Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

Solution of diffrential equation $dy/dx= \frac{1-y}{\cos ^2x}$ is

Option 1)
$e^{\tan x}( y+1 )= C$

Option 2)
$e^{ x}( y-1 )= C$

Option 3)
$e^{\tan x}( y-1 )= C$

Option 4)
$e^{\sin x}( y-1 )= C$

Answers (1)

best_answer

As we have learned

Linear Differential Equation -

Multiply by $e^{SPdx}$ which is the Integrating factor

- wherein

P is the function of x alone

$\frac{dy}{dx} = \frac{1-y}{\cos ^2 x } \Rightarrow dy/dx = \sec ^2x (1-y)$

$\Rightarrow \frac{dy}{dx} + (\sec^2x) y = \sec^2 x$

on comparing it with $\frac{dy}{dx} + Py =Q , we get$

$P =\sec ^2 x ..and ..Q= sec ^2 x$

, so integrating factor will be $e^{\int \sec^2xdx} = e^{\tan x }$

multiplying on both sides , we get $\rightarrow$

$e^{\tan x} dy/dx + y e^{\tan x} \sec^2x = e^{\tan x} \sec ^2x$

$\Rightarrow d/dx (e^{\tan x } y) = e^{\tan x} \sec ^2 x$

$\Rightarrow d(e^{\tan x}y)- e^{\tan x} \sec^2x dx = 0$

$\Rightarrow \int d(e^{\tan x}y)- \int e^{\tan x} \sec^2x dx = c$

$\Rightarrow e^{\tan x} y - e^{\tan x}= C$

$\Rightarrow e^{\tan x} (y -1)= C$

Option 1)

$e^{\tan x}( y+1 )= C$

Option 2)

$e^{ x}( y-1 )= C$

Option 3)

$e^{\tan x}( y-1 )= C$

Option 4)

$e^{\sin x}( y-1 )= C$

Posted by

gaurav

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2026 application correction begins on jeemain.nta.nic.in; edit details by December 2

anam-khan

JEE Mains 2026 LIVE: NTA to conduct session 1 from January 21 to 30; exam pattern, syllabus

anam-khan

JEE Main 2026 correction window opens tomorrow; NTA allows exam city change

Latest Question