Q106 / 160 · TS EAMCET 2024 (09 May Shift 1) · Mathematics

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

  • Correct answer
    A
    $\left(b^2-a^2\right) \sin a x$
  • B
    $\left(b^2-a^2\right) \cos b x$
  • C
    $\left(a^2-b^2\right) \tan a x$
  • D
    $\left(b^2-a^2\right) \cot b x$

Solution

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

Hence, the correct answer is option: 'A'.

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