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If any differentisl equation in the form...

If any differentisl 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 intergrated separately.
For example,
`intsinxyd(xy)+int((x)/(y))d((x)/(y))=-cos xy+(1)/(2)((x)/(y))^(2)+C`
The solution of the differential equation
`(xy^(4)+y)dx-xdy=0` is

A

`(x^(3))/(4)+(1)/(2)((x)/(y))^(2)=C`

B

`(x^(4))/(4)+(1)/(3)((x)/(y))^(3)=C`

C

`(x^(4))/(4)-(1)/(2)((x)/(y))^(3)=C`

D

`(x^(4))/(4)-(1)/(2)((x)/(y))^(2)=C`

Text Solution

Verified by Experts

The correct Answer is:
B
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