Question
Question: If for the differential equation ydx + y<sup>2</sup>dy = xdy, x Ī R, y > 0 and y (1) = 1, then y (–3...
If for the differential equation ydx + y2dy = xdy, x Ī R, y > 0 and y (1) = 1, then y (–3) is equal to
A
1
B
2
C
3
D
5
Answer
3
Explanation
Solution
Given equation can be written as
y2ydx–xdy = – dy Ž d(yx) = – dy
Ž yx = – y + c by x = 1, y = 1 Ž c = 2
\yx+ y = 2 Ž y (– 3) = 3