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Solve-the-following-system-of-differential-equations-for-functions-x-t-and-y-t-m-d-2-x-dt-2-kx-x-2-y-2-2-m-d-2-y-dt-2-ky-x-2-y-2-2-




Question Number 4625 by Yozzis last updated on 14/Feb/16
Solve the following system of differential   equations for functions x(t) and y(t).                      m(d^2 x/dt^2 )=((kx)/((x^2 +y^2 )^2 ))                     m(d^2 y/dt^2 )=((ky)/((x^2 +y^2 )^2 ))  m and k are constants.
$${Solve}\:{the}\:{following}\:{system}\:{of}\:{differential}\: \\ $$$${equations}\:{for}\:{functions}\:{x}\left({t}\right)\:{and}\:{y}\left({t}\right). \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{m}\frac{{d}^{\mathrm{2}} {x}}{{dt}^{\mathrm{2}} }=\frac{{kx}}{\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{m}\frac{{d}^{\mathrm{2}} {y}}{{dt}^{\mathrm{2}} }=\frac{{ky}}{\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)^{\mathrm{2}} } \\ $$$${m}\:{and}\:{k}\:{are}\:{constants}. \\ $$

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