Question
Download Solution PDFtan−1x + tan−1y = c is the general solution of the differential equation
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation
Let us find the differential equation by differentiating y with respect to x
⇒ tan-1x + tan-1y = c
Differentiating with respect to x
\(\Rightarrow \frac{1}{1+x^2} + \frac{1}{1+y^2} (\frac{dy}{dx}) = 0\)
\(\Rightarrow \frac{(1+y^2)dx + (1+x^2)dy}{(1+x^2)(1+y^2)dx} = 0\)
\(\Rightarrow (1+y^2)dx + (1+x^2)dy = 0\)
Hence option 3 is correct
Last updated on Jul 3, 2025
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