A curve passing through (2, 3) and satisfying the differential equ | Filo
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Class 12

Math

Calculus

Differential Equations

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A curve passing through (2, 3) and satisfying the differential equation ∫x0ty(t)dt=x2y(x),(x>0) is

  1. x2+y2=13
  2. y2=92x
  3. x28+y218=1
  4. xy=c
Correct Answer: Option(d)
Solution: [d] Differentiate xy(x)=x2y′(x)+2xy(x) or xy(x)+x2y′(x)=0   or xdydx+y=0 or lny+lnx=lnc          or xy=c
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