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GATE 2014 EE (EE1) – Question 13

Engineering Mathematics · Differential Equations: Initial and boundary value problems · 1 mark · Multiple choice

Solve $d^2x/dt^2=-9x$, with x(0) = 1 and x′(0) = 1.

  1. $t^2+t+1$
  2. $\sin3t+\frac13\cos3t+\frac23$
  3. $\frac13\sin3t+\cos3t$
  4. $\cos3t+t$

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Correct answer: (C) $\frac13\sin3t+\cos3t$

Explanation

The general solution is x=Acos3t+Bsin3t. From x(0)=1, A=1. Differentiating gives x′(0)=3B=1, so B=1/3. Thus **x(t)=cos3t+(1/3)sin3t,C**, satisfying both the equation and initial conditions.