TS EAMCET · Maths · Differential Equations
If \(\quad d x+d y=(x+y)(d x-d y), \quad\) then \(\log (x+y)\) is equal to
- A \(x+y+c\)
- B \(x+2y+c\)
- C \(x-y+c\)
- D \(2 x+y+c\)
Answer & Solution
Correct Answer
(C) \(x-y+c\)
Step-by-step Solution
Detailed explanation
Given that \(d x+d y=(x+y)(d x-d y)\) \(\Rightarrow \quad d x(x+y-1)=d y(x+y+1)\) \(\Rightarrow \quad \frac{d y}{d x}=\frac{x+y-1}{x+y+1}\) ...(i) Let \(x+y=t\) \(\Rightarrow \quad \frac{d y}{d x}=\frac{d t}{d x}-1\) \(\therefore\) From Eq. (i)…
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