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Q.

Consider the family of curves Ax2+By2=1  . If this family of curves is represented by the differential equation Py"+Qy'2=yy', where P and Q are functions of x and y, here  y'=dydx  and  y"=d2ydx2  then which of the following statement(s) is/are true ?

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a

P=xy

b

Q=xy

c

P+Q=xy+1

d

P−Q=yx−1

answer is A.

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Detailed Solution

Ax2+By2=1⇒A=1−By2x2Differentiate both sides 0=x2−2Byy'−1−By2⋅2x1−By2=−Byxy'⇒B=1y2−yxy'1B=y2−yxy'⇒2yy'−yxy"−yy'−xy'2=0xy'2−yy'+yxy"=0xyy"+xy'2=yy'P=xy,Q=x
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