If y=(x+1+x2−−−−−√)n, then (1+x2)d2ydx2+xdydx is | Filo
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Differential Equations

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If y=(x+1+x2−−−−−√)n, then (1+x2)d2ydx2+xdydx is

  1. n2y
  2. −n2y
  3. −y
  4. 2x2y
Correct Answer: Option(a)
Solution: [a] y=(x+1+x2−−−−−√)n dydx=n(x+1+x2−−−−−√)n−1(1+12(1+x2)−1/2.2x); dydx=n(x+1+x2−−−−−√)n−1(1+x2−−−−−√+x)1+x2−−−−−√=n(1+x2−−−−−√+x)n1+x2−−−−−√ or 1+x2−−−−−√dydx=ny or 1+x2−−−−−√y1=ny(y1=dydx) Squaring, (1+x2)y12.n2y2 Differentiating, (1+x2)2y1y2+y12.2x=n2.2yy1 (Here,y2=d2ydx2) or (1+x2)y2+xy1=n2y
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