can-t-Solve-Differantial-Equation-Diff-Equa-dy-t-dt-2-4y-t-8t-2-32t-28-Sadly-it-s-impossible-to-obtain-an-exact-closed-form-expression-of-the-Solution-of-Diff-Equa-But-if-the-Runge-Kut

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Question Number 205833 by MathedUp last updated on 31/Mar/24

$${\mathrm{can}}^{\prime }\mathrm{t}\mathrm{Solve}\mathrm{Differantial}\mathrm{Equation}$$$$\mathrm{Diff}\mathrm{Equa}:{\left(\frac{\mathrm{d}y\left(t\right)}{\mathrm{d}t}\right)}^2+4y\left(t\right)=8t^2-32t+28\dots .$$$$\mathrm{Sadly}{\mathrm{it}}^{\prime }\mathrm{s}\mathrm{impossible}\mathrm{to}\mathrm{obtain}\mathrm{an}\mathrm{exact}$$$$\mathrm{closed}-\mathrm{form}\mathrm{expression}\mathrm{of}\mathrm{the}\mathrm{Solution}\mathrm{of}\mathrm{Diff}\mathrm{Equa}$$$$\mathrm{But}\mathrm{if}\mathrm{the}\mathrm{Runge}-\mathrm{Kutta}\mathrm{method}\mathrm{is}\mathrm{used}.$$$$\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{the}\mathrm{function}\mathrm{at}\mathrm{any}\mathrm{one}\mathrm{point}\mathrm{can}\mathrm{be}\mathrm{estimated}$$

Commented by mr W last updated on 31/Mar/24

$$y\left(t\right)=t^2-4t+3$$$$or$$$$y\left(t\right)=-2t^2+8t-9$$

Commented by MathedUp last updated on 31/Mar/24

$$\mathrm{r}\mathrm{u}\mathrm{assumed}y\left(t\right)\mathrm{as}{at}^2+bt+c????$$$${(2at+b)}^2+4{at}^2+4bt+4c=8t^2-32t+28$$

Commented by mr W last updated on 31/Mar/24

$$whynot?$$

Commented by MathedUp last updated on 31/Mar/24

$$\mathrm{Oh}\dots .\mathrm{yeah}\mathrm{you}\mathrm{were}\mathrm{right}\dots$$$$\mathrm{i}\mathrm{thought}\mathrm{he}\mathrm{was}\mathrm{looking}\mathrm{for}\mathrm{a}\mathrm{more}\mathrm{general}\mathrm{solution}$$$$:($$

Commented by mr W last updated on 31/Mar/24

$$theremightbeothersolutions.$$

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