2.2.175 Problems 17401 to 17500

Table 2.367: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

17401

\begin{align*} y^{\prime \prime }+100 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}

[[_2nd_order, _missing_x]]

2.737

17402

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

[[_2nd_order, _missing_x]]

0.598

17403

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

[[_2nd_order, _missing_x]]

0.595

17404

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.570

17405

\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.563

17406

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

[[_2nd_order, _missing_x]]

0.532

17407

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

[[_2nd_order, _missing_x]]

0.593

17408

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

[[_2nd_order, _missing_x]]

0.602

17409

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

[[_2nd_order, _missing_x]]

0.557

17410

\begin{align*} 6 y^{\prime \prime }+5 y^{\prime }+y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.342

17411

\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.451

17412

\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.339

17413

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

[[_Emden, _Fowler]]

3.329

17414

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

[[_Emden, _Fowler]]

2.413

17415

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

[[_2nd_order, _missing_x]]

1.783

17416

\begin{align*} y^{\prime \prime }+6 y^{\prime }+2 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.387

17417

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.340

17418

\begin{align*} y^{\prime \prime }-6 y^{\prime }-16 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.339

17419

\begin{align*} y^{\prime \prime }-16 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

2.823

17420

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.378

17421

\begin{align*} {y^{\prime \prime }}^{2}-5 y^{\prime \prime } y^{\prime }+4 y^{2}&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.109

17422

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

[[_2nd_order, _missing_x]]

0.043

17423

\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= a \\ y^{\prime }\left (0\right ) &= b \\ \end{align*}

[[_2nd_order, _missing_x]]

0.427

17424

\begin{align*} y^{\prime \prime }+y&=8 \,{\mathrm e}^{2 t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.559

17425

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=-{\mathrm e}^{-9 t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.544

17426

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

[[_2nd_order, _with_linear_symmetries]]

0.632

17427

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

[[_2nd_order, _with_linear_symmetries]]

0.516

17428

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

[[_2nd_order, _with_linear_symmetries]]

0.658

17429

\begin{align*} y^{\prime \prime }+2 y^{\prime }&=3-4 t \\ \end{align*}

[[_2nd_order, _missing_y]]

1.352

17430

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.602

17431

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.807

17432

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.919

17433

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.566

17434

\begin{align*} y^{\prime \prime }&=3 t^{4}-2 t \\ \end{align*}

[[_2nd_order, _quadrature]]

1.273

17435

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=2 t \,{\mathrm e}^{-2 t} \sin \left (3 t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.975

17436

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

[[_2nd_order, _missing_x]]

0.503

17437

\begin{align*} 5 y^{\prime \prime }+y^{\prime }-4 y&=-3 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.525

17438

\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=32 t \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.533

17439

\begin{align*} 16 y^{\prime \prime }-8 y^{\prime }-15 y&=75 t \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.553

17440

\begin{align*} y^{\prime \prime }+2 y^{\prime }+26 y&=-338 t \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.603

17441

\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=-32 t^{2} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.546

17442

\begin{align*} 8 y^{\prime \prime }+6 y^{\prime }+y&=5 t^{2} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.546

17443

\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&=-256 t^{3} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.562

17444

\begin{align*} y^{\prime \prime }-2 y^{\prime }&=52 \sin \left (3 t \right ) \\ \end{align*}

[[_2nd_order, _missing_y]]

1.415

17445

\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=25 \sin \left (2 t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.628

17446

\begin{align*} y^{\prime \prime }-9 y&=54 t \sin \left (2 t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.905

17447

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=-78 \cos \left (3 t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.579

17448

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=-32 t^{2} \cos \left (2 t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.431

17449

\begin{align*} y^{\prime \prime }-y^{\prime }-20 y&=-2 \,{\mathrm e}^{t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.552

17450

\begin{align*} y^{\prime \prime }-4 y^{\prime }-5 y&=-648 t^{2} {\mathrm e}^{5 t} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.684

17451

\begin{align*} y^{\prime \prime }-7 y^{\prime }+12 y&=-2 t^{3} {\mathrm e}^{4 t} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.599

17452

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

[[_2nd_order, _missing_y]]

1.660

17453

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

[[_2nd_order, _missing_y]]

1.477

17454

\begin{align*} y^{\prime \prime }+4 y^{\prime }&=-24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \\ \end{align*}

[[_2nd_order, _missing_y]]

1.512

17455

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

[[_2nd_order, _missing_y]]

1.366

17456

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

[[_2nd_order, _quadrature]]

1.888

17457

\begin{align*} y^{\prime \prime }+3 y^{\prime }&=18 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}

[[_2nd_order, _missing_x]]

2.809

17458

\begin{align*} y^{\prime \prime }-y&=4 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

2.743

17459

\begin{align*} y^{\prime \prime }-4 y&=32 t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.660

17460

\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=-2 \\ y \left (0\right ) &= {\frac {2}{3}} \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.652

