Question
Download Solution PDFफलन u(x, y) = c क्या है जो अवकल समीकरण x(dx - dy) + y(dy - dx) = 0 को संतुष्ट करता है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFगणना:
∫x dy में, x को स्थिर माना जाएगा
∫x dy में, x को स्थिर माना जाएगा
प्रयुक्त सूत्र:
∫xndx = xn+1/(n+1)
गणना:
यहाँ x(dx - dy) + y(dy - dx) = 0
⇒ xdx - x dy + ydy - ydx = 0
समाकलन करने पर, हमें प्राप्त होता है:
∫ xdx - ∫ x dy + ∫ ydy - ∫ ydx = 0
उपरोक्त सूत्र का उपयोग करने पर
⇒ \(\rm \frac{x^2}{2}-xy+\frac{y^2}{2}-xy+c=0\\ \)
⇒ \(\rm x^2+y^2-4xy+c=0\)
\(\Rightarrow \rm x^2+y^2 =4xy+c\)
अतः विकल्प (2) सही है।
Last updated on Jun 18, 2025
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