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Mathematics
Differential Equations
Solution form for the following differential equation
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[QUOTE="RPinPA, post: 6073946, member: 651116"] I tried sending it to Wolfram Alpha, which I think is run on Mathematica. It required the Pro package (which I have) to solve it, but even so what I got was a complicated integral expression involving the Lambert W function rather than a closed form analytical expression. [URL='https://www.wolframalpha.com/input/?i=m%C2%B7x(t)%E2%80%99%E2%80%99%2B(k%2Bc%C2%B7x(t)%E2%80%99)%C2%B7x(t)%5En%3D0']https://www.wolframalpha.com/input/?i=m·x(t)’’+(k+c·x(t)’)·x(t)^n=0[/URL] Solution: $$\alpha_1 + t = \int_1^{x(t)} \frac {c} {k\left( -W\left(\frac {-\sqrt[n+1]{\exp\left(\frac{c^2 \xi^{n+1}}{km}\right) - n - \frac{c^2n\alpha_1}{k} - \frac{c^2\alpha_1}{k} - 1}} {k}\right) \right) - k} d\xi$$ But then it also said the computation time was exceeded, so maybe there was more it could do with this. If you have access to Mathematica, this is the code it generated to evaluate the expression. [code]DSolve[{x[t]^n (k + c x'[t]) + m x''[t] == 0}, x[t], t][/code] [/QUOTE]
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Mathematics
Differential Equations
Solution form for the following differential equation
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