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Assignment #  1MTH401 (Fall 2013)

   Total marks: 20

        Lecture # 1 to 10  

          Due date:  27/11/2013  

                                                           

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Question 1:                                                                                                          Marks 6+4

 

 

 

a)      Determine whether the given differential equations are homogeneous or non-homogeneous. Also, mention the degree of homogeneous differential equations.

  1.                                 i.           
  2.                               ii.           
  3.                             iii.           

 

 

b)      Find the integrating factor of the following differential equation.

                                       

Question 2:                                                                                                         Marks 10

 

Convert the given Bernoulli differential equation into linear form and find its solution.

                                      

 

 

 


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M(x,y)dx+(x,y)dy=0

M= -(cotx+sinx)

N = cosx 

then 

      M(-cotx-sinx)dx+(cosx)dy=0

-(cotx+sinx)

here no intigrating factor because equation is exect 

dm/dy= dn/dx both are equal to -sinx

IF find krna hai. equ. nt exact

see my posts abov

i agree with waqar bhei

Momal write equ as foloows and aftr that find IF:Now

so equ. nt exact. now find IF

How can you write this equation is exact first solution is sinx and 2nd is -sinx .HOw can you say it is exact

yes yes, equ. extct he hai. i checked it again. '-' miss ho gya tha mere se. so exct equ. ka IF nikalna he ni hota hain. it's already exct equ.

you are doing wrong bro yah exact a raha hay cosx nahe ahy -cosx ata hay jab hum equation ko solve karty hay otherwise phr cotx -ve may ata hay agar ap cosx ko +ve karty hay what you say ?

i shared how to write equ. and then equ. nt exact. aftr tht find IF

o bhai is ma DMA rule kidr aa gya???? first we have to convert given equ. into standard form that is M(x,y)dx-cosxdy=0. aftr this proceed to prove that it is nt exact. ye prov krna zrori nhi k equ exct nhi hai. because teachr jst said IF malom kre, tu IF usi equ. ka malom kiya jata hai jo exct nhi hoti. so zrori nhi k ye prov kiya jae k equ exct nhi hai. standrd form ma likhne k bd direct IF bi malom kiya ja skta hai. hope u undrstnd

ye b zrori ni hai k q exact ho or os ka if b zrori ni

anmol in Q1(b), the equ. wil be writen as:Nowthe equ. nt exact. now find IF

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