6.146 Problems 14501 to 14600

Table 6.291: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

14501

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

14502

\[ {} \left [y_{1}^{\prime }\left (x \right ) = \frac {5 y_{1} \left (x \right )}{x}+\frac {4 y_{2} \left (x \right )}{x}, y_{2}^{\prime }\left (x \right ) = -\frac {6 y_{1} \left (x \right )}{x}-\frac {5 y_{2} \left (x \right )}{x}\right ] \]

14503

\[ {} \left [y_{1}^{\prime }\left (x \right ) = \frac {5 y_{1} \left (x \right )}{x}+\frac {4 y_{2} \left (x \right )}{x}-2 x, y_{2}^{\prime }\left (x \right ) = -\frac {6 y_{1} \left (x \right )}{x}-\frac {5 y_{2} \left (x \right )}{x}+5 x\right ] \]

14504

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

14505

\[ {} [y_{1}^{\prime }\left (x \right ) = 5 y_{1} \left (x \right )-5 y_{2} \left (x \right )-5 y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -y_{1} \left (x \right )+4 y_{2} \left (x \right )+2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )-5 y_{2} \left (x \right )-3 y_{3} \left (x \right )] \]

14506

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

14507

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

14508

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

14509

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

14510

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

14511

\[ {} [y_{1}^{\prime }\left (x \right ) = y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -3 y_{1} \left (x \right )+2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = y_{4} \left (x \right ), y_{4}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )-5 y_{3} \left (x \right )] \]

14512

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

14513

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

14514

\[ {} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right )] \]

14515

\[ {} [x^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right )] \]

14516

\[ {} [x^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )] \]

14517

\[ {} [x^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+y \left (t \right )] \]

14518

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

14519

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

14520

\[ {} [x^{\prime }\left (t \right ) = -5 x \left (t \right )-y \left (t \right )+2, y^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right )-3] \]

14521

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

14522

\[ {} y^{\prime } = \frac {1+y}{t +1} \]

14523

\[ {} y^{\prime } = t^{2} y^{2} \]

14524

\[ {} y^{\prime } = t^{4} y \]

14525

\[ {} y^{\prime } = 2 y+1 \]

14526

\[ {} y^{\prime } = 2-y \]

14527

\[ {} y^{\prime } = {\mathrm e}^{-y} \]

14528

\[ {} x^{\prime } = 1+x^{2} \]

14529

\[ {} y^{\prime } = 2 t y^{2}+3 y^{2} \]

14530

\[ {} y^{\prime } = \frac {t}{y} \]

14531

\[ {} y^{\prime } = \frac {t}{t^{2} y+y} \]

14532

\[ {} y^{\prime } = t y^{{1}/{3}} \]

14533

\[ {} y^{\prime } = \frac {1}{2 y+1} \]

14534

\[ {} y^{\prime } = \frac {2 y+1}{t} \]

14535

\[ {} y^{\prime } = y \left (1-y\right ) \]

14536

\[ {} y^{\prime } = \frac {4 t}{1+3 y^{2}} \]

14537

\[ {} v^{\prime } = t^{2} v-2-2 v+t^{2} \]

14538

\[ {} y^{\prime } = \frac {1}{t y+t +y+1} \]

14539

\[ {} y^{\prime } = \frac {{\mathrm e}^{t} y}{1+y^{2}} \]

14540

\[ {} y^{\prime } = y^{2}-4 \]

14541

\[ {} w^{\prime } = \frac {w}{t} \]

14542

\[ {} y^{\prime } = \sec \left (y\right ) \]

14543

\[ {} x^{\prime } = -t x \]

14544

\[ {} y^{\prime } = t y \]

14545

\[ {} y^{\prime } = -y^{2} \]

14546

\[ {} y^{\prime } = t^{2} y^{3} \]

14547

\[ {} y^{\prime } = -y^{2} \]

14548

\[ {} y^{\prime } = \frac {t}{y-t^{2} y} \]

