f any differential equation in the form ...

f any differential equation in the form
`f(f_(1)(x,y)d(f_(1)(x,y)+phi(f_(2)(x,y)d(f_(2)(x,y))+....=0`
then each term can be integrated separately.
For example,
`intsinxyd(xy)+int((x)/(y))d((x)/(y))=-cos xy+(1)/(2)((x)/(y))^(2)+C`
Solution of differential equation
`(2xcosy+y^(2)cosx)dx+(2ysinx-x^(2)siny)dy=0` is

A

A) `x^(2)cosy+y^(2)sinx=C`

B

B) `xcosy+ysinx=C`

C

C) `x^(2)cos^(2)y+y^(2)sin^(2)x=C`

D

D) None of the above

Verified by Experts

The correct Answer is:

A

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