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GATE 2026 AG – Question 13

Engineering Mathematics · Differential Equations · 1 mark · Multiple choice

Find the general solution of $d^2y/dx^2=\cos 2x$.

  1. $y=-\cos(2x)/4+C_1x+C_2$
  2. $y=\sin(2x)/2+C_1$
  3. $y=\cos(2x)/4+C_1x+C_2$
  4. $y=-\sin(2x)/2+C_1$

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Correct answer: (A) $y=-\cos(2x)/4+C_1x+C_2$

Explanation

Integrate once:$y^{\prime}=\sin(2x)/2+C_1$. Integrate again:$y=-\cos(2x)/4+C_1x+C_2$. Two independent constants are needed because the equation is second order. Differentiating this expression twice recovers $\cos 2x$,so **A**.

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