ODE No. 1924

11.12 ODE No. 1924

${({(x (t))}^{2} + {(y (t))}^{2} - t^{2}) \frac{d}{d t} x (t) = - 2 t x (t), ({(x (t))}^{2} + {(y (t))}^{2} - t^{2}) \frac{d}{d t} y (t) = - 2 t y (t)}$

Mathematica: cpu = 0.071009 (sec), leaf count = 191 ${{y (t) \to \frac{c_{1} (e^{c_{2}} - \sqrt{- 4 c_{1}^{2} t^{2} + e^{2 c_{2}} - 4 t^{2}})}{2 (c_{1}^{2} + 1)}, x (t) \to \frac{e^{c_{2}} - \sqrt{- 4 c_{1}^{2} t^{2} + e^{2 c_{2}} - 4 t^{2}}}{2 (c_{1}^{2} + 1)}}, {y (t) \to \frac{c_{1} (\sqrt{- 4 c_{1}^{2} t^{2} + e^{2 c_{2}} - 4 t^{2}} + e^{c_{2}})}{2 (c_{1}^{2} + 1)}, x (t) \to \frac{\sqrt{- 4 c_{1}^{2} t^{2} + e^{2 c_{2}} - 4 t^{2}} + e^{c_{2}}}{2 (c_{1}^{2} + 1)}}}$

Maple: cpu = 0.234 (sec), leaf count = 186 ${[{x (t) = 0}, {y (t) = \frac{1}{2_C 1} (1 + \sqrt{- 4 {_C 1}^{2} t^{2} + 1}), y (t) = - \frac{1}{2_C 1} (- 1 + \sqrt{- 4 {_C 1}^{2} t^{2} + 1})}], [{x (t) = - \frac{1}{2_C 2} (-_C 1 + \sqrt{- 2_C 2 t^{2} + {_C 1}^{2}}), x (t) = \frac{1}{2_C 2} (_C 1 + \sqrt{- 2_C 2 t^{2} + {_C 1}^{2}})}, {y (t) = \frac{1}{\frac{d}{d t} x (t)} \sqrt{- (\frac{d}{d t} x (t)) ({(x (t))}^{2} \frac{d}{d t} x (t) - (\frac{d}{d t} x (t)) t^{2} + 2 t x (t))}, y (t) = - \frac{1}{\frac{d}{d t} x (t)} \sqrt{- (\frac{d}{d t} x (t)) ({(x (t))}^{2} \frac{d}{d t} x (t) - (\frac{d}{d t} x (t)) t^{2} + 2 t x (t))}}]}$

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