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

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

[[_2nd_order, _with_linear_symmetries]]

1.086

7402

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (-x^{3}+3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.954

7403

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

[[_2nd_order, _with_linear_symmetries]]

1.066

7404

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

[_Bessel]

1.246

7405

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

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

1.470

7406

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

[_Gegenbauer]

0.634

7407

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

[_separable]

1.145

7408

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

[_separable]

3.020

7409

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

[_separable]

1.272

7410

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

[_separable]

1.430

7411

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

[_separable]

3.371

7412

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

[_quadrature]

1.002

7413

\[ {}y^{\prime } = 2 \sqrt {y} \]
i.c.

[_quadrature]

1.212

7414

\[ {}y^{\prime } = 2 \sqrt {y} \]
i.c.

[_quadrature]

0.976

7415

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

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

2.597

7416

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

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

36.718

7417

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

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

2.064

7418

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

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

17.124

7419

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

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

2.569

7420

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

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

3.076

7421

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

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

1.298

7422

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

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

2.095

7423

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

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

0.235

7424

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

[_quadrature]

0.181

7425

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

[_separable]

0.293

7426

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

[_separable]

0.403

7427

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

[_separable]

0.587

7428

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

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

0.311

7429

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

[_exact]

0.293

7430

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

[_linear]

0.198

7431

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

[_separable]

0.500

7432

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

[_separable]

0.349

7433

\[ {}5 x^{3} y^{2}+2 y+\left (3 x^{4} y+2 x \right ) y^{\prime } = 0 \]

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

0.333

7434

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

[_quadrature]

0.304

7435

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

[[_2nd_order, _missing_x]]

1.408

7436

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

[[_2nd_order, _missing_y]]

0.830

7437

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

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.192

7438

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

[[_2nd_order, _missing_x]]

1.639

7439

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

[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.619

7440

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

[[_2nd_order, _missing_y]]

1.138

7441

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

0.720

7442

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]]

2.638

7443

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

346.226

7444

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

148.853

7445

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{1} \\ y_{2}^{\prime }=y_{1}+y_{2} \end {array}\right ] \]
i.c.

system_of_ODEs

0.408

7446

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{2} \\ y_{2}^{\prime }=6 y_{1}+y_{2} \end {array}\right ] \]
i.c.

system_of_ODEs

0.495

7447

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+y_{2} \\ y_{2}^{\prime }=y_{1}+y_{2}+{\mathrm e}^{3 x} \end {array}\right ] \]
i.c.

system_of_ODEs

0.556

7448

\[ {}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+x y_{3} \\ y_{2}^{\prime }=y_{2}+x^{3} y_{3} \\ y_{3}^{\prime }=2 x y_{1}-y_{2}+{\mathrm e}^{x} y_{3} \end {array}\right ] \]

system_of_ODEs

0.060

7449

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

[_quadrature]

0.263

7450

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

[_separable]

1.576

7451

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

[_separable]

1.362

7452

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

[_quadrature]

0.716

7453

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

[[_2nd_order, _missing_x]]

1.959

7454

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

[[_2nd_order, _missing_x]]

2.089

7455

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

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

4.122

7456

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

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

1.391

7457

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

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

2.820

7458

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

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

7.406

7459

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

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

1.918

7460

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

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

4.066

7461

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

[[_1st_order, _with_linear_symmetries]]

1.609

7462

\[ {}1+y^{2}+y^{2} y^{\prime } = 0 \]

[_quadrature]

3.979

7463

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

[_quadrature]

0.305

7464

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

[_quadrature]

0.316

7465

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

[_quadrature]

0.340

7466

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

[_quadrature]

0.347

7467

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

[_quadrature]

0.402

7468

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

[_quadrature]

0.309

7469

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

[_quadrature]

0.296

7470

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

[_quadrature]

0.461

7471

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

[_quadrature]

0.585

7472

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

[_quadrature]

0.378

7473

\[ {}y^{\prime } = x \,{\mathrm e}^{x} \]
i.c.

[_quadrature]

0.556

7474

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

[_quadrature]

0.543

7475

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

[_quadrature]

0.510

7476

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

[_quadrature]

0.461

7477

\[ {}x \left (x^{2}-4\right ) y^{\prime } = 1 \]
i.c.

[_quadrature]

0.618

7478

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

[_quadrature]

1.095

7479

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

[_linear]

0.895

7480

\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

0.828

7481

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

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

1.401

7482

\[ {}2 y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+2 y = 0 \]

[[_3rd_order, _missing_x]]

0.069

7483

\[ {}x^{5} y^{\prime }+y^{5} = 0 \]

[_separable]

4.889

7484

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

[_separable]

1.158

7485

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

[_separable]

1.344

7486

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

[_separable]

1.820

7487

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

[_separable]

1.617

7488

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

[_separable]

2.049

7489

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

[_separable]

1.331

7490

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

[_separable]

1.387

7491

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

[_separable]

1.364

7492

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

[_separable]

1.192

7493

\[ {}y^{\prime } y = x +1 \]
i.c.

[_separable]

2.991

7494

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

[_separable]

1.529

7495

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

[_separable]

1.819

7496

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

[_separable]

2.516

7497

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

[_separable]

2.085

7498

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

[_separable]

1.874

7499

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

[[_2nd_order, _missing_y]]

0.620

7500

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

[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]]

1.790