2.2.66 Problems 6501 to 6600

Table 2.133: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

6501

\[ {}y^{\prime \prime }+6 y^{\prime }+10 y = 50 x \]

[[_2nd_order, _with_linear_symmetries]]

13.428

6502

\[ {}x^{\prime \prime }+2 x^{\prime }+2 x = 85 \sin \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

5.243

6503

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.464

6504

\[ {}\frac {x^{\prime \prime }}{2} = -48 x \]
i.c.

[[_2nd_order, _missing_x]]

3.380

6505

\[ {}x^{\prime \prime }+5 x^{\prime }+6 x = \cos \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.750

6506

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

[[_2nd_order, _with_linear_symmetries]]

1.139

6507

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

[[_2nd_order, _with_linear_symmetries]]

1.010

6508

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.455

6509

\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 2 \sin \left (\frac {t}{2}\right )-\cos \left (\frac {t}{2}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

51.975

6510

\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 64 \,{\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

12.145

6511

\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 50 t^{3}-36 t^{2}-63 t +18 \]

[[_2nd_order, _linear, _nonhomogeneous]]

19.491

6512

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 2 x \,{\mathrm e}^{-x} \]

[[_3rd_order, _linear, _nonhomogeneous]]

0.119

6513

\[ {}y^{\prime \prime } = 9 x^{2}+2 x -1 \]

[[_2nd_order, _quadrature]]

1.859

6514

\[ {}y^{\prime \prime }-5 y = 2 \,{\mathrm e}^{5 x} \]

[[_2nd_order, _with_linear_symmetries]]

1.302

6515

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

[[_linear, ‘class A‘]]

2.303

6516

\[ {}y^{\prime }-5 y = 3 \,{\mathrm e}^{x}-2 x +1 \]

[[_linear, ‘class A‘]]

1.532

6517

\[ {}y^{\prime }-5 y = x^{2} {\mathrm e}^{x}-x \,{\mathrm e}^{5 x} \]

[[_linear, ‘class A‘]]

1.795

6518

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

[[_2nd_order, _with_linear_symmetries]]

1.224

6519

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

1.125

6520

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.445

6521

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

[[_2nd_order, _with_linear_symmetries]]

1.158

6522

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.157

6523

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

[[_linear, ‘class A‘]]

1.283

6524

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

[[_linear, ‘class A‘]]

1.440

6525

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

[[_linear, ‘class A‘]]

2.247

6526

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

[[_3rd_order, _with_linear_symmetries]]

0.124

6527

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

[[_3rd_order, _missing_y]]

0.560

6528

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

[[_3rd_order, _missing_y]]

0.306

6529

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.273

6530

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

[[_2nd_order, _with_linear_symmetries]]

1.005

6531

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.590

6532

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

[[_2nd_order, _with_linear_symmetries]]

1.874

6533

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

[_linear]

1.625

6534

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

[[_high_order, _quadrature]]

0.098

6535

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.229

6536

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.856

6537

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

[[_2nd_order, _with_linear_symmetries]]

1.015

6538

\[ {}y^{\prime \prime }-60 y^{\prime }-900 y = 5 \,{\mathrm e}^{10 x} \]

[[_2nd_order, _with_linear_symmetries]]

1.443

6539

\[ {}y^{\prime \prime }-7 y^{\prime } = -3 \]

[[_2nd_order, _missing_x]]

2.072

6540

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

2.178

6541

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

[[_2nd_order, _missing_y]]

0.778

6542

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

[_linear]

1.679

6543

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

[_quadrature]

0.341

6544

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

[_quadrature]

0.325

6545

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

[[_linear, ‘class A‘]]

0.438

6546

\[ {}y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.185

6547

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.292

6548

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

[[_2nd_order, _with_linear_symmetries]]

0.319

6549

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.479

6550

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.365

6551

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

[[_2nd_order, _missing_x]]

0.441

6552

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-2 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.399

6553

\[ {}y^{\prime \prime }+5 y^{\prime }-3 y = \operatorname {Heaviside}\left (x -4\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.861

6554

\[ {}y^{\prime \prime \prime }-y = 5 \]
i.c.

[[_3rd_order, _missing_x]]

0.556

6555

\[ {}y^{\prime \prime \prime \prime }-y = 0 \]
i.c.

[[_high_order, _missing_x]]

0.411

6556

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

[[_3rd_order, _linear, _nonhomogeneous]]

0.360

6557

\[ {}x^{\prime \prime }+4 x^{\prime }+4 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.226

6558

\[ {}q^{\prime \prime }+9 q^{\prime }+14 q = \frac {\sin \left (t \right )}{2} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.397

6559

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

[[_2nd_order, _with_linear_symmetries]]

0.556

6560

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

[[_Emden, _Fowler]]

0.086

6561

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

[[_Emden, _Fowler]]

0.305

6562

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.350

6563

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.347

6564

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

[[_2nd_order, _with_linear_symmetries]]

0.374

6565

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

[[_Emden, _Fowler]]

0.230

6566

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.344

6567

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

[[_Emden, _Fowler]]

0.288

6568

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

[[_2nd_order, _with_linear_symmetries]]

0.367

6569

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

[_separable]

2.296

6570

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

[_separable]

4.148

6571

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

2.608

6572

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

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

74.972

6573

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

[[_2nd_order, _missing_x]]

0.976

6574

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

[[_2nd_order, _with_linear_symmetries]]

1.246

6575

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

[[_2nd_order, _missing_x]]

2.106

6576

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

[[_2nd_order, _with_linear_symmetries]]

1.175

6577

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

[[_2nd_order, _missing_x]]

0.866

6578

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.199

6579

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

[_separable]

2.309

6580

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

[_separable]

1.936

6581

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

[_separable]

3.013

6582

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

[_separable]

2.101

6583

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

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

1.975

6584

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

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

4.375

6585

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

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

1.707

6586

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

[[_homogeneous, ‘class G‘], _dAlembert]

123.365

6587

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

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

1.895

6588

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

[_separable]

2.075

6589

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

[_separable]

1.736

6590

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

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

4.980

6591

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

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

9.289

6592

\[ {}3 y-7 x +7+\left (3-3 x +7 y\right ) y^{\prime } = 0 \]

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

3.471

6593

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

[_separable]

1.689

6594

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

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

69.890

6595

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

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

2.055

6596

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

[_separable]

2.434

6597

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

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

12.596

6598

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

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

1.911

6599

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

[_separable]

2.680

6600

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

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

1647.947