The solution of the DE (dy/dx) = (1+2/(1+x^2) is ​A. (y +x) = C (1-yx) B. (y-x) = C (1 +yx)

Question

The solution of the DE \(\frac{dy}{dx} = \frac{(1+y^2)}{(1+x^2)}\) is

A. (y +x) = C (1-yx)

B. (y-x) = C (1 +yx)

C. y = (1+x) c

D. None of these

Answer 1

Given \(\frac{dy}{dx} = \frac{(1+y^2)}{(1+x^2)}\)

On integrating on both sides, we get

y-x = C(1+yx)

Conclusion: Therefore, y-x = C(1+yx) is the solution of \(\frac{dy}{dx} = \frac{1+y^2}{1+x^2}\)