A curve y = f(x) is passing through (0, 0). If the slope of the curve at any point (x, y) is equal to (x + xy), then the number of solution of the equation f(x)=1, is:
A curve y = f(x) is passing through (0, 0). If the slope of the curve at any point (x, y) is equal to (x + xy), then the number of solution of the equation f(x)=1, is:
Option 1 -
0
Option 2 -
1
Option 3 -
2
Option 4 -
4
Asked by Shiksha User
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1 Answer
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Correct Option - 3
Detailed Solution:f' (x) = x (1+y)
dy/ (y+1) = xdx
ln (y+1) = x²/2 + c
(0,0)
c = 0
y+1 = e^ (x²/2) ⇒ e^ (x²/2) = 2
x²/2 = k = (ln2 > 0)
x = ±√2k
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