Question and Answers Forum

All Questions      Topic List

Differentiation Questions

Previous in All Question      Next in All Question      

Previous in Differentiation      Next in Differentiation      

Question Number 198688 by tri26112004 last updated on 23/Oct/23

$$y^{″}+\frac{2}{x}.y^{\prime }+y=0$$$$y=¿$$

Answered by witcher3 last updated on 23/Oct/23

$$\mathrm{xy}=\mathrm{z}$$$${\mathrm{xy}}^{\prime }+\mathrm{y}={\mathrm{z}}^{\prime }$$$${2\mathrm{y}}^{\prime }+{\mathrm{xy}}^{″}={\mathrm{z}}^{″}$$$${\mathrm{y}}^{″}+\frac{2}{\mathrm{x}}{\mathrm{y}}^{\prime }+\mathrm{y}=0\iff {\mathrm{z}}^{″}+\mathrm{z}=0$$$$\mathrm{z}=\mathrm{acos}\left(\mathrm{x}\right)+\mathrm{bsin}\left(\mathrm{x}\right)$$$$\mathrm{y}=\frac{\mathrm{acos}\left(\mathrm{x}\right)+\mathrm{bsin}\left(\mathrm{x}\right)}{\mathrm{x}},(\mathrm{a},\mathrm{b})\in {\mathbb{R}}^2$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com