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Solving multivariable equation with integration

  1. Mar 9, 2014 #1

    gingermom

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    Gold Member

    1. The problem statement, all variables and given/known data

    dy/dx = (1+x)/xy solve y(1) = -4





    2. Relevant equations



    3. The attempt at a solution What threw me was the solve for if y(1) = -4

    I grouped variables and then integrated both sides and solved for y.

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

    I then switched the x and y to get the inverse of the equation and set that equal to -4

    -4=-+ √2ln1+1+c
    16= 2*(1+c)
    8-1=c
    7=c

    However, I am not sure this was the correct approach. I could not figure out how to isolate x in the beginning, but I am not 100 percent sure of my logic of using the inverse, and whether I applied it appropriately. If this is way off base, can you point me in the correct direction? We have not had any problems quite like this and I am not sure I am making the correct leap in combining concepts.

    Thanks.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 9, 2014 #2

    Zondrina

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    Homework Helper

    Slight miscommunication here. Your second line should read:

    ##y= +- \sqrt{2ln|x| + 2x + 2c}##

    Then ##y(1) = -4## would indeed imply ##c = 7##.

    Then simply subbing ##c## into your solution from prior would be the last thing to do.
     
  4. Mar 9, 2014 #3

    gingermom

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    Gold Member

    Thanks - Yes, sorry about that I had used parenthesis but they disappeared and I didn't notice. So using the inverse to find C was the right thing to do. Yeah, maybe I am getting this after all! I was so focused on finding C I forgot about putting it back in. Should have posted that part, too I guess. First time here. Will try and do better if ( I probably should say when) I need additional help. Thanks again.
     
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