Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 201582 by MathedUp last updated on 09/Dec/23

Solve....  y′′(t)−sin(t)y(t)=0 ,   y^((2)) (0)=0 , y^((1)) (0)=−1 , y(0)=0                      L{y′′(t)−sin(t)y(t)}=0  s^2 F(s)−sy(0)−y′(0)−L{sin(t)y(t)}=0  Holy...×uck  I already know y′′(t)−ty(t)=0   solution  C_1 Ai(t)+C_2 Bi(t)  But I Can′t Solve y′′(t)−sin(t)y(t)=0....

$$\mathrm{Solve}.... \\ $$$${y}''\left({t}\right)−\mathrm{sin}\left({t}\right){y}\left({t}\right)=\mathrm{0}\:,\: \\ $$$${y}^{\left(\mathrm{2}\right)} \left(\mathrm{0}\right)=\mathrm{0}\:,\:{y}^{\left(\mathrm{1}\right)} \left(\mathrm{0}\right)=−\mathrm{1}\:,\:{y}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\boldsymbol{\mathcal{L}}\left\{{y}''\left({t}\right)−\mathrm{sin}\left({t}\right){y}\left({t}\right)\right\}=\mathrm{0} \\ $$$${s}^{\mathrm{2}} \boldsymbol{\mathrm{F}}\left({s}\right)−{sy}\left(\mathrm{0}\right)−{y}'\left(\mathrm{0}\right)−\boldsymbol{\mathcal{L}}\left\{\mathrm{sin}\left({t}\right){y}\left({t}\right)\right\}=\mathrm{0} \\ $$$$\mathrm{Holy}...×\mathrm{uck} \\ $$$$\mathrm{I}\:\mathrm{already}\:\mathrm{know}\:{y}''\left({t}\right)−{ty}\left({t}\right)=\mathrm{0}\:\:\:\mathrm{solution} \\ $$$$\mathrm{C}_{\mathrm{1}} \mathrm{Ai}\left({t}\right)+{C}_{\mathrm{2}} \mathrm{Bi}\left({t}\right) \\ $$$$\mathrm{But}\:\mathrm{I}\:\mathrm{Can}'\mathrm{t}\:\mathrm{Solve}\:{y}''\left({t}\right)−\mathrm{sin}\left({t}\right){y}\left({t}\right)=\mathrm{0}....\: \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com