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Math Help - Lagrange Equation

  1. #1
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    Lagrange Equation

    Please help me to solve this one:

    <br />
y=xy'+\sqrt{b^{2}+a^{2}(y')^{2}}<br />
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  2. #2
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    Quote Originally Posted by sinichko View Post
    Please help me to solve this one:

    <br />
y=xy'+\sqrt{b^{2}+a^{2}(y')^{2}}<br />
    If you differentiate both sides you get

     <br />
y' = y' + x y'' + \frac{a^2 y' y''}{\sqrt{b^{2}+a^{2}(y')^{2}}}<br />

    or

     <br />
\left(\frac{a^2 y'}{\sqrt{b^{2}+a^{2}(y')^{2}}} + x\right) y'' = 0<br />
.

    You now have two cases which can be solved. Remember, sub in your answer into the original ODE to make sure both (if any) are actual solutions.
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