Sanjay Gupta, Dev Samaj College For Women, Ferozepur City

EXACT DIFFERENTIAL EQUATIONS CHAPTER - 1

EXERCISE 1.2

Q.1

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Sanjay Gupta, Dev Samaj College For Women, Ferozepur City

Q.2

Q.3

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Q.4

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Q.5

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Q.6

Q.7

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WORKING RULE FOR SOLVING EXACT OR NON-EXACT DIFFERENTIAL EQUATIONS OF FIRST ORDER AND FIRST DEGREE

Differential Equation

Mdx  Ndy  0 …………..(1)

IF

M N  , then equation (1) is EXACT y x

IF

M N  , then equation (1) is NOT EXACT y x

Its Solution is

 M dx   (Terms of N not containing x ) dy  c

Using Inspection Method

Using Standard Rules

y  Cons tan t

Rule-I If (1) is Homogeneous Equation, then 1 I.F.  Mx  Ny where Mx  Ny  0

Rule-II If (1) is of the form y f ( xy) dx  x g ( xy) dy  0 , 1 then I.F.  Mx  Ny where Mx  Ny  0

Rule-III

Rule-IV

M N  y x  f (x) , If N f ( x ) dx then I.F.  e 

N M  x y  g (y ) , If M g ( y ) dy then I.F.  e 

Rule-V If (1) is of the form

x a y b (my dx  nx dy)  x a y b (my dx  nx dy)  0 , then I.F.  x h y k where a  h 1 b  k  1 a  h  1 b  k  1  and  m n m n

Multiplying equation (1) by I.F. obtained in each Rule so that it will become exact differential equation and hence its solution is given by  M dx   (Terms of N not containing x ) dy  c . y  Cons tan t

Designed by : SANJAY GUPTA

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EXACT DIFFERENTIAL FORMS USED IN INSPECTION METHOD

Group of Terms

Integrating Factor (I.F)

Exact Differential Forms

Form - I

Form - II

Form - III

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