Question

x + y = tan^–1y is a solution of the differential equation `y^2 "dy"/"dx" + y^2 + 1` = 0.

Options

• True

• False

Answer 1

This statement is True.

Explanation:

x + y = tan^–1y

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

⇒ `"dy"/"dx"(1/(1 + y^2) - 1)` = 1

i.e., `"dy"/"dx" = (-(1 + y^2))/y^2`

Which satisfies the given equation.