2.2.185 Problems 18401 to 18500

Table 2.371: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

18401

\[ {}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=3 y \end {array}\right ] \]

system_of_ODEs

0.408

18402

\[ {}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=4 x-5 y \end {array}\right ] \]

system_of_ODEs

0.565

18403

\[ {}\left [\begin {array}{c} x^{\prime }=-3 x+4 y \\ y^{\prime }=-2 x+3 y \end {array}\right ] \]

system_of_ODEs

0.453

18404

\[ {}\left [\begin {array}{c} x^{\prime }=5 x+2 y \\ y^{\prime }=-17 x-5 y \end {array}\right ] \]

system_of_ODEs

0.548

18405

\[ {}\left [\begin {array}{c} x^{\prime }=-4 x-y \\ y^{\prime }=x-2 y \end {array}\right ] \]

system_of_ODEs

0.443

18406

\[ {}\left [\begin {array}{c} x^{\prime }=4 x-3 y \\ y^{\prime }=8 x-6 y \end {array}\right ] \]

system_of_ODEs

0.503

18407

\[ {}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=5 x+2 y \end {array}\right ] \]

system_of_ODEs

0.576

18408

\[ {}x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5} = 0 \]

[[_2nd_order, _missing_x]]

2.263

18409

\[ {}x^{\prime } = 3 t^{2}+4 t \]
i.c.

[_quadrature]

0.694

18410

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

[_quadrature]

0.315

18411

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

[_quadrature]

0.760

18412

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

[_quadrature]

0.773

18413

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

[_quadrature]

0.751

18414

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

[_quadrature]

1.139

18415

\[ {}x^{\prime } = x^{2}-3 x+2 \]
i.c.

[_quadrature]

1.634

18416

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

[_quadrature]

0.943

18417

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

[_quadrature]

1.176

18418

\[ {}x^{\prime } = \sqrt {x^{2}-1} \]
i.c.

[_quadrature]

4.401

18419

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

[_quadrature]

1.583

18420

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

[_quadrature]

3.045

18421

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

[_separable]

3.939

18422

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

[_separable]

1.881

18423

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

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

2.768

18424

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

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

18.569

18425

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

[[_linear, ‘class A‘]]

1.872

18426

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

[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]

1.487

18427

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

[[_linear, ‘class A‘]]

1.358

18428

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

[_separable]

1.790

18429

\[ {}x^{\prime }-x \tan \left (t \right ) = 4 \sin \left (t \right ) \]

[_linear]

1.965

18430

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

[_linear]

2.533

18431

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

[_separable]

2.663

18432

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

[_linear]

1.352

18433

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

[_linear]

1.165

18434

\[ {}t^{2} x^{\prime \prime }-6 t x^{\prime }+12 x = 0 \]

[[_Emden, _Fowler]]

0.937

18435

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

[_quadrature]

0.856

18436

\[ {}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=x+2 y \end {array}\right ] \]

system_of_ODEs

0.426

18437

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

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

1.024

18438

\[ {}x^{\prime \prime }-5 x^{\prime }+6 x = 0 \]

[[_2nd_order, _missing_x]]

0.842

18439

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

[[_2nd_order, _missing_x]]

0.963

18440

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

[[_2nd_order, _missing_x]]

2.105

18441

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

[[_2nd_order, _missing_x]]

1.895

18442

\[ {}x^{\prime \prime }-3 x^{\prime }+2 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.154

18443

\[ {}x^{\prime \prime }+x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2.052

18444

\[ {}x^{\prime \prime }+2 x^{\prime }+x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.323

18445

\[ {}x^{\prime \prime }-2 x^{\prime }+2 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2.143

18446

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

[[_2nd_order, _with_linear_symmetries]]

1.182

18447

\[ {}x^{\prime \prime }-x = {\mathrm e}^{t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

1.219

18448

\[ {}x^{\prime \prime }+2 x^{\prime }+4 x = {\mathrm e}^{t} \cos \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

67.877

18449

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

[[_2nd_order, _linear, _nonhomogeneous]]

