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Thread: differential equations

  1. #1
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    differential equations

    Solve the following differential equations.

    y' = ((y^2)+xy)/(x^2)

    Whats the method of solving this? What theorem am i using?
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  2. #2
    Super Member PaulRS's Avatar
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    First divide by $\displaystyle y^2$ both sides : $\displaystyle
    \tfrac{{y'}}
    {{y^2 }} = \tfrac{1}
    {{x^2 }} + \tfrac{1}
    {x} \cdot \tfrac{1}
    {y}
    $

    But note that: $\displaystyle
    \tfrac{{y'}}
    {{y^2 }} = - \left( {\tfrac{1}
    {y}} \right)^\prime
    $

    Let: $\displaystyle
    \tfrac{1}
    {y} = z
    $ we have: $\displaystyle
    - z' = \tfrac{1}
    {{x^2 }} + \tfrac{1}
    {x} \cdot z
    $

    You can solve this last one by the integrating factor method
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  3. #3
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    Why do you divide by Y^2?
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  4. #4
    Math Engineering Student
    Krizalid's Avatar
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    Santiago, Chile
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    $\displaystyle \frac{y^{2}+xy}{x^{2}}=\bigg( \frac{y}{x} \bigg)^{2}+\frac{y}{x}.$

    Then let $\displaystyle y=xz.$
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