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Differential Equations by E. Rukmangadachari

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Charpit's method

We will now consider a general method of solving a non-linear partial differential equation of the first order due to Charpit. This method is to be applied when the given equation cannot be reduced to any of the standard forms discussed earlier.

Let the equation to be solved be denoted by

 

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Since z is a function of x and y we have

 

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Now if we can find another relation

 

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satisfied by p and q we could solve Eqs. (8.565) ...

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