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Math Help - 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 y^2 both sides : <br />
\tfrac{{y'}}<br />
{{y^2 }} = \tfrac{1}<br />
{{x^2 }} + \tfrac{1}<br />
{x} \cdot \tfrac{1}<br />
{y}<br />

    But note that: <br />
\tfrac{{y'}}<br />
{{y^2 }} =  - \left( {\tfrac{1}<br />
{y}} \right)^\prime  <br />

    Let: <br />
\tfrac{1}<br />
{y} = z<br />
we have: <br />
 - z' = \tfrac{1}<br />
{{x^2 }} + \tfrac{1}<br />
{x} \cdot z<br />

    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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    \frac{y^{2}+xy}{x^{2}}=\bigg( \frac{y}{x} \bigg)^{2}+\frac{y}{x}.

    Then let y=xz.
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