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