Solution of the differential equationx=1+xydydx+x2y22!(dydx)2+x3y3 | Filo
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Differential Equations

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Solution of the differential equationx=1+xydydx+x2y22!(dydx)2+x3y33!(dydx)3+............

  1. y=ln(x)+c
  2. y=(lnx)2+c
  3. y=±ln(x)+c
  4. xy=xy+c
Correct Answer: Option(c)
Solution: [c] The given equation is reduced to x=exy(dy/dx) ⇒ℓnx=xydydx⇒∫ydy=∫1xℓnxdx ⇒y22=(ℓnx)22+c ⇒y=±(ℓnx)2−−−−−√+c=±ℓnx+c
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