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Home » Mark (√) against the correct answer in the following: The solution of the is. A. B. C. D. None of these
Mark (√) against the correct answer in the following: The solution of the D E \frac{d y}{d x}=\frac{\left(1+y^{2}\right)}{\left(1+x^{2}\right)} is.
A. (y+x)=\mathrm{C}(1-y x)
B. (y-x)=\mathrm{C}(1+y x)
C. y=(1+x) \mathrm{C}
D. None of these
CBSE | Class 12 | Linear Differential Equations | Maths | RS Aggarwal
Mark (√) against the correct answer in the following: The solution of the D E \frac{d y}{d x}=\frac{\left(1+y^{2}\right)}{\left(1+x^{2}\right)} is.
A. (y+x)=\mathrm{C}(1-y x)
B. (y-x)=\mathrm{C}(1+y x)
C. y=(1+x) \mathrm{C}
D. None of these

Solution:

\frac{d y}{d x}=\frac{1+y^{2}}{1+x^{2}}
On integrating on both sides, we get
\begin{array}{l} \tan ^{-1} y=\tan ^{-1} x+c \\ \frac{y-x}{1+y x}=\mathrm{c} \\ \mathrm{y}-\mathrm{x}=\mathrm{C}(1+\mathrm{yx}) \end{array}
Therefore, \mathrm{y}-\mathrm{x}=\mathrm{C}(1+\mathrm{yx}) is the solution of \frac{d y}{d x}=\frac{1+y^{2}}{1+x^{2}}

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