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TS EAMCET · Maths · Differential Equations

If \(y=\sin a x+\cos b x\) then \(y^{\prime \prime}+b^2 y=\)

  1. A \(\left(b^2-a^2\right) \sin a x\)
  2. B \(\left(b^2-a^2\right) \cos b x\)
  3. C \(\left(a^2-b^2\right) \tan a x\)
  4. D \(\left(b^2-a^2\right) \cot b x\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\left(b^2-a^2\right) \sin a x\)

Step-by-step Solution

Detailed explanation

\(y=\sin a x+\cos b x\) \(\begin{aligned} & y^{\prime}=a \cos a x-b \sin b x \\ & y^{\prime \prime}=-a^2 \sin a x-b^2 \cos b x \\ & y^{\prime \prime}+b^2 y=-a^2 \sin a x-b^2 \cos b x+b^2 \sin a x+b^2 \cos b x \\ & =\left(b^2-a^2\right) \sin a x .\end{aligned}\)