QJEEM19Ma07dc: JEE Main 2019 Mathematics - Class 12 JEEM19Ma07dc Solution: If     and  …

Question

Verified Solution • 2025–26 Session moderate

If

{{dy} \over {dx}} + {3 \over {{{\cos }^2}x}}y = {1 \over {{{\cos }^2}x}},\,\,x \in \left( {{{ - \pi } \over 3},{\pi \over 3}} \right)

and

y\left( {{\pi \over 4}} \right) = {4 \over 3},

then

y\left( { - {\pi \over 4}} \right)

equals -

Accepted Answer

{{dy} \over {dx}} + 3{\sec ^2}x.y = {\sec ^2}x

I.F. =

{e^{3\int {{{\sec }^2}xdx} }} = {e^{3\tan x}}

or

y.e{}^{3\tan x} = \int {{{\sec }^2}x.{e^{3\tan x}}}

or

y.{e^{3\tan x}} = {1 \over 3}{e^{3\tan x}} + C

Given

y\left( {{\pi \over 4}} \right) = {4 \over 3}

\therefore

{4 \over 3}.{e^3} = {1 \over 3}{e^3} + C

\therefore

C = e³

QJEEM19Ma07dc: JEE Main 2019 Mathematics - Class 12 JEEM19Ma07dc Solution: If &nbsp; &nbsp;&nbsp;and&nbsp;&nbsp;…