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Q.

A curve passes through (2,3) and satisfying the D.E ∫0x ty⁡(t)dt=x2y(x),x>0 is

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a

x2+y2=13

b

y2=92x

c

x28+y218=1

d

xy=C

answer is D.

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Detailed Solution

∫0x ty(t)dt=x2y(x) Differentiating w.r.t. x, we getxy(x)+x2y1(x)=0→xdydx+y=0⇒log⁡x+log⁡y=log⁡C⇒xy=C
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A curve passes through (2,3) and satisfying the D.E ∫0x ty⁡(t)dt=x2y(x),x>0 is