JEE Mains · Maths · STD 12 - 9. differential equations
If the solution curve, of the differential equation \(\frac{d y}{d x}=\frac{x+y-2}{x-y}\) passing through the point \((2,1)\) is \(\tan ^{-1}\left(\frac{y-1}{x-1}\right)-\frac{1}{\beta} \log _e\left(\alpha+\left(\frac{y-1}{x-1}\right)^2\right)=\log _e|x-1|\), then \(5 \beta+\alpha\) is equal to
- A \(12\)
- B \(11\)
- C \(14\)
- D \(0\)
Answer & Solution
Correct Answer
(B) \(11\)
Step-by-step Solution
Detailed explanation
\( \frac{d y}{d x}=\frac{x+y-2}{x-y} \) \( \mathrm{x}=\mathrm{X}+\mathrm{h}, \mathrm{y}=\mathrm{Y}+\mathrm{k} \) \(4 \frac{d Y}{d X}=\frac{X+Y}{X-Y} \) \(\mathrm{h}+\mathrm{k}-2=0 \) \(\mathrm{~h}-\mathrm{k}=0\) \( \mathrm{Y}=\mathrm{vX} \)…
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