Dear Fellows, I want to solve 4 differential homogeneous equations for non trivial solution. I have found two methods(adsbygoogle = window.adsbygoogle || []).push({});

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+D^{2}z=0

9Dx+4y-6D^{3}z=0

x+D^{2}+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?

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# Solving ODEs by Elimination

Can you offer guidance or do you also need help?

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