2.2.26 Problems 2501 to 2600

Table 2.53: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

2501

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

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

2.984

2502

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

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

4.343

2503

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

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

102.989

2504

\[ {}\left (t -\sqrt {t y}\right ) y^{\prime } = y \]

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

15.571

2505

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

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

38.855

2506

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

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

5.091

2507

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

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

37.174

2508

\[ {}1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime } = 0 \]

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

3.427

2509

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

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

2.025

2510

\[ {}2 t \sin \left (y\right )+{\mathrm e}^{t} y^{3}+\left (t^{2} \cos \left (y\right )+3 \,{\mathrm e}^{t} y^{2}\right ) y^{\prime } = 0 \]

[_exact]

3.816

2511

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

[_exact]

1.895

2512

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

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

13.168

2513

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

[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]]

2.683

2514

\[ {}2 t y^{3}+3 t^{2} y^{2} y^{\prime } = 0 \]
i.c.

[_separable]

2.755

2515

\[ {}2 t \cos \left (y\right )+3 t^{2} y+\left (2 t^{2}+2 y\right ) y^{\prime } = 0 \]
i.c.

[‘x=_G(y,y’)‘]

40.476

2516

\[ {}3 t^{2}+4 t y+\left (2 t^{2}+2 y\right ) y^{\prime } = 0 \]
i.c.

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

1.754

2517

\[ {}2 t -2 \,{\mathrm e}^{t y} \sin \left (2 t \right )+{\mathrm e}^{t y} \cos \left (2 t \right ) y+\left (-3+{\mathrm e}^{t y} t \cos \left (2 t \right )\right ) y^{\prime } = 0 \]
i.c.

[_exact]

38.186

2518

\[ {}3 t y+y^{2}+\left (t^{2}+t y\right ) y^{\prime } = 0 \]
i.c.

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

388.704

2519

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

[_separable]

1.868

2520

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

[[_Riccati, _special]]

1.583

2521

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

[_Riccati]

2.157

2522

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

[_Riccati]

4.968

2523

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

[_Riccati]

16.151

2524

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

[[_Riccati, _special]]

14.900

2525

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

[_Riccati]

1.630

2526

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

[_Riccati]

1.633

2527

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

[_Riccati]

1.631

2528

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

[‘y=_G(x,y’)‘]

1.566

2529

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

[_Abel]

1.101

2530

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

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

3.263

2531

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

[‘y=_G(x,y’)‘]

1.839

2532

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

[‘y=_G(x,y’)‘]

2.066

2533

\[ {}y^{\prime } = \frac {\left (1+\cos \left (4 t \right )\right ) y}{4}-\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800} \]
i.c.

[_Bernoulli]

5.563

2534

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

[[_Riccati, _special]]

1.938

2535

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

[_separable]

1.670

2536

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

[_separable]

9.391

2537

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

[_separable]

6.415

2538

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

[‘y=_G(x,y’)‘]

1.504

2539

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

[_Riccati]

1.681

2540

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

[_rational]

1.425

2541

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

[[_1st_order, _with_linear_symmetries], _Bernoulli]

1.794

2542

\[ {}y^{\prime } = t y^{3}-y \]
i.c.

[_Bernoulli]

5.082

2543

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.447

2544

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.158

2545

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

[[_2nd_order, _missing_x]]

2.024

2546

\[ {}6 y^{\prime \prime }-7 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

0.855

2547

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

[[_2nd_order, _missing_x]]

1.115

2548

\[ {}3 y^{\prime \prime }+6 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

1.119

2549

\[ {}y^{\prime \prime }-3 y^{\prime }-4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.406

2550

\[ {}2 y^{\prime \prime }+y^{\prime }-10 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.478

2551

\[ {}5 y^{\prime \prime }+5 y^{\prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.633

2552

\[ {}y^{\prime \prime }-6 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.497

2553

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.908

2554

\[ {}t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y = 0 \]

[[_Emden, _Fowler]]

1.665

2555

\[ {}t^{2} y^{\prime \prime }+5 t y^{\prime }-2 y = 0 \]
i.c.

[[_Emden, _Fowler]]

2.482

2556

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

[[_2nd_order, _missing_x]]

2.142

2557

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

[[_2nd_order, _missing_x]]

2.046

2558

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

[[_2nd_order, _missing_x]]

1.961

2559

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

[[_2nd_order, _missing_x]]

2.097

2560

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

[[_2nd_order, _missing_x]]

3.049

2561

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2.655

2562

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

[[_2nd_order, _missing_x]]

3.992

2563

\[ {}3 y^{\prime \prime }-2 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

4.530

2564

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

[[_2nd_order, _missing_x]]

1.697

2565

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

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

1.178

2566

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

[[_Emden, _Fowler]]

2.666

2567

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

0.946

2568

\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

0.959

2569

\[ {}9 y^{\prime \prime }+6 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.378

2570

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

[[_2nd_order, _missing_x]]

1.329

2571

\[ {}6 y^{\prime \prime }+2 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

3.521

2572

\[ {}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.407

2573

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

[[_2nd_order, _with_linear_symmetries]]

0.104

2574

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

[[_2nd_order, _with_linear_symmetries]]

0.094

2575

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

[_Gegenbauer]

0.106

2576

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

[[_2nd_order, _with_linear_symmetries]]

0.096

2577

\[ {}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y = 0 \]

[_Gegenbauer]

0.120

2578

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

[[_2nd_order, _with_linear_symmetries]]

0.109

2579

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

[[_2nd_order, _with_linear_symmetries]]

0.141

2580

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

[[_2nd_order, _with_linear_symmetries]]

0.114

2581

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.064

2582

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

[[_Emden, _Fowler]]

0.987

2583

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.868

2584

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.234

2585

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.262

2586

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.165

2587

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.835

2588

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = t^{{5}/{2}} {\mathrm e}^{-2 t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.359

2589

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \sqrt {t +1} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2.125

2590

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.556

2591

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

0.918

2592

\[ {}y^{\prime \prime }+p \left (t \right ) y^{\prime }+q \left (t \right ) y = t +1 \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.449

2593

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

[[_2nd_order, _with_linear_symmetries]]

1.601

2594

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

[[_2nd_order, _linear, _nonhomogeneous]]

4.174

2595

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = t \,{\mathrm e}^{\alpha t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.287

2596

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.231

2597

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

[[_2nd_order, _with_linear_symmetries]]

29.601

2598

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

[[_2nd_order, _with_linear_symmetries]]

1.109

2599

\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = t^{2} {\mathrm e}^{7 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.182

2600

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

[[_2nd_order, _linear, _nonhomogeneous]]

4.836