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Question Number 82476 by abdomathmax last updated on 21/Feb/20

$$solve{xy}^{{}^{″}}+2y^{{}^{\prime }}+xy=0withinitialconditions$$$$y\left(o\right)=1and{y}^{{}^{\prime }}\left(1\right)=0$$

Answered by mind is power last updated on 21/Feb/20

$$z=xy$$$$\Rightarrow z^{\prime }=y+{xy}^{\prime }$$$$z^{″}=2y^{\prime }+{xy}^{″}$$$${xy}^{″}+2y^{\prime }+xy=0$$$$\Rightarrow z^{″}+z=0$$

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