If y=e4x+2e−x satisfies the relation d3ydx3+Adydx+By=0, then value | Filo
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Class 12

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Calculus

Differential Equations

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If y=e4x+2e−x satisfies the relation d3ydx3+Adydx+By=0, then values of A and B respectively are:

  1. -13, 14
  2. -13, -12
  3. -13, 12
  4. 12, -13
Correct Answer: Option(b)
Solution: [b] Given y=e4x+2e−x Differentiating we get dydx=4e4x−2e−x⇒d2ydx2=16e14x+2e−x ⇒d3ydx3=64e4x−2e−x Putting these values in d3ydx3+Adydx+By=0 We have, (64+4A+B)e4x+(−2−2A+2B)e−x=0 ⇒64+4A+B=0,−2−2A+2B=0 Solving these eqs. we get A=−13,B=−12
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