Confused on how my professor did this last step, DiffEQ, 2nd OrdER

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SUMMARY

The discussion centers on solving a second-order differential equation using Abel's Theorem. The equation presented is t²y'' + 3ty' + y = 0, with a known solution y1(t) = 1/t. The professor emphasizes using Abel's Theorem over methods like Euler's or reduction of order, which are deemed more complex. The participants clarify the confusion surrounding the final steps of the solution process, particularly regarding the appearance and disappearance of the variable t.

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mr_coffee
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Hello everyone!
My professor was going over a problem real fast for the exam and now that i went over it again, I'm lost on how he did this last step. He is using a method called Abels Theorum. THe problem says:
Find a second solution of the given differential equation:
t^2y''+3ty' + y = 0;
y1(t) = 1/t;

U could use Eulers, but he doesn't want us to use that method, you could also use reduction of order but that would be more work and he doesn't want us to use that method either. He wants us to use Abels therom which seems to be the simplest out of all of them. Here is my work and I noted where I was confused at the very bottom of the page:


http://suprfile.com/src/1/2bgbtx/lastscan.jpg

Thanks if your confused on my work, let me know and i'll explain!
 
Last edited by a moderator:
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Are you sure that the line shouldn't be [itex]ty_2=ln|t|+C[/itex]
 
oooo,
w00t
yeah ur right! the t magically dissapears then reappears!
thanks again assyrian!
 

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