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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
`xdy-ydx=sqrt(x^(2)-y^(2))dx` is

A

`Cx=e^(sin^(-1^""(y)/(x)))`

B

`xe^(sin^(-1^""(y)/(x)=c))`

C

`x+e^(sin^(-1^""(y)/(x)=c))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
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