JEE Mains · Maths · STD 12 - 9. differential equations
If \(y =\left(\frac{2}{\pi} x -1\right) \operatorname{cosec} x\) is the solution of the differential equation, \(\frac{d y}{d x}+p(x) y=\frac{2}{\pi} \operatorname{cosec} x, 0 < x < \frac{\pi}{2},\) then the function \(p ( x )\) is equal to
- A \(\cot x\)
- B \(\tan x\)
- C \(\operatorname{cosec} x\)
- D \(\sec x\)
Answer & Solution
Correct Answer
(A) \(\cot x\)
Step-by-step Solution
Detailed explanation
\(y=\left(\frac{2 x}{\pi}-1\right) \operatorname{cosec} x\) \(\frac{ dy }{ dx }=\frac{2}{\pi} \operatorname{cosec} x -\left(\frac{2 x }{\pi}-1\right) \operatorname{cosec} x \cot x\) \(\frac{d y}{d x}=\frac{2 \operatorname{cosec} x}{\pi}-y \cot x\) using equation (1)…
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