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Differential equations assignment T2

  1. Dec 2, 2013 #1
    Hi!

    I would like to ask anyone with some spare time to check my assignment questions. Last time I was asked to post one task at a time so I will.
    Thank you in advance for your time.

    Task 2:

    Determine the equation of the curve which satisfies the differential equation:

    2xy(dy/dx)=x2+1

    and which passes through the point (1, 2)

    Solution:

    2xy(dy/dx)=x2+1 /:2x
    y(dy/dx)=(x2+1)/(2x)
    y(dy/dx)=(1/2)[(x2+1)/x]

    ∫ y dy=(1/2)∫ x+(1/x) dx
    (1/2)y2=(1/2)(lnx+(1/2)x2)+c

    General Solution
    (1/2)y2=(1/2)lnx+(1/4)x2+c

    x=1 when y=2

    ∴(1/2)(2)2=(1/2)ln(1)+(1/4)(1)2+c
    ∴c=7/4

    Particular Solution:
    (1/2)y2=(1/2)lnx+(1/4)x2+7/4
    ∴y=√[lnx+x2/2+3.5]
     
  2. jcsd
  3. Dec 2, 2013 #2

    ShayanJ

    User Avatar
    Gold Member

    Everything seems OK!
     
  4. Dec 3, 2013 #3
    Thanks a lot!
     
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