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Question Number 82579 by M±th+et£s last updated on 22/Feb/20

$$ify=cos\left(ln\left(x\right)\right)+sin\left(ln\left(x\right)\right)$$$$showthat$$$$y^{″}+y^{{}^{\prime }}+y=0$$

Answered by mind is power last updated on 23/Feb/20

$$y^{\prime }=\frac{1}{x}(-sin\left(ln\left(x\right)\right)+cos\left(ln\left(x\right)\right)$$$$y^{″}=\frac{1}{x^2}(-2cos\left(ln\left(x\right)\right)$$$$x^2{y}^{″}+{xy}^{\prime }+y=0$$$$$$$$$$

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