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Grade: 12th pass
        
Xy^2(1+x^2) dy+(1+y^2) x=0
Find its differential equation by variable separation method. 
3 months ago

Answers : (1)

Arun
22825 Points
							

=tan[C- arctan(x)]

The original equation is separable, so you should get:

Integral of [(1/(1 + y^2))dy] = Integral of [(1/(1 + x^2))dx]

which integrates to give:

arctan(y) = - arctan(x) + C

[where arctan(x) = tan^-1(x)]

Thus, on taking the tangent of both sides, we have

=tan[C- arctan(x)]

3 months ago
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