Question

Question 31
The integrating factor (1.F) of the differential equation + Px = where P and Q are functions of yis
given by
a) F= el per
b) L.F.= e-SP &
qu= elp ay
d) None of the given option
a
G
Ο Ο Ο Ο​

Answer 1

Answer:

Consider the differential equation of type

dy

dx

​  

+P(y)x=Q(y)

Then, the integrating factor for the above integral is

I.F=e  

∫P(y).dy

 

Hence multiplying the above integral by I.F

e  

∫P(y)dy

.dx+P(y)xe  

∫P(y)dy

.dy=e  

∫P(y)dy

Q(y).dy

d(xe.  

∫P(y)dy

)=e  

∫P(y)dy

Q(y).dy

∫d(xe.  

∫P(y)dy

)=∫e  

∫P(y)dy

Q(y).dy

xe.  

∫P(y)dy

=∫e  

∫P(y)dy

Q(y).dy

x.IF=∫IFQ(y).dy+C

Step-by-step explanation:

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