4.9.76 Problems 7501 to 7600

Table 4.989: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

21200

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

21201

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

21202

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

21203

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

21204

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

21205

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

21206

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

21207

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

21208

\[ {} x^{\prime }+2 t x = -4 t x^{3} \]

21209

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

21217

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

21396

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

21397

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

21401

\[ {} x^{\prime }-x = \operatorname {Heaviside}\left (t -a \right ) \]

21402

\[ {} x^{\prime }+x = \operatorname {Heaviside}\left (t -a \right ) \]

21403

\[ {} x^{\prime }-x = k \delta \left (t \right ) \]

21429

\[ {} x^{\prime } = \lambda x-x^{5} \]

21430

\[ {} x^{\prime } = \lambda x-x^{3}-x^{5} \]

21446

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

21447

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

21448

\[ {} y^{\prime } = -5 y \]

21449

\[ {} y^{\prime } = f \left (x \right ) g \left (y\right ) \]

21450

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

21451

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

21452

\[ {} y y^{\prime }+x = 0 \]

21453

\[ {} x y^{\prime }+y = 0 \]

21454

\[ {} -2 y+x y^{\prime } = 0 \]

21455

\[ {} \sqrt {x}\, y^{\prime }+1 = 0 \]

21456

\[ {} 2 x \left (1+y\right )-y y^{\prime } = 0 \]

21457

\[ {} y^{\prime } = -\frac {x}{y} \]

21458

\[ {} y^{\prime } = \frac {2 y}{x} \]

21459

\[ {} -2+2 y+x^{2} \sin \left (y\right ) y^{\prime } = 0 \]

21460

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

21461

\[ {} y^{\prime } = \frac {a x +b}{y^{n}+d} \]

21462

\[ {} y^{\prime } = -\frac {x}{y} \]

21463

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

21464

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

21465

\[ {} x \cos \left (x \right )+\left (1-6 y^{5}\right ) y^{\prime } = 0 \]

21466

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

21467

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

21468

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

21469

\[ {} x y^{2}-x +\left (y+x^{2} y\right ) y^{\prime } = 0 \]

21470

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

21471

\[ {} y^{\prime } = \frac {y \ln \left (x \right )}{x} \]

21472

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

21473

\[ {} {\mathrm e}^{x}-y y^{\prime } = 0 \]

21474

\[ {} 2 x -6 y+3-\left (1+x -3 y\right ) y^{\prime } = 0 \]

21475

\[ {} 2 x +y+1+\left (4 x +2 y+3\right ) y^{\prime } = 0 \]

21476

\[ {} 2 x +3 y-1+\left (2 x -3 y+2\right ) y^{\prime } = 0 \]

21477

\[ {} x +2 y-4-\left (2 x +y-5\right ) y^{\prime } = 0 \]

21478

\[ {} x +2 y-1+3 \left (2 y+x \right ) y^{\prime } = 0 \]

21479

\[ {} {\mathrm e}^{-y} \left (1+y^{\prime }\right ) = x \,{\mathrm e}^{x} \]

21480

\[ {} y^{\prime } = \frac {x +y}{x} \]

21481

\[ {} x -y+\left (x -4 y\right ) y^{\prime } = 0 \]

21482

\[ {} x^{2}-x y+y^{2}-y y^{\prime } x = 0 \]

21483

\[ {} y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime } = 0 \]

21484

\[ {} x^{2}-2 y^{2}+y y^{\prime } x = 0 \]

21485

\[ {} x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \]

21486

\[ {} y+x y^{\prime }+\frac {y^{3} \left (y-x y^{\prime }\right )}{x} = 0 \]

21487

\[ {} \left (x -4\right ) y^{4}-x^{3} \left (y^{2}-3\right ) y^{\prime } = 0 \]

21488

\[ {} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0 \]

21489

\[ {} x \sin \left (y\right )+\left (x^{2}+1\right ) \cos \left (y\right ) y^{\prime } = 0 \]

21490

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

21491

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

21492

\[ {} \left (x +y^{2}\right ) y^{\prime }+y = 0 \]

21493

\[ {} y^{\prime }+\frac {2 x \sin \left (y\right )+y^{3} {\mathrm e}^{x}}{x^{2} \cos \left (y\right )+3 y^{2} {\mathrm e}^{x}} = 0 \]

21494

\[ {} \left (x +y\right ) y^{\prime }+3 x +y = 0 \]

21495

\[ {} 3 x \left (x y-2\right )+\left (x^{3}+2 y\right ) y^{\prime } = 0 \]

21496

\[ {} 3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{2}\right ) y^{\prime } = 0 \]

21497

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

21498

\[ {} \left (x +y^{2}\right ) y^{\prime }+y-x^{2} = 0 \]

21499

\[ {} 3 x^{2}+4 x y+\left (2 x^{2}+2 y\right ) y^{\prime } = 0 \]

21500

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

21501

\[ {} y^{2}-x^{2}-2 y y^{\prime } x = 0 \]

21502

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

21503

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

21504

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

21505

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

21506

\[ {} x +y-\left (x -y\right ) y^{\prime } = 0 \]

21507

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

21508

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

21509

\[ {} x^{2}-3 y^{2}+2 y y^{\prime } x = 0 \]

21510

\[ {} y y^{\prime } x +x^{2}+y^{2} = 0 \]

21511

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

21512

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

21513

\[ {} y+\sqrt {x^{2}+y^{2}}-x y^{\prime } = 0 \]

21514

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

21515

\[ {} y-x y^{2}+x y^{\prime } = 0 \]

21516

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

21517

\[ {} y^{\prime }+2 x y = 0 \]

21518

\[ {} 1+3 x \sin \left (y\right )-x^{2} \cos \left (y\right ) y^{\prime } = 0 \]

21519

\[ {} \left (2+3 x -x y\right ) y^{\prime }+y = 0 \]

21520

\[ {} \left (x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right ) y = x \,{\mathrm e}^{-x} \]

21521

\[ {} x^{\prime }-x \tan \left (t \right ) = \sin \left (t \right ) \]

21522

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

21523

\[ {} y^{\prime }+\left (b x +a \right ) y = f \left (x \right ) \]

21524

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

21525

\[ {} 2 y-8 x^{2}+x y^{\prime } = 0 \]

21526

\[ {} y^{\prime }-3 y = 6 \]

21527

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