Help with one simple problem

• June 21st 2014, 07:45 PM
catenary
Help with one simple problem
Attachment 31153
Here I am supposed to show that the equation of the right is a solution of the differential equation on the left. I have solved a few problems of this type already but I have trouble with this one. Did I make a mistake and overlooked something somewhere or the condition 'for x>0' sort of means that it is okay even if the other side of the equation turns out to be negative? In the book's answer key it says that for this problem the equation on the right is a solution of the DE
• June 21st 2014, 10:32 PM
romsek
Re: Help with one simple problem
There must be a typo in here somewhere. I'm showing the solution to this differential equation is what mathematica calls

$C x+\frac{1}{2} x \left(Ei(x)-\frac{e^x}{x}\right)$

$Ei(x)=\int_{-x}^\infty \dfrac {e^{-t}} t~dt$
• June 21st 2014, 11:19 PM
catenary
Re: Help with one simple problem
Quote:

Originally Posted by romsek
There must be a typo in here somewhere.

Oh so you mean that perhaps there was a typo in the book.. I have after all been able to solve the other problems..
Can you show me where you got that solution by the way so I may make use of it too?
• June 21st 2014, 11:37 PM
SlipEternal
Re: Help with one simple problem
Quote:

Originally Posted by catenary
Attachment 31153
Here I am supposed to show that the equation of the right is a solution of the differential equation on the left. I have solved a few problems of this type already but I have trouble with this one. Did I make a mistake and overlooked something somewhere or the condition 'for x>0' sort of means that it is okay even if the other side of the equation turns out to be negative? In the book's answer key it says that for this problem the equation on the right is a solution of the DE

You may have missed a negative sign... If the original problem were $y' = -\dfrac{2y+e^x}{2x}$, then $y = \dfrac{C-e^x}{2x}$. Are you sure you didn't miss a negative sign in the original problem?
• June 22nd 2014, 04:29 AM
catenary
Re: Help with one simple problem
Oh it seems that it was not my solution that was wrong but rather I forgot to copy the negative sign in $y' = -\dfrac{2y+e^x}{2x}$ when I copied it on the paper.. Thanks again so much SlipEternal you are my savior! By the way what is the difference between\dfrac and \frac?
• June 22nd 2014, 04:50 AM
Prove It
Re: Help with one simple problem
\dfrac is a fraction in displaystyle - so usually appears bigger. But if you use the \displaystyle command at the beginning of your LaTeX that makes everything large size anyway :)