Lagrange's Method : Partial Differential Equations - Lecture 04

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In this video, we solve some more first-order partial differential equations using Lagrange's method.
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Sir, a small clarification...
In the last problem while finding the second fn., We added the numerators ydx and xdy ..
But we didn't add the denominators 1 + 1 = 2 ..
Then mustn't we get that 2 which is then cancelled while integrating z ?
Then second fn. Is xy - z^2 ..
Isn't it correct sir ..

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