2.2.216 Problems 21501 to 21600

Table 2.445: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

21501

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.083

21502

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.080

21503

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }-3 y^{\prime }+18 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.084

21504

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ y^{\prime \prime }\left (\pi \right ) &= 1 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.180

21505

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }-3 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.103

21506

\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.108

21507

\begin{align*} y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+18 y^{\prime \prime }-20 y^{\prime }+8 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.095

21508

\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+24 y^{\prime \prime }+32 y^{\prime }+16 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.097

21509

\begin{align*} y^{\prime }-y&=x \\ \end{align*}

[[_linear, ‘class A‘]]

1.972

21510

\begin{align*} y^{\prime }-y&=3 x^{2}+x \\ \end{align*}

[[_linear, ‘class A‘]]

5.480

21511

\begin{align*} y^{\prime }-5 y&=3 \,{\mathrm e}^{x}-2 x +1 \\ \end{align*}

[[_linear, ‘class A‘]]

6.129

21512

\begin{align*} y^{\prime }-5 y&={\mathrm e}^{x} x^{3}-x \,{\mathrm e}^{5 x} \\ \end{align*}

[[_linear, ‘class A‘]]

5.543

21513

\begin{align*} y^{\prime }-5 y&=\sin \left (x \right ) \left (x -1\right )+\left (x +1\right ) \cos \left (x \right ) \\ \end{align*}

[[_linear, ‘class A‘]]

5.740

21514

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=\sin \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.465

21515

\begin{align*} y^{\prime \prime }&=9 x^{2}+2 x -1 \\ \end{align*}

[[_2nd_order, _quadrature]]

1.577

21516

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.541

21517

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=x^{2}+2 x \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.454

21518

\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=x^{3}+3 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.672

21519

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=2 x^{3}+5 x^{2}-7 x +2 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.468

21520

\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.685

21521

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.440

21522

\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (x \right )+\sin \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.160

21523

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=2 \cos \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.691

21524

\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=3 \sin \left (x +\frac {\pi }{4}\right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.724

21525

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=2 x^{2}+{\mathrm e}^{x}+2 x \,{\mathrm e}^{x}+4 \,{\mathrm e}^{3 x} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.030

21526

\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \sin \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.673

21527

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.457

21528

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\left (x^{2}-1\right ) {\mathrm e}^{2 x}+\left (3 x +4\right ) {\mathrm e}^{x} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.155

21529

\begin{align*} y^{\prime \prime }+y^{\prime }+8 y&=\left (10 x^{2}+21 x +9\right ) \sin \left (3 x \right )+x \cos \left (3 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

2.953

21530

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=2 \sin \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.430

21531

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=2 x -40 \cos \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.691

21532

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=2 \,{\mathrm e}^{x}-10 \sin \left (x \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.873

21533

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=3 \,{\mathrm e}^{x} \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.181

21534

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y&=4 \sin \left (2 x \right ) \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.187

21535

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=2 x \,{\mathrm e}^{-x} \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.178

21536

\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=3 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{-x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}

[[_3rd_order, _missing_y]]

0.320

21537

\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime }&=3 x^{2}+4 \sin \left (x \right )-2 \cos \left (x \right ) \\ \end{align*}

[[_high_order, _missing_y]]

0.334

21538

\begin{align*} y^{\prime }+\frac {4 y}{x}&=x^{4} \\ \end{align*}

[_linear]

5.556

21539

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=x^{2}+2 x \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.400

21540

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {1}{1+{\mathrm e}^{-x}} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.449

21541

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.373

21542

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.837

21543

\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.442

21544

\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \tan \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.729

21545

\begin{align*} 4 y+y^{\prime \prime }&=\sec \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.829

21546

\begin{align*} y^{\prime \prime }+y&=\csc \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.565

21547

\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.630

21548

\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.598

21549

\begin{align*} a_{0} \left (x \right ) y^{\prime \prime }+a_{1} \left (x \right ) y^{\prime }+a_{2} \left (x \right ) y&=f \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

2.839

21550

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{x} \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.171

21551

\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=\sec \left (x \right ) \\ \end{align*}

[[_3rd_order, _missing_y]]

0.510

21552

\begin{align*} y^{\prime \prime \prime \prime }&=5 x \\ \end{align*}

[[_high_order, _quadrature]]

0.145

21553

\begin{align*} y^{\prime \prime } x +y^{\prime }-\frac {4 y}{x}&=x^{3}+x \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

3.368

21554

\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=6 \left (x^{2}+1\right )^{2} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

1.560

21555

\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{3} \sin \left (x \right ) \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

3.547

21556

\begin{align*} \left (x^{2}-3 x +1\right ) y^{\prime \prime }-\left (x^{2}-x -2\right ) y^{\prime }+\left (2 x -3\right ) y&=x \left (x^{2}-3 x +1\right )^{2} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.298

21557

\begin{align*} y^{\prime \prime } x -\frac {\left (1-2 x \right ) y^{\prime }}{1-x}+\frac {\left (x^{2}-3 x +1\right ) y}{1-x}&=\left (1-x \right )^{2} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

1.744

21558

\begin{align*} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 y^{\prime } x -8 y&=4 \ln \left (x \right ) \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.381

