4.1.38 Problems 3701 to 3800

Table 4.75: First order ode

#

ODE

Mathematica

Maple

Sympy

7439

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

7440

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

7441

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

7442

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

7443

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

7444

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

7445

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

7446

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

7447

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

7448

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

7449

\[ {} y^{\prime } = \frac {2 y-x +5}{2 x -y-4} \]

7450

\[ {} y^{\prime } = -\frac {4 x +3 y+15}{2 x +y+7} \]

7451

\[ {} y^{\prime } = \frac {x +3 y-5}{x -y-1} \]

7452

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

7453

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

7454

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

7455

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

7456

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

7457

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

7458

\[ {} y^{\prime } = \frac {x -2 y+5}{y-2 x -4} \]

7459

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

7460

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

7461

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

7462

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

7463

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

7464

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

7465

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

7466

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

7467

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

7468

\[ {} \frac {2 x y y^{\prime }}{3} = \sqrt {x^{6}-y^{4}}+y^{2} \]

7469

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

7470

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

7471

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

7472

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

7473

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

7474

\[ {} x \left (2-9 x y^{2}\right )+y \left (4 y^{2}-6 x^{3}\right ) y^{\prime } = 0 \]

7475

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

7476

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

7477

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

7502

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

7503

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

7504

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

7505

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

7506

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

7507

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

7508

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

7509

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

7510

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

7511

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

7512

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

7513

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

7514

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

7515

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

7516

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

7543

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

7544

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

7547

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

7548

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

7549

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

7550

\[ {} \phi ^{\prime }-\frac {\phi ^{2}}{2}-\phi \cot \left (\theta \right ) = 0 \]

7552

\[ {} \left (\phi ^{\prime }-\frac {\phi ^{2}}{2}\right ) \sin \left (\theta \right )^{2}-\phi \sin \left (\theta \right ) \cos \left (\theta \right ) = \frac {\cos \left (2 \theta \right )}{2}+1 \]

7555

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

7556

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

7560

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

7561

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

7562

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

7563

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

7564

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

7580

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

7583

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

7584

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

7588

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

7590

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

7591

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

7592

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

7593

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

7594

\[ {} 3 y^{\prime }+y = 2 \,{\mathrm e}^{-x} \]

7595

\[ {} y^{\prime }+3 y = {\mathrm e}^{i x} \]

7596

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

7597

\[ {} L y^{\prime }+R y = E \]

7598

\[ {} L y^{\prime }+R y = E \sin \left (\omega x \right ) \]

7599

\[ {} L y^{\prime }+R y = E \,{\mathrm e}^{i \omega x} \]

7600

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

7601

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

7602

\[ {} x y^{\prime }+y = 3 x^{3}-1 \]

7603

\[ {} y^{\prime }+y \,{\mathrm e}^{x} = 3 \,{\mathrm e}^{x} \]

7604

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

7605

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

7606

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

7607

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

7608

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

7609

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

7610

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

7611

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

7731

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

7732

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

7733

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

7734

\[ {} y^{\prime } = \frac {{\mathrm e}^{x -y}}{1+{\mathrm e}^{x}} \]

7735

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

7736

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