Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If the solution of the differential equation  \(<img alt="\frac{dy}{dx}=\frac{1}{x, \cos y+\sin 2y}\;\; is\;\; x=ce^{\sin y}-k(

If the solution of the differential equation  \(\frac{dy}{dx}=\frac{1}{x, \cos y+\sin 2y}\;\; is\;\; x=ce^{\sin y}-k(1+\sin y)), then k =

Option: 1 1

Option: 2 2

Option: 3 3

Option: 4 4

Answers (1)

best_answer

 

Linear Differential Equation -

 

\frac{dy}{dx}+Py= Q

yhh- wherein

P, Q are functions of x alone.

 

 

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}{x\cos y+2\sin y \cos y}

\therefore \frac{dx}{dy}=x\cos y+2\sin y \cos y

\Rightarrow \frac{dx}{dy}+(-\cos y )x =2\sin y \cos y

\therefore I.F.=e^{-\int \cos y dy}=e^{-\sin y}

\therefore The\:\:solution\:\:is

x.e^{-\sin y}=2\int e^{-\sin y}. \sin y \cos y \:\:dy

\Rightarrow x.e^{-\sin y}= -2 \sin y\: e ^{-\sin y}-2 \int (-e^{-\sin y }) \cos y \:\:dy

\Rightarrow x.e^{-\sin y}= -2 \sin y\: e ^{-\sin y}+2 \int (e^{-\sin y }) \cos y \:\:dy

                        =-2 \sin y\:\: e ^{- \sin y}-2\: e ^{-\sin y }+c

\Rightarrow x=-2 \sin y -2 + c\:\: e ^{\sin y}=c\:\:e^{\sin y}-2(1+\sin y)

\therefore k=2

 

 

Posted by

Shailly goel

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

BTech Admission 2025 Live: JEE Main correction window closes at 11:50 pm; VITEEE, SRMJEE, AEEE dates out
anam-khan

JEE Main 2025 application form correction begins at jeemain.nta.nic.in; editable fields
anam-khan

JEE Main 2025 application form correction window opens today; apply at jeemain.nta.nic.in

Latest Question