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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

ydxxdyy2\frac{ydx–xdy}{y^{2}} = – dy Ž d(xy)\left( \frac{x}{y} \right) = – dy

Ž xy\frac{x}{y} = – y + c by x = 1, y = 1 Ž c = 2

\xy\frac{x}{y}+ y = 2 Ž y (– 3) = 3