If y=2/(π)x-1cosecx is the solution of the differential equation, dy/dx+pxy=-2/(π)cosecx, 0<x<(π)/2, then the function px is equal to :

Correct answer: (A) cotx. y=2/(π)x-1cosec x ⇒dy/dx=2/(π)cosec x-2x/(π)-1cosecx cotx cot⁡x ⇒dy/dx+2x/(π)-1cosecx cotx=2/(π)cosecx ⇒dy/dx+ycotx=2/(π)cosecx ⇒px=cotx

Q32 / 75 · JEE Main 2020 (06 Sep Shift 2) · Mathematics

If $y = (\frac{2}{π} x - 1) cosec x$ is the solution of the differential equation, $\frac{d y}{d x} + p (x) y = - \frac{2}{π} cosec x, 0 < x < \frac{π}{2}$ , then the function $p (x)$ is equal to :

Correct answer
A
$\cot x$
B
$cosec x$
C
$\sec x$
D
$\tan x$

Solution

$y = (\frac{2}{π} x - 1) cosec x$

$\Rightarrow \frac{d y}{d x} = \frac{2}{π} cosec x - (\frac{2 x}{π} - 1) cosec x \cot x$ $\cot x$

$\Rightarrow \frac{d y}{d x} + (\frac{2 x}{π} - 1) cosec x \cot x = \frac{2}{π} cosec x$

$\Rightarrow \frac{d y}{d x} + y \cot x = \frac{2}{π} cosec x$

$\Rightarrow p (x) = \cot x$

Hence, the correct answer is option: 'A'.

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If y=2πx-1cosecx is the solution of the differential equation, dydx+pxy=-2πcosecx, 0<x<π2, then the function px is equal to :

Solution

Relevant Questions

If $y = (\frac{2}{π} x - 1) cosec x$ is the solution of the differential equation, $\frac{d y}{d x} + p (x) y = - \frac{2}{π} cosec x, 0 < x < \frac{π}{2}$ , then the function $p (x)$ is equal to :