Question

The solution of the differential equation `dy/dx = ((1 + x)y)/((y - 1)x)` is ______ 

पर्याय

• log xy + x + y = c

• `log(x/y) + x - y = c`

• log xy + x - y = c

• None of these

Answer 1

The solution of the differential equation `dy/dx = ((1 + x)y)/((y - 1)x)` is log xy + x - y = c.

Explanation:

 `dy/dx = ((1 + x)y)/((y - 1)x)`

⇒ `(y - 1)/y dy = ((1 + x))/x dx`

⇒ `(1 - 1/y)dy = (1 + 1/x)dx`

Integrating on both sides, we get

x + log x = y - log y + c

⇒ x - y + log xy = c