homogeneous differential equation problem

Discussion in 'Math' started by PG1995, Nov 13, 2011.

  1. PG1995

    Thread Starter Active Member

    Apr 15, 2011
    753
    5
    Hi

    Please have a look on the attachment. It has my queries there. Please help me with them. It would be really kind of you. Thanks.

    Regards
    PG
     
  2. PG1995

    Thread Starter Active Member

    Apr 15, 2011
    753
    5
    Update: I have solved Q1. Thanks for giving it a look. If someone is in process of writing a reply, then I still genuinely thank you.
     
  3. steveb

    Senior Member

    Jul 3, 2008
    2,433
    469
    It looks like you figured out that Q1 is answered by considering that the dx term you thought was missing was simply moved over to the other term.

    For Q2, one simply has to use the log properties that adding logarithms is like multiplying the arguments and subtracting is like dividing. From this, multiplication by 2 on the log is like a power of two on the argument. I would write it out in TeX, but it's a little tedious, so I'll just sketch it out.

    y/x=2 log|1+y/x|+log|x|-log|c|

    y/x=log|(1+y/x)^2|+log|x|-log|c|

    y/x=log|(x(1+y/x)^2)/c|

    y/x=log|(x^2(1+y/x)^2)/(cx)|

    y/x=log|(x+y)^2)/(cx)|
     
    PG1995 likes this.
  4. PG1995

    Thread Starter Active Member

    Apr 15, 2011
    753
    5
    Thank you very much, Steve.

    With best wishes
    PG
     
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