Question
Download Solution PDFअवकल समीकरण dy = (1 + y2) dx का हल क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
\(\rm \displaystyle \int \frac{dx}{1+x^2} = \tan^{-1} x + c\)
गणना:
दिया गया है: dy = (1 + y2) dx
\(\rm \Rightarrow \frac{dy}{1+y^2}=dx\)
दोनों पक्षों का समाकलन करने पर, हमें निम्न प्राप्त होता है
\(\rm \Rightarrow \displaystyle \int \frac{dy}{1+y^2}=\displaystyle \int dx\\\rm \Rightarrow \tan^{-1} y = x + c \)
⇒ y = tan (x + c)
∴ दिए गए अवकल समीकरण का हल y = tan (x + c) है।
Last updated on May 30, 2025
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