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JEE Mains · Maths · STD 12 - 9. differential equations
If a curve passes through the point \(\left( {2\,,\,\frac{7}{2}} \right)\) and has slope \(\left( {1 - \frac{1}{{{x^2}}}} \right)\) at anypoint \((x, y)\) on it, then the ordinate of the point on the curve whose abscissa is \(- 2\) is
- A \(-\frac{3}{2}\)
- B \(\frac{3}{2}\)
- C \(\frac{5}{2}\)
- D \(-\frac{5}{2}\)
Answer & Solution
Correct Answer
(A) \(-\frac{3}{2}\)
Step-by-step Solution
Detailed explanation
Slope \(=\frac{d y}{d x}=1-\frac{1}{x^{2}}\) \(\Rightarrow \int d y=\int\left(1-\frac{1}{x^{2}}\right) d x\) \(\Rightarrow y=x+\frac{1}{x}+\mathrm{C},\) which is the equation of the curve since curve passes through the point \(\left(2, \frac{7}{2}\right)\)…
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