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Math Help - IVP, what am I doing wrong?

  1. #1
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    Question IVP, what am I doing wrong?

    Hi, I am trying to solve a differential ivp and I can't seem to get the correct answer. The homogeneous differential equation is: 3x^2y+7y^3-3x^3y'=0, y(1)=1 Here is my work:
    Thanks for your time!
    -Matt
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  2. #2
    Super Member Random Variable's Avatar
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    It looks like you just made one silly error.

     y' = \frac{y}{x} + \frac{7}{3} \frac{y^{3}}{x^{3}}
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  3. #3
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    Ah, thank you! But I am still not getting the right answer.
    After the integration:
    -\frac{3}{14v^2}=ln|x|+c
    v^{-2}=-\frac{14}{3}ln|x|-\frac{14}{3}c
    v=\frac{1}{\sqrt{\frac{14}{3}ln|x|-\frac{14}{3}c}}
    \frac{y}{x}=\frac{1}{\sqrt{\frac{14}{3}ln|x|-\frac{14}{3}c}}
    y=\frac{x}{\sqrt{\frac{14}{3}ln|x|-\frac{14}{3}c}}
    After the substitution for y(1)=1 I get c=-\frac{3}{14}
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  4. #4
    Super Member Random Variable's Avatar
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    It looks correct to me (except you're missing a negative sign inside of the radical). What answer is given in the book?

    You can multiply the top and bottom by 3 and get the equivalent solution

     y(x) = \frac{3x}{\sqrt{9-42 \ln x}}
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  5. #5
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    Thank you! Yea, I forgot the negative... I am using webwork online so it tells me if the answer I put in is correct.
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