4.9.56 Problems 5501 to 5600

Table 4.735: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

14400

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

14401

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

14402

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

14403

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

14404

\[ {} y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \]

14405

\[ {} y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \]

14406

\[ {} y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \]

14407

\[ {} y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \]

14408

\[ {} y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \]

14438

\[ {} y^{\prime }-i y = 0 \]

14450

\[ {} y^{\prime }-y = 0 \]

14452

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

14457

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

14458

\[ {} y^{\prime }-y = 2 \,{\mathrm e}^{x} \]

14464

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

14465

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

14472

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

14479

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

14480

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

14530

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

14531

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

14532

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

14533

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

14534

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

14535

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

14536

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

14537

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

14538

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

14539

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

14540

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

14541

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

14542

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

14543

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

14544

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

14545

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

14546

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

14547

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

14548

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

14549

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

14550

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

14551

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

14552

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

14553

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

14554

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

14555

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

14556

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

14557

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

14558

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

14559

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

14560

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

14561

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

14562

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

14563

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

14564

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

14565

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

14566

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

14567

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

14568

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

14569

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

14570

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

14571

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

14572

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

14573

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

14574

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

14575

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

14576

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

14577

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

14578

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

14579

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

14580

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

14581

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

14582

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

14583

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

14584

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

14585

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

14586

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

14587

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

14588

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

14589

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

14590

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

14591

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

14592

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

14593

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

14594

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

14595

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

14596

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

14597

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

14598

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

14599

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

14600

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

14601

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

14602

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

14603

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

14604

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

14605

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

14606

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

14607

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

14608

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

14609

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

14610

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