अवकल समीकरण dy = (1 + y2) dx का हल क्या है?

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  1. y = tan x + c
  2. y = tan (x + c)
  3. tan-1 (y + c) = x
  4. tan-1 (y + c) = 2x

Answer (Detailed Solution Below)

Option 2 : y = tan (x + c)
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संकल्पना:

\(\rm \displaystyle \int \frac{dx}{1+x^2} = \tan^{-1} x + c\)

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।

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