Menu Close

solve-xy-2y-xy-0-with-initial-conditions-y-o-1-and-y-1-0-




Question Number 82476 by abdomathmax last updated on 21/Feb/20
solve  xy^(′′)  +2y^′  +xy=0 with initial conditions  y(o)=1 and y^′ (1)=0
$${solve}\:\:{xy}^{''} \:+\mathrm{2}{y}^{'} \:+{xy}=\mathrm{0}\:{with}\:{initial}\:{conditions} \\ $$$${y}\left({o}\right)=\mathrm{1}\:{and}\:{y}^{'} \left(\mathrm{1}\right)=\mathrm{0} \\ $$
Answered by mind is power last updated on 21/Feb/20
z=xy  ⇒z′=y+xy′  z′′=2y′+xy′′  xy′′+2y′+xy=0  ⇒z′′+z=0
$${z}={xy} \\ $$$$\Rightarrow{z}'={y}+{xy}' \\ $$$${z}''=\mathrm{2}{y}'+{xy}'' \\ $$$${xy}''+\mathrm{2}{y}'+{xy}=\mathrm{0} \\ $$$$\Rightarrow{z}''+{z}=\mathrm{0} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *