JEE Mains · Maths · STD 12 - 9. differential equations
Let \(y = y(x)\) be the solution of the differential equation \((x^2 - x\sqrt{x^2 - 1})dy + (y(x - \sqrt{x^2 - 1}) - x)dx = 0\), \(x \geq 1\). If \(y(1) = 1\), then the greatest integer less than \(y(\sqrt{5})\) is _______.
- A 3
- B 4
- C 5
- D 6
Answer & Solution
Correct Answer
(A) 3
Step-by-step Solution
Detailed explanation
The given differential equation is: \((x^2 - x\sqrt{x^2 - 1})dy + (y(x - \sqrt{x^2 - 1}) - x)dx = 0\) Dividing the entire equation by \(dx\) and rearranging, we get: \(x(x - \sqrt{x^2 - 1}) \dfrac{dy}{dx} + y(x - \sqrt{x^2 - 1}) = x\) Dividing by \(x(x - \sqrt{x^2 - 1})\), we…
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