I think is another way to write one of your solutions. That will change your characteristic equation, won't it?
Hi again all,
After solving my last problem i have a new one for you all, i`ve done it but not sure if it is correct!
Wronskian is 8
Find a (nonhomogeneous) third-order linear dierential equation with general so-
lution using the above
This is what i have,
there for the equation is
hence Diff Equation is
I realize that. What I'm saying is that if you have a characteristic equation then one solution is corresponding to not Therefore, I think you need to change your characteristic equation you put forward en route to your DE.I`m working backwards from the solutions i`ve been given to work of the 3rd order differential equations.
Ok. Let me start from a third-order DE, and work the problem in the usual way. I know you're solving the inverse problem of producing a DE, but bear with me. Let's say I have the DE The usual procedure with constant coefficient problems like this is to assume a solution of the form plug it in, and solve for We have and finally Plugging into the DE yields
Now hence we may divide out to obtain the characteristic equation
Now you can show that the roots of this equation are That is, it factors as Hence, the solution to this DE is as follows:
Do you see (and this is really where I'm going with this), that the root corresponds, because of our initial guess of , to the solution It does NOT correspond to the solution
If you don't believe me, think of it this way: according to the OP, you are claiming that solves the homogeneous ODE
I altered your DE with some obvious corrections. Plug into this DE, and you will see that it does not satisfy it.
Do you follow me now?