AP EAMCET · Maths · Differential Equations
If a curve passes through \((1,2)\) and has the slope of its tangent \(1-\frac{1}{x^2}\) at a point \((x, y)\), then the equation of that curve is
- A \(y=3 x-\frac{1}{x}\)
- B \(y=x+\frac{1}{x}\)
- C \(y=2 x+\frac{1}{x}-1\)
- D \(y=x+\frac{2}{x}-1\)
Answer & Solution
Correct Answer
(B) \(y=x+\frac{1}{x}\)
Step-by-step Solution
Detailed explanation
Given \(\frac{\mathrm{dy}}{\mathrm{dx}}=-\frac{1}{}\) \(\begin{aligned} & \Rightarrow \int \mathrm{dy}=\int\left(1-\frac{1}{\mathrm{x}^2}\right) \mathrm{dx} \\ & \Rightarrow \mathrm{y}=\mathrm{x}+\frac{1}{\mathrm{x}}+\mathrm{C} \end{aligned}\) Since y \((1)=2 \Rightarrow C=0\)…
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