MHT CET · Maths · Differential Equations
The solution of the differential equation \((1+x) y \mathrm{~d} x+(1-y) x \mathrm{~d} y=0\) is
- A \(\log x y-x+y=C\)
- B \(\log \left(\frac{x}{y}\right)-x+y=C\)
- C \(\log x y-x-y=C\)
- D \(\log (x y)+x-y=C\)
Answer & Solution
Correct Answer
(D) \(\log (x y)+x-y=C\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & (1+x) y \mathrm{~d} x+(1-y) x \mathrm{~d} y=0 \\ & \Rightarrow \int \frac{1+x}{x} \mathrm{~d} x=\int \frac{y-1}{y} \mathrm{~d} y \\ & \Rightarrow \log |x|+x=y-\log |y|+C \\ & \Rightarrow \log (x y)+x-y=C\end{aligned}\)
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