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Math Help - Solve

  1. #1
    Super Member dhiab's Avatar
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    Solve

    Solve this diferntiel equation :
     {y}'=y+y^{3}

    x{{y}'=y+\sqrt{x^{2}+y^{2}}}
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  2. #2
    Flow Master
    mr fantastic's Avatar
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    Quote Originally Posted by dhiab View Post
    Solve this diferntiel equation :
     {y}'=y+y^{3}

    x{{y}'=y+\sqrt{x^{2}+y^{2}}}
    1) \frac{dy}{dx} = y + y^3 \Rightarrow \int \frac{dy}{y + y^3} = \int \, dx. Do the left hand integral by using partial fractions.

    2) The DE re-arranges into \frac{dy}{dx} = \frac{y}{x} + \sqrt{1 + \left( \frac{y}{x}\right)^2} and the standard technique is to make the substitution y = xv.

    If you need more help, please post all your work and say where you are stuck.
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