The general solution of the differential equation d2ydx2=cosnx is | Filo
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Class 12

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Calculus

Differential Equations

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The general solution of the differential equation d2ydx2=cosnx is

  1. n2y+cosnx=n2(Cx+D)
  2. n2y−sinnx=n2(−Cx+D)
  3. n2y+cosnx=Cx+Dn2
  4. None of these. [Where C and D are arbitrary constants]
Correct Answer: Option(a)
Solution: [a] The differential equation is d2ydx2=cosnx Integrating we get dydx=sinnxn+C                              ? (i) Integrating again y=−cosnxn2+Cx+D ⇒n2y+cosnx=n2(Cx+D)
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