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Nonhomogenous equation..lifesaver1

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Date Posted: 7/23/2008 2:20:18 PM  Status: Live
Nonhomogenous equation..lifesaver1
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Question Details:
Verify the the given functions yi and y2 form a fundamental set of solutions of the reduced equation of the given non homogeneous equation; then find a particular solution of the nonhomogenous equation and give the general solution of the equation
 
 
y''
y1(x)=x^2
y2(x)=x^-1
 
When the I did the problem I got
 
y=
 
but it is wrong..please explain in detail if possible what I did wrong?
 
Thanks!!
 
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Karma Points: 388
(University of Alabama at Birmingham)
Date Posted: 7/24/2008 1:58:43 AM  Status: Live
Asker's Rating: Lifesaver   
Response:
To determine if the two solutions are a fundamental set of solutions we need to find the Wronskian.
 
which we can see is not equal to zero therefore this IS a fundamental set of solutions.
 
Now using variation of parameters
the particular solution is:
 
   
Where y1=x2  and y2=x-1
It doesn't really matter if you choose them the other way around it still yields the correct answer.
Now simply plug it all in.
 
solving the integrals...
the particular solution is:
and the general solution is:
y(x)=yc+yp
Granted I did not have any computation errors, I think this should be the solution.
 
 



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