Solution of differential equation x2=1+(xy)−1dydx+(xy)−2(dydx)22!+ | Filo
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Calculus

Differential Equations

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Solution of differential equation x2=1+(xy)−1dydx+(xy)−2(dydx)22!+(xy)−3(dydx)33!+......... is

  1. y2=x2(lnx2−1)+C
  2. y=x2(lnx−1)+C
  3. y2=x(lnx−1)+C
  4. y=x2ex2+C
Correct Answer: Option(a)
Solution: [a] x2=e(xy)−1(dydx)⇒x2=e(yx)(dydx) ⇒ ln x2=yxdydx or ∫xlnx2dx=∫ydy Put x2=t⇒2xdx=dt∴12∫lntdt=y22 C+tlnort−t=y2ory2=x2(lnx2−1)+C
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