78.315

18450

\[ {}x^{\prime \prime }+4 x^{\prime }+3 x = t \sin \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.694

18451

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.517

18452

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

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

0.133

18453

\[ {}y^{\prime }+c y = a \]

[_quadrature]

0.872

18454

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

[[_2nd_order, _with_linear_symmetries]]

0.808

18455

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

[[_2nd_order, _with_linear_symmetries]]

1.395

18456

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

[_separable]

5.431

18457

\[ {}v^{\prime \prime } = \left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}} \]

[[_2nd_order, _missing_x]]

3.306

18458

\[ {}v^{\prime }+u^{2} v = \sin \left (u \right ) \]

[_linear]

1.676

18459

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

[NONE]

0.435

18460

\[ {}v^{\prime }+\frac {2 v}{u} = 3 \]

[_linear]

2.504

18461

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

[_separable]

3.977

18462

\[ {}y^{\prime }+\sqrt {\frac {1-y^{2}}{-x^{2}+1}} = 0 \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

26.539

18463

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

[_separable]

1.033

18464

\[ {}x^{\prime } = k \left (A -n x\right ) \left (M -m x\right ) \]

[_quadrature]

7.715

18465

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

[_separable]

1.595

18466

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

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

39.711

18467

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

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

75.541

18468

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

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

3.614

18469

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

[_separable]

38.659

18470

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

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

12.075

18471

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

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

34.314

18472

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

[_exact]

3.225

18473

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

[_separable]

1.483

18474

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

[_linear]

1.446

18475

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

[_Bernoulli]

35.661

18476

\[ {}p^{\prime } = \frac {p+a \,t^{3}-2 p t^{2}}{t \left (-t^{2}+1\right )} \]

[_linear]

1.175

18477

\[ {}\left (T \ln \left (t \right )-1\right ) T = t T^{\prime } \]

[_Bernoulli]

2.440

18478

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

[_linear]

2.412

18479

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

[_Bernoulli]

6.082

18480

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

[_rational, _dAlembert]

0.978

18481

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

[_quadrature]

0.347

18482

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

[_quadrature]

0.521

18483

\[ {}\sqrt {t^{2}+T} = T^{\prime } \]

[[_homogeneous, ‘class G‘]]

4.308

18484

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

[_quadrature]

0.352

18485

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

[[_homogeneous, ‘class C‘], _Riccati]

1.482

18486

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

[[_2nd_order, _missing_x]]

1.655

18487

\[ {}\sec \left (\theta \right )^{2} = \frac {m s^{\prime }}{k} \]

[_quadrature]

0.350

18488

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

[[_2nd_order, _missing_x]]

2.990

18489

\[ {}\phi ^{\prime \prime } = \frac {4 \pi n c}{\sqrt {v_{0}^{2}+\frac {2 e \left (\phi -V_{0} \right )}{m}}} \]

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

58.454

18490

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

[_separable]

2.460

18491

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

[_separable]

2.016

18492

\[ {}v^{\prime }+\frac {2 v}{u} = 3 v \]

[_separable]

1.684

18493

\[ {}\sqrt {-u^{2}+1}\, v^{\prime } = 2 u \sqrt {1-v^{2}} \]

[_separable]

9.791

18494

\[ {}\sqrt {1+v^{\prime }} = \frac {{\mathrm e}^{u}}{2} \]

[_quadrature]

0.517

18495

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

[_separable]

2.138

18496

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

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

39.421

18497

\[ {}v^{\prime }+2 v u = 2 u \]

[_separable]

1.485

18498

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

[_separable]

2.920

18499

\[ {}u \ln \left (u \right ) v^{\prime }+\sin \left (v\right )^{2} = 1 \]

[_separable]

3.790

18500

\[ {}4 y {y^{\prime }}^{3}-2 x^{2} {y^{\prime }}^{2}+4 x y y^{\prime }+x^{3} = 16 y^{2} \]

[[_1st_order, _with_linear_symmetries]]

115.909