Question

-1/x + y
x + y
tan
3.
xy <1=
1 - xy​

Answer 1

Answer:

Step-by-step explanation:

The given differential equation can be written as  

dy

dx

​  

=xy(x  

2

siny  

2

+1)⇒  

x  

3

 

1

​  

 

dy

dx

​  

−  

x  

2

 

1

​  

y=ysiny  

2

 

This equation is reducible to linear equation.

So putting v=−  

x  

2

 

1

​  

 

∴  

dy

dv

​  

+2vy=2ysiny  

2

 

The integrating factor of this equation is e  

y  

2

 

 

So the required equation is  

ve  

y  

2

 

=∫2ysiny  

2

e  

y  

2

 

dy+c=−  

2

1

​  

e  

y  

2

 

(siny  

2

−cosy  

2

)+c

⇒2v=(siny  

2

−cosy  

2

)+e  

−y  

2

 

 

⇒2=x  

2

(cosy  

2

−siny  

2

−2ce  

−y  

2

 

)

hope it helps u

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