Question Number 205833 by MathedUp last updated on 31/Mar/24
$$\mathrm{can}'\mathrm{t}\:\mathrm{Solve}\:\mathrm{Differantial}\:\mathrm{Equation} \\ $$$$\mathrm{Diff}\:\mathrm{Equa}\::\:\left(\frac{\mathrm{d}{y}\left({t}\right)}{\mathrm{d}{t}}\right)^{\mathrm{2}} +\mathrm{4}{y}\left({t}\right)=\mathrm{8}{t}^{\mathrm{2}} −\mathrm{32}{t}+\mathrm{28}…. \\ $$$$\mathrm{Sadly}\:\mathrm{it}'\mathrm{s}\:\mathrm{impossible}\:\mathrm{to}\:\mathrm{obtain}\:\mathrm{an}\:\mathrm{exact} \\ $$$$\mathrm{closed}−\mathrm{form}\:\mathrm{expression}\:\mathrm{of}\:\mathrm{the}\:\mathrm{Solution}\:\mathrm{of}\:\mathrm{Diff}\:\mathrm{Equa} \\ $$$$\mathrm{But}\:\mathrm{if}\:\mathrm{the}\:\mathrm{Runge}−\mathrm{Kutta}\:\mathrm{method}\:\mathrm{is}\:\mathrm{used}. \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}\:\mathrm{at}\:\mathrm{any}\:\mathrm{one}\:\mathrm{point}\:\mathrm{can}\:\mathrm{be}\:\mathrm{estimated} \\ $$
Commented by mr W last updated on 31/Mar/24
$${y}\left({t}\right)={t}^{\mathrm{2}} −\mathrm{4}{t}+\mathrm{3} \\ $$$${or} \\ $$$${y}\left({t}\right)=−\mathrm{2}{t}^{\mathrm{2}} +\mathrm{8}{t}−\mathrm{9} \\ $$
Commented by MathedUp last updated on 31/Mar/24
$$\mathrm{r}\:\mathrm{u}\:\mathrm{assumed}\:{y}\left({t}\right)\:\mathrm{as}\:{at}^{\mathrm{2}} +{bt}+{c}\:???? \\ $$$$\left(\mathrm{2}{at}+{b}\right)^{\mathrm{2}} +\mathrm{4}{at}^{\mathrm{2}} +\mathrm{4}{bt}+\mathrm{4}{c}=\mathrm{8}{t}^{\mathrm{2}} −\mathrm{32}{t}+\mathrm{28} \\ $$
Commented by mr W last updated on 31/Mar/24
$${why}\:{not}? \\ $$
Commented by MathedUp last updated on 31/Mar/24
$$\mathrm{Oh}….\:\mathrm{yeah}\:\mathrm{you}\:\mathrm{were}\:\mathrm{right}… \\ $$$$\mathrm{i}\:\mathrm{thought}\:\mathrm{he}\:\mathrm{was}\:\mathrm{looking}\:\mathrm{for}\:\mathrm{a}\:\mathrm{more}\:\mathrm{general}\:\mathrm{solution} \\ $$$$:\left(\right. \\ $$
Commented by mr W last updated on 31/Mar/24
$${there}\:{might}\:{be}\:{other}\:{solutions}. \\ $$