1
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Question

# What is B equal to ?

A
-1
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B
1
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C
2
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D
None of the above
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Solution

## The correct option is A -1(x2+x+1)dy+(y2+y+1)dx=0⇒dy(y2+y+1)=−dx(x2+x+1)⇒∫dy(y2+y+1)=−∫dx(x2+x+1)⇒∫dy(y+12)2+(√32)2=−∫dx(x+12)2+(√32)2⇒2√3tan−1⎛⎜ ⎜ ⎜ ⎜⎝y+12√32⎞⎟ ⎟ ⎟ ⎟⎠+2√3tan−1⎛⎜ ⎜ ⎜ ⎜⎝x+12√32⎞⎟ ⎟ ⎟ ⎟⎠=cFor ease of solving let c=2√3tan−1c where c is a constant⇒tan−1⎛⎜ ⎜ ⎜ ⎜⎝y+12√32⎞⎟ ⎟ ⎟ ⎟⎠+tan−1⎛⎜ ⎜ ⎜ ⎜⎝x+12√32⎞⎟ ⎟ ⎟ ⎟⎠=tan−1c We know thattan−1x+tan−1y=tan−1x+y1+xyOn solving for c, we getc=2√3(x+y+1)−4xy−2y−2x+2(x+y+1)=c√3(1−x−y−2xy)Given general solution of the equation(x+y+1)=A(1+Bx+Cy+Dxy)Comparing, we getB=−1

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