14549

\[ {} y^{\prime } = 2 y+1 \]

14550

\[ {} y^{\prime } = t y^{2}+2 y^{2} \]

14551

\[ {} x^{\prime } = \frac {t^{2}}{x+t^{3} x} \]

14552

\[ {} y^{\prime } = \frac {1-y^{2}}{y} \]

14553

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

14554

\[ {} y^{\prime } = \frac {1}{2 y+3} \]

14555

\[ {} y^{\prime } = 2 t y^{2}+3 t^{2} y^{2} \]

14556

\[ {} y^{\prime } = \frac {y^{2}+5}{y} \]

14557

\[ {} y^{\prime } = t^{2}+t \]

14558

\[ {} y^{\prime } = t^{2}+1 \]

14559

\[ {} y^{\prime } = 1-2 y \]

14560

\[ {} y^{\prime } = 4 y^{2} \]

14561

\[ {} y^{\prime } = 2 y \left (1-y\right ) \]

14562

\[ {} y^{\prime } = y+t +1 \]

14563

\[ {} y^{\prime } = 3 y \left (1-y\right ) \]

14564

\[ {} y^{\prime } = 2 y-t \]

14565

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

14566

\[ {} y^{\prime } = \left (t +1\right ) y \]

14567

\[ {} S^{\prime } = S^{3}-2 S^{2}+S \]

14568

\[ {} S^{\prime } = S^{3}-2 S^{2}+S \]

14569

\[ {} S^{\prime } = S^{3}-2 S^{2}+S \]

14570

\[ {} S^{\prime } = S^{3}-2 S^{2}+S \]

14571

\[ {} S^{\prime } = S^{3}-2 S^{2}+S \]

14572

\[ {} y^{\prime } = y^{2}+y \]

14573

\[ {} y^{\prime } = y^{2}-y \]

14574

\[ {} y^{\prime } = y^{3}+y^{2} \]

14575

\[ {} y^{\prime } = -t^{2}+2 \]

14576

\[ {} y^{\prime } = t y+t y^{2} \]

14577

\[ {} y^{\prime } = t^{2}+t^{2} y \]

14578

\[ {} y^{\prime } = t +t y \]

14579

\[ {} y^{\prime } = t^{2}-2 \]

14580

\[ {} \theta ^{\prime } = \frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \]

14581

\[ {} \theta ^{\prime } = 2 \]

14582

\[ {} \theta ^{\prime } = \frac {11}{10}-\frac {9 \cos \left (\theta \right )}{10} \]

14583

\[ {} v^{\prime } = -\frac {v}{R C} \]

14584

\[ {} v^{\prime } = \frac {K -v}{R C} \]

14585

\[ {} v^{\prime } = 2 V \left (t \right )-2 v \]

14586

\[ {} y^{\prime } = 2 y+1 \]

14587

\[ {} y^{\prime } = t -y^{2} \]

14588

\[ {} y^{\prime } = y^{2}-4 t \]

14589

\[ {} y^{\prime } = \sin \left (y\right ) \]

14590

\[ {} w^{\prime } = \left (3-w\right ) \left (w+1\right ) \]

14591

\[ {} w^{\prime } = \left (3-w\right ) \left (w+1\right ) \]

14592

\[ {} y^{\prime } = {\mathrm e}^{\frac {2}{y}} \]

14593

\[ {} y^{\prime } = {\mathrm e}^{\frac {2}{y}} \]

14594

\[ {} y^{\prime } = y^{2}-y^{3} \]

14595

\[ {} y^{\prime } = 2 y^{3}+t^{2} \]

14596

\[ {} y^{\prime } = \sqrt {y} \]

14597

\[ {} y^{\prime } = 2-y \]

14598

\[ {} \theta ^{\prime } = \frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \]

14599

\[ {} y^{\prime } = y \left (y-1\right ) \left (y-3\right ) \]

14600

\[ {} y^{\prime } = y \left (y-1\right ) \left (y-3\right ) \]