Question

Solution of the differential equation `dy/dx = (xy^2 + x)/(x^2y + y)` is ______.

पर्याय

• `(1 + y^2)/(1 + x^2)` = c

• (1 + y²)(1 + x²) = c

• x(1 + x²) + y = c

• y(1 + x²) = c

Answer 1

Solution of the differential equation `dy/dx = (xy^2 + x)/(x^2y + y)` is `underlinebb((1 + y^2)/(1 + x^2) = c)`.

Explanation:

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

∴ `y/(1 + y^2)dy = x/(1 + x^2)dx`

∴ `int(2y)/(1 + y^2)dy = int (2x)/(1 + x^2)dx`

∴ log(1 + y²) – log(1 + x²) = log c

∴ `log((1 + y^2)/(1 + x^2))` = log c

∴ `(1 + y^2)/(1 + x^2)` = c