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

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

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 mr W last updated on 31/Mar/24

$$whynot?$$

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

$$theremightbeothersolutions.$$

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