6.256 Problems 25501 to 25513

Table 6.511: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

25501

\[ {} [y_{1}^{\prime }\left (t \right ) = y_{2} \left (t \right )+y_{3} \left (t \right )+{\mathrm e}^{2 t}, y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )+y_{2} \left (t \right )-y_{3} \left (t \right )+{\mathrm e}^{2 t}, y_{3}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )+y_{2} \left (t \right )+3 y_{3} \left (t \right )-{\mathrm e}^{2 t}] \]

25502

\[ {} [y_{1}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )+y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -4 y_{1} \left (t \right )+3 y_{2} \left (t \right )] \]

25503

\[ {} [y_{1}^{\prime }\left (t \right ) = 5 y_{1} \left (t \right )-3 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )] \]

25504

\[ {} [y_{1}^{\prime }\left (t \right ) = t y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -t y_{1} \left (t \right )] \]

25505

\[ {} [y_{1}^{\prime }\left (t \right ) = t y_{1} \left (t \right )+t y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -t y_{1} \left (t \right )-t y_{2} \left (t \right )] \]

25506

\[ {} \left [y_{1}^{\prime }\left (t \right ) = \frac {y_{1} \left (t \right )}{t}+y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -y_{1} \left (t \right )+\frac {y_{2} \left (t \right )}{t}\right ] \]

25507

\[ {} [y_{1}^{\prime }\left (t \right ) = \left (2 t +1\right ) y_{1} \left (t \right )+2 t y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -2 t y_{1} \left (t \right )+\left (1-2 t \right ) y_{2} \left (t \right )] \]

25508

\[ {} \left [y_{1}^{\prime }\left (t \right ) = y_{1} \left (t \right )+y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = \frac {y_{1} \left (t \right )}{t}+\frac {y_{2} \left (t \right )}{t}\right ] \]

25509

\[ {} \left [y_{1}^{\prime }\left (t \right ) = \frac {y_{1} \left (t \right )}{t}+1, y_{2}^{\prime }\left (t \right ) = \frac {y_{2} \left (t \right )}{t}+t\right ] \]

25510

\[ {} \left [y_{1}^{\prime }\left (t \right ) = -\frac {y_{2} \left (t \right )}{t}+1, y_{2}^{\prime }\left (t \right ) = \frac {y_{1} \left (t \right )}{t}+\frac {2 y_{2} \left (t \right )}{t}-1\right ] \]

25511

\[ {} \left [y_{1}^{\prime }\left (t \right ) = \frac {4 t y_{1} \left (t \right )}{t^{2}+1}+\frac {6 y_{2} \left (t \right ) t}{t^{2}+1}-3 t, y_{2}^{\prime }\left (t \right ) = -\frac {2 t y_{1} \left (t \right )}{t^{2}+1}-\frac {4 y_{2} \left (t \right ) t}{t^{2}+1}+t\right ] \]

25512

\[ {} [y_{1}^{\prime }\left (t \right ) = 3 \sec \left (t \right ) y_{1} \left (t \right )+5 \sec \left (t \right ) y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -\sec \left (t \right ) y_{1} \left (t \right )-3 \sec \left (t \right ) y_{2} \left (t \right )] \]

25513

\[ {} [y_{1}^{\prime }\left (t \right ) = t y_{1} \left (t \right )+t y_{2} \left (t \right )+4 t, y_{2}^{\prime }\left (t \right ) = -t y_{1} \left (t \right )-t y_{2} \left (t \right )+4 t] \]