Let $y = y(x)$ satisfies the equation $\frac{{dy}}{{dx}} - \left| A \right| = 0$, for all $x > 0$ where $A = \left[ {\begin{array}{*{20}{c}} y&{\sin x}&1\\ 0&{ - 1}&1\\ 2&0&{\frac{1}{x}} \end{array}} \right]$. If $y(\pi ) = \pi + 2$, then the value of $y\left( {\frac{\pi }{2}} \right)$ is

$\frac{\pi }{2} - \frac{1}{\pi }$

$\frac{{3\pi }}{2} - \frac{1}{\pi }$

JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

1 Easy

1 of 1

Application +4 | -1

Let

y = y(x)

satisfies the equation

\frac{{dy}}{{dx}} - \left| A \right| = 0

, for all

x > 0

where

A = \left[ {\begin{array}{cccccccccccccccccccc} y&{\sin x}&1\\ 0&{ - 1}&1\\ 2&0&{\frac{1}{x}} \end{array}} \right]

. If

y(\pi ) = \pi + 2

, then the value of

y\left( {\frac{\pi }{2}} \right)

View answer and explanation

Correct option: A

\frac{\pi }{2} + \frac{4}{\pi }

Option A (

\frac{\pi}{2} + \frac{4}{\pi}

) is correct because solving the differential equation and applying the given condition yields this result.