4.1.65 Problems 6401 to 6500

Table 4.129: First order ode

#

ODE

Mathematica

Maple

Sympy

14456

\[ {} y^{\prime }-2 y = 6 \]

14457

\[ {} y^{\prime }+y = {\mathrm e}^{x} \]

14464

\[ {} y^{\prime }+2 y = \left \{\begin {array}{cc} 2 & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \]

14471

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

14472

\[ {} y^{\prime }-3 y = \delta \left (x -1\right )+2 \operatorname {Heaviside}\left (x -2\right ) \]

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

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

14601

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

14602

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

14603

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

14604

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

14605

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

14606

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

14607

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

14608

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

14609

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

14610

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

14611

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

14612

\[ {} y^{\prime } = y^{2}-4 y-12 \]

14613

\[ {} y^{\prime } = y^{2}-4 y-12 \]

14614

\[ {} y^{\prime } = y^{2}-4 y-12 \]

14615

\[ {} y^{\prime } = y^{2}-4 y-12 \]

14616

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