Question Number 221498 by wewji12 last updated on 07/Jun/25
![Solve differantial Equation ((d )/dt)[((dy(t))/dt)]+ty(t)=0](https://www.tinkutara.com/question/Q221498.png)
$$\mathrm{Solve}\:\mathrm{differantial}\:\mathrm{Equation} \\ $$$$\frac{{d}\:\:}{{dt}}\left[\frac{{dy}\left({t}\right)}{{dt}}\right]+{ty}\left({t}\right)=\mathrm{0} \\ $$
Answered by MrGaster last updated on 07/Jun/25
$${y}\left({t}\right)={C}_{\mathrm{1}} \underset{{m}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{m}} {t}^{\mathrm{3}{m}} }{\mathrm{3}^{{m}} {m}!\underset{{j}=\mathrm{1}} {\overset{{m}} {\prod}}\left(\mathrm{3}{j}−\mathrm{1}\right)}+{C}_{\mathrm{2}} \underset{{m}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{m}} {t}^{\mathrm{3}{m}+\mathrm{1}} }{\mathrm{3}^{{m}} {m}!\underset{{j}=\mathrm{1}} {\overset{{m}} {\prod}}\left(\mathrm{3}{j}+\mathrm{1}\right)} \\ $$$$\underset{{j}=\mathrm{1}} {\overset{\mathrm{0}} {\prod}}\equiv\mathrm{1} \\ $$