21559

\begin{align*} -y^{\prime }+y^{\prime \prime } x&=3 x^{2} \\ \end{align*}

[[_2nd_order, _missing_y]]

1.268

21560

\begin{align*} y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}

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

23.627

21561

\begin{align*} {y^{\prime }}^{2}-4 y&=0 \\ \end{align*}

[_quadrature]

1.705

21562

\begin{align*} y-\frac {y^{\prime } x}{2}-\frac {x}{2 y^{\prime }}&=0 \\ \end{align*}

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

1.676

21563

\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.915

21564

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}&=2 \\ \end{align*}

[[_2nd_order, _missing_y]]

0.867

21565

\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\ \end{align*}

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

23.924

21566

\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.273

21567

\begin{align*} y^{\prime \prime }&=\cos \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _quadrature]]

1.504

21568

\begin{align*} y^{\prime \prime }+k^{2} y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

4.260

21569

\begin{align*} y^{\prime \prime }-2 s y^{\prime }-2 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.253

21570

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.077

21571

\begin{align*} 2 y^{\prime \prime }+5 y^{\prime }-12 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.233

21572

\begin{align*} y^{\prime \prime }-y&=2 x +{\mathrm e}^{2 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.418

21573

\begin{align*} y^{\prime \prime \prime \prime }+12 y^{\prime \prime \prime }+54 y^{\prime \prime }+108 y^{\prime }+81 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.088

21574

\begin{align*} y^{\left (6\right )}+8 y^{\prime \prime \prime }&=a \,{\mathrm e}^{x} \\ \end{align*}

[[_high_order, _missing_y]]

0.211

21575

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=16 x^{3} {\mathrm e}^{3 x} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.701

21576

\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=a \sin \left (b x \right ) \\ \end{align*}

[[_3rd_order, _missing_y]]

0.179

21577

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x}+7 x -2 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.599

21578

\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+16 y^{\prime \prime }&=96 \,{\mathrm e}^{-4 x} \\ \end{align*}

[[_high_order, _missing_y]]

0.188

21579

\begin{align*} y^{\prime \prime }-2 a y^{\prime }+\left (a^{2}+b^{2}\right ) y&=f \left (x \right ) \\ y \left (x_{0} \right ) &= y_{0} \\ y^{\prime }\left (x_{0} \right ) &= y_{1} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

5.630

21580

\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{2 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.584

21581

\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.560

21582

\begin{align*} y^{\prime \prime \prime }+y^{\prime }+y&=\sin \left (3 x \right ) \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.200

21583

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+3 y^{\prime }+9 y&={\mathrm e}^{3 x} \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.176

21584

\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{x} \cos \left (x \right ) x \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.921

21585

\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&={\mathrm e}^{2 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.398

21586

\begin{align*} y^{\prime \prime }-y&=x^{2}-x +1 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.386

21587

\begin{align*} 4 y+4 y^{\prime }+y^{\prime \prime }+y^{\prime \prime \prime }&=\cos \left (2 x \right ) \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.513

21588

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{2 x} \left (x +1\right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.540

21589

\begin{align*} y^{\prime \prime \prime \prime }-y&=\cos \left (2 x \right ) \\ \end{align*}

[[_high_order, _linear, _nonhomogeneous]]

0.161

21590

\begin{align*} y^{\left (5\right )}+y^{\prime \prime }&=x^{5}-3 x^{2} \\ \end{align*}

[[_high_order, _missing_y]]

0.204

21591

\begin{align*} y^{\prime \prime }+y^{\prime }-12 y&={\mathrm e}^{x} x^{2} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.427

21592

\begin{align*} 2 x^{\prime }-3 x-2 y^{\prime }&=t \\ 2 x^{\prime }+3 x+2 y^{\prime }+8 y&=2 \\ \end{align*}

system_of_ODEs

1.195

21593

\begin{align*} y^{\prime }&=\frac {x +y+1}{x +2 y+3} \\ \end{align*}

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

108.659

21594

\begin{align*} y^{\prime }&=\frac {x +y+1}{x +y+2} \\ \end{align*}

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

16.361

21595

\begin{align*} x +2 y+3+\left (2 x +4 y-1\right ) y^{\prime }&=0 \\ \end{align*}

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

8.163

21596

\begin{align*} y^{\prime }&=\frac {2 x +y}{y} \\ \end{align*}

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

34.476

21597

\begin{align*} 2 x +y-3+\left (x +y-1\right ) y^{\prime }&=0 \\ \end{align*}

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

15.631

21598

\begin{align*} x -2 y+1+\left (4 x -3 y-6\right ) y^{\prime }&=0 \\ \end{align*}

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

85.507

21599

\begin{align*} x^{2} u^{\prime \prime }-3 x u^{\prime }+13 u&=0 \\ u \left (1\right ) &= -1 \\ u^{\prime }\left (1\right ) &= 1 \\ \end{align*}

[[_Emden, _Fowler]]

3.480

21600

\begin{align*} \left (x -1\right )^{2} y^{\prime \prime }-4 \left (x -1\right ) y^{\prime }-14 y&=x^{3}-3 x^{2}+3 x -8 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

1.562