1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Help with very easy differential equation

  1. May 10, 2012 #1
    1. The problem statement, all variables and given/known data
    dy/dx=y/x


    2. Relevant equations



    3. The attempt at a solution
    ok heres what I got... dy/dx=y/x so dy/y=dx/x. Then just integrate both sides and you get ln(y)=ln(x)+C. Next raise both sides to a power of e and you get y=e^(ln(x)+C). This can be rewritten y=e^ln(x)*e^C. so the answer i got is y=xe^C. however, i checked the answer in the back of my textbook and it says that the answer is y=Cx. Help please??
     
  2. jcsd
  3. May 10, 2012 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You have the right idea, but need to use a little more care. When you integrate you get$$
    \ln(|y|) = \ln(|x|) + C$$
    Writing in exponential form$$
    |y| = e^{\ln(|x|+C)}=|x|e^C$$Note that while ##C## can be any constant, ##e^C## is positive, so both sides of this equation are positive. You can drop the absolute value signs like this$$
    y = \pm e^Cx$$where ##\pm e^C## can now be any nonzero constant so you can call it a new constant K.$$
    y = Kx$$One other point. By dividing by ##y## in your solution, you ruled out the possibility of finding ##y=0## if it would happen to be a solution. Checking it you will see that ##y=0## also works, so you can include that by saying ##K## is any constant, not just a nonzero one.

    Finally, the way the equation is written, no solution can be valid for ##x=0##. That would be solved by writing the DE in the form ##x\frac{dy}{dx}= y## in the first place.
     
  4. May 10, 2012 #3
    thanks a lot lckurtz
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Help with very easy differential equation
Loading...