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

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−Kutta method is used. the value of the function at any one point can be estimated

$$\mathrm{can}'\mathrm{t}\:\mathrm{Solve}\:\mathrm{Differantial}\:\mathrm{Equation} \\ $$$$\mathrm{Diff}\:\mathrm{Equa}\::\:\left(\frac{\mathrm{d}{y}\left({t}\right)}{\mathrm{d}{t}}\right)^{\mathrm{2}} +\mathrm{4}{y}\left({t}\right)=\mathrm{8}{t}^{\mathrm{2}} −\mathrm{32}{t}+\mathrm{28}.... \\ $$$$\mathrm{Sadly}\:\mathrm{it}'\mathrm{s}\:\mathrm{impossible}\:\mathrm{to}\:\mathrm{obtain}\:\mathrm{an}\:\mathrm{exact} \\ $$$$\mathrm{closed}−\mathrm{form}\:\mathrm{expression}\:\mathrm{of}\:\mathrm{the}\:\mathrm{Solution}\:\mathrm{of}\:\mathrm{Diff}\:\mathrm{Equa} \\ $$$$\mathrm{But}\:\mathrm{if}\:\mathrm{the}\:\mathrm{Runge}−\mathrm{Kutta}\:\mathrm{method}\:\mathrm{is}\:\mathrm{used}. \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}\:\mathrm{at}\:\mathrm{any}\:\mathrm{one}\:\mathrm{point}\:\mathrm{can}\:\mathrm{be}\:\mathrm{estimated} \\ $$

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

y(t)=t^2 −4t+3 or y(t)=−2t^2 +8t−9

$${y}\left({t}\right)={t}^{\mathrm{2}} −\mathrm{4}{t}+\mathrm{3} \\ $$$${or} \\ $$$${y}\left({t}\right)=−\mathrm{2}{t}^{\mathrm{2}} +\mathrm{8}{t}−\mathrm{9} \\ $$

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

why not?

$${why}\:{not}? \\ $$

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

there might be other solutions.

$${there}\:{might}\:{be}\:{other}\:{solutions}. \\ $$

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