(1+y^2).y''=2y(y')^2
y''/(1+y^2)- 2y(y')^2/(1+y^2)^2 =0
[y''.(1+y^2)-2y(y')^2]/(1+y^2)^2 =0
d/dx [ y'/(1+y^2)] =0
y'/(1+y^2) = C1
y' =C1.(1+y^2)
∫dy/(1+y^2) =∫ C1.dx
arctany = C1.x +C2
y= tan(C1x+C2)
y''/(1+y^2)- 2y(y')^2/(1+y^2)^2 =0
[y''.(1+y^2)-2y(y')^2]/(1+y^2)^2 =0
d/dx [ y'/(1+y^2)] =0
y'/(1+y^2) = C1
y' =C1.(1+y^2)
∫dy/(1+y^2) =∫ C1.dx
arctany = C1.x +C2
y= tan(C1x+C2)
