Verify that y = (c-x)/(1+cx) is a solution of the differential equation (1+x^2)dy/dx+(1+y^2)=0.

Question

Verify that y = (c-x)/(1+cx) is a solution of the differential equation \((1+x^2)\cfrac{dy}{dx}+(1+y^2)=0.\)

(1+x²)dy/dx+(1+y²)=0.

Answer 1

Given \(y=\cfrac{c-x}{1+cx}\)

On differentiating with x, we get

\(\cfrac{dy}{dx}=\cfrac{-1-c^2}{(1+cx)^2}\)

Now let’s see what is the value of \((1+x^2)\cfrac{dy}{dx}+(1+y^2)\)