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Question

If curve satisfying x(x+1)y1y=x(x+1) passes through (1,0), then the value of 54y(4)log4 is

A
3
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B
2
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C
1
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D
0
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Solution

The correct option is A 3
x(x+1)dydxy=x(x+1)dydxyx2+x=1 ...(1)
Let u=edxx2+x=1x+1
Multiplying both sides of (1) by u, we get
(1x+1)dydx(1x+1)yx2+x=(1x+1)(1x+1)dydx+ddx(1x+1)y=(1x+1)
Using gdfdx+fdgdx=d(fg)dx
ddx((1x+1)y)=(1x+1)
Integrating both sides
ddx((1x+1)y)dx=(1x+1)dx(1x+1)y=x+logx+c
As it passes through (1,0), we get c=1
Now for x=4
(14+1)y(4)=4+log4154y(4)log4=3

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