Dear Fellows, I want to solve 4 differential homogeneous equations for non trivial solution. I have found two methods 1) Determinent. 2) Elimination By det. I got 8th order resultant equation and by second method I got 10th order. As each of initial equation is 2nd order so 8th is correct. But what goes wrong in Elimination I could not understand. Example. x+2Dy+D2z=0 9Dx+4y-6D3z=0 x+D2+Dz=0 determinant gives 5th order equation while if we eliminate by taking value of z from eq i and put in ii and iii, and we will get iv , v. which finally gives 4th order equation. I doubt in taking the value of z from first equation, is this thing allowed or not? if no then why?