2.2.75 Problems 7401 to 7500

Table 2.151: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

7401

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

[_separable]

1.570

7402

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

[_separable]

2.428

7403

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

[_separable]

12.209

7404

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

[_separable]

3.366

7405

\[ {}z^{\prime } = 10^{x +z} \]

[_separable]

2.927

7406

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

[_quadrature]

0.458

7407

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

[[_homogeneous, ‘class C‘], _dAlembert]

2.374

7408

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

[[_linear, ‘class A‘]]

1.316

7409

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

[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]

2.502

7410

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

[[_linear, ‘class A‘]]

1.263

7411

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

[[_homogeneous, ‘class C‘], _dAlembert]

2.822

7412

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

[[_homogeneous, ‘class C‘], _dAlembert]

3.996

7413

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

[[_homogeneous, ‘class C‘], _dAlembert]

2.094

7414

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

[[_homogeneous, ‘class C‘], _Riccati]

4.098

7415

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

[_separable]

1.658

7416

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

[_separable]

2.358

7417

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

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

38.392

7418

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

[_separable]

1.924

7419

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

[_rational, _Bernoulli]

1.560

7420

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

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

72.921

7421

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

5.997

7422

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

[[_homogeneous, ‘class A‘], _dAlembert]

3.925

7423

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

[[_homogeneous, ‘class A‘], _dAlembert]

18.777

7424

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

[[_homogeneous, ‘class A‘], _dAlembert]

3.741

7425

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

[[_homogeneous, ‘class A‘], _dAlembert]

3.415

7426

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

5.131

7427

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

98.532

7428

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

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

38.328

7429

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

110.095

7430

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

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3.138

7431

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

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

7.300

7432

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

[[_homogeneous, ‘class A‘], _rational, _Riccati]

2.522

7433

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

16.227

7434

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

35.079

7435

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

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

3.967

7436

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

6.525

7437

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

[[_homogeneous, ‘class A‘], _dAlembert]

43.104

7438

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

[[_homogeneous, ‘class A‘], _dAlembert]

3.411

7439

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

[_quadrature]

0.531

7440

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

[[_homogeneous, ‘class A‘], _dAlembert]

66.839

7441

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

[_separable]

0.972

7442

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

8.358

7443

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

1.721

7444

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

[_linear]

2.682

7445

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

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3.200

7446

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

[_linear]

4.207

7447

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

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3.370

7448

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

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3.820

7449

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

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3.653

7450

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

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3.838

7451

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

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2.813

7452

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

[[_homogeneous, ‘class C‘], _rational]

1.898

7453

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

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1.950

7454

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

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1.910

7455

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

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3.799

7456

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

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4.150

7457

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

[[_homogeneous, ‘class C‘], _exact, _dAlembert]

7.585

7458

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

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3.579

7459

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

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7.480

7460

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

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

3.529

7461

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

[[_homogeneous, ‘class G‘], _rational]

0.618

7462

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

[[_homogeneous, ‘class G‘], _rational, _Riccati]

0.396

7463

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

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

0.621

7464

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

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

0.612

7465

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

[[_1st_order, _with_linear_symmetries], _Chini]

0.995

7466

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

[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]

0.565

7467

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

[[_homogeneous, ‘class G‘]]

5.743

7468

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

[[_homogeneous, ‘class G‘]]

4.505

7469

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

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

0.576

7470

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

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

0.609

7471

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

[[_homogeneous, ‘class G‘], _rational]

0.673

7472

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

[[_homogeneous, ‘class G‘], _rational]

2.314

7473

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

[[_homogeneous, ‘class G‘]]

0.815

7474

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

[_exact, _rational]

2.128

7475

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

[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]

1.544

7476

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

[_separable]

3.155

7477

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

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5.980

7478

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

[[_2nd_order, _missing_x]]

1.142

7479

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.309

7480

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

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

2.521

7481

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

[[_2nd_order, _with_linear_symmetries]]

2.382

7482

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

[[_Emden, _Fowler]]

0.829

7483

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

[[_2nd_order, _with_linear_symmetries]]

1.044

7484

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

[[_2nd_order, _exact, _linear, _homogeneous]]

2.010

7485

\[ {}y^{\prime \prime \prime }-2 x y^{\prime \prime }+4 x^{2} y^{\prime }+8 x^{3} y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

0.048

7486

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

[[_2nd_order, _with_linear_symmetries]]

0.532

7487

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }+4 y = 0 \]

[[_Emden, _Fowler]]

2.758

7488

\[ {}x^{4} y^{\prime \prime \prime \prime }-x^{2} y^{\prime \prime }+y = 0 \]

[[_high_order, _with_linear_symmetries]]

0.332

7489

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

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

2.433

7490

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

2.345

7491

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

[[_2nd_order, _with_linear_symmetries]]

1.485

7492

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

2.432

7493

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

[[_2nd_order, _with_linear_symmetries]]

2.426

7494

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1.853

7495

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

[[_2nd_order, _with_linear_symmetries]]

1.396

7496

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.991

7497

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

[[_2nd_order, _with_linear_symmetries]]

1.045

7498

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

[[_2nd_order, _linear, _nonhomogeneous]]

4.419

7499

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.743

7500

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

[[_2nd_order, _linear, _nonhomogeneous]]

268.212