in your system and you only use p'[x] in a single place, you might have more success if you differentiate your p[x] equation, substitute that for your p'[x], eliminate your initial condition for p[10] by determining what that really defines for the rest of your system and then try to use NDSolve for {a,u}. p[x] == 2 (1 - a[x]^(-3/2)) - 50 a''[x] + 1 so p'[x] == 3*a'[x]/a[x]^(5/2) - 50*a'''[x] and substitute that for p'[x]. Unfortunately I can't see how to then incorporate the p[10] into the result, but perhaps you can. Sometimes Solve and NDSolve have fewer difficulties if you solve for all the variables instead of just solving for a subset. That may apply in your case. I am also concerned that you have a[x]^(-3/2). It is possible that this is the reason for the errors that you are getting. If you can justify rearranging the equations of your system to get that a[x] out of the denominator then this might also help find a solution.