Question Number 104240 by bemath last updated on 20/Jul/20

(dy/dx) = 1+x^2 +y^2 +(xy)^2

Commented bybemath last updated on 20/Jul/20

thank you all. correct

Answered by OlafThorendsen last updated on 20/Jul/20

(dy/dx) = (1+x^2 )(1+y^2 ) (dy/(1+y^2 )) = (1+x^2 )dx arctany = C+x+(x^3 /3) y = tan(C+x+(x^3 /3))

Answered by 1549442205PVT last updated on 20/Jul/20

(dy/dx)=1+x^2 +y^2 +x^2 y^2 =(1+x^2 )(1+y^2 ) ⇔(dy/(1+y^2 ))=(1+x^2 )dx.Integrate two sides we get arctan y=x+(x^3 /3)+C_1 ⇒y=tan(x+(x^3 /3))+C Is it correct,Sir?.Please check to help me.

Answered by Dwaipayan Shikari last updated on 20/Jul/20

(dy/dx)=(1+x^2 )(1+y^2 ) ∫(dy/(1+y^2 ))=∫(1+x^2 )dx tan^(−1) y=(x+(x^3 /3)+C_1 ) y=tan(x+(x^3 /3)+C_1 )