17461

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=3 t \\ y \left (0\right ) &= {\frac {23}{12}} \\ y^{\prime }\left (0\right ) &= -{\frac {3}{2}} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.673

17462

\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=4 \\ y \left (0\right ) &= {\frac {5}{4}} \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.800

17463

\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=t \,{\mathrm e}^{-t} \\ y \left (0\right ) &= -{\frac {5}{16}} \\ y^{\prime }\left (0\right ) &= {\frac {9}{16}} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.701

17464

\begin{align*} y^{\prime \prime }+6 y^{\prime }+25 y&=-1 \\ y \left (0\right ) &= -{\frac {1}{25}} \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.736

17465

\begin{align*} y^{\prime \prime }-3 y^{\prime }&=-{\mathrm e}^{3 t}-2 t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= {\frac {8}{9}} \\ \end{align*}

[[_2nd_order, _missing_y]]

1.782

17466

\begin{align*} y^{\prime \prime }-y^{\prime }&=-3 t -4 \,{\mathrm e}^{2 t} t^{2} \\ y \left (0\right ) &= -{\frac {7}{2}} \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_y]]

2.068

17467

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

[[_2nd_order, _missing_y]]

1.580

17468

\begin{align*} y^{\prime \prime }+4 y^{\prime }&=-24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_y]]

1.750

17469

\begin{align*} y^{\prime \prime }-3 y^{\prime }&={\mathrm e}^{-3 t}-{\mathrm e}^{3 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _missing_y]]

1.744

17470

\begin{align*} y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

4.155

17471

\begin{align*} y^{\prime \prime }+9 \pi ^{2} y&=\left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 2 t -2 \pi & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

17.358

17472

\begin{align*} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 10 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

4.532

17473

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

[[_linear, ‘class A‘]]

3.580

17474

\begin{align*} y+y^{\prime }&=\cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}

[[_linear, ‘class A‘]]

2.975

17475

\begin{align*} -y+y^{\prime }&={\mathrm e}^{4 t} \\ y \left (0\right ) &= 0 \\ \end{align*}

[[_linear, ‘class A‘]]

3.007

17476

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

[[_linear, ‘class A‘]]

2.532

17477

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

[[_linear, ‘class A‘]]

4.636

17478

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=f \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= a \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.139

17479

\begin{align*} x^{\prime \prime }+9 x&=\sin \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.839

17480

\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+37 y&=\cos \left (3 t \right ) \\ y \left (0\right ) &= a \\ y^{\prime }\left (\pi \right ) &= a \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.849

17481

\begin{align*} y^{\prime \prime }+4 y&=1 \\ \end{align*}

[[_2nd_order, _missing_x]]

3.638

17482

\begin{align*} y^{\prime \prime }+16 y^{\prime }&=t \\ \end{align*}

[[_2nd_order, _missing_y]]

1.319

17483

\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&={\mathrm e}^{3 t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.523

17484

\begin{align*} y^{\prime \prime }+16 y&=2 \cos \left (4 t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.640

17485

\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&=2 t \,{\mathrm e}^{-2 t} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.572

17486

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.995

17487

\begin{align*} y^{\prime \prime }+16 y&=\csc \left (4 t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.180

17488

\begin{align*} y^{\prime \prime }+16 y&=\cot \left (4 t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.344

17489

\begin{align*} y^{\prime \prime }+2 y^{\prime }+50 y&={\mathrm e}^{-t} \csc \left (7 t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.013

17490

\begin{align*} y^{\prime \prime }+6 y^{\prime }+25 y&={\mathrm e}^{-3 t} \left (\sec \left (4 t \right )+\csc \left (4 t \right )\right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.980

17491

\begin{align*} y^{\prime \prime }-2 y^{\prime }+26 y&={\mathrm e}^{t} \left (\sec \left (5 t \right )+\csc \left (5 t \right )\right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.194

17492

\begin{align*} y^{\prime \prime }+12 y^{\prime }+37 y&={\mathrm e}^{-6 t} \csc \left (t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.126

17493

\begin{align*} y^{\prime \prime }-6 y^{\prime }+34 y&={\mathrm e}^{3 t} \tan \left (5 t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.148

17494

\begin{align*} y^{\prime \prime }-10 y^{\prime }+34 y&={\mathrm e}^{5 t} \cot \left (3 t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.975

17495

\begin{align*} y^{\prime \prime }-12 y^{\prime }+37 y&={\mathrm e}^{6 t} \sec \left (t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.080

17496

\begin{align*} y^{\prime \prime }-8 y^{\prime }+17 y&={\mathrm e}^{4 t} \sec \left (t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.132

17497

\begin{align*} y^{\prime \prime }-9 y&=\frac {1}{1+{\mathrm e}^{3 t}} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.688

17498

\begin{align*} y^{\prime \prime }-25 y&=\frac {1}{1-{\mathrm e}^{5 t}} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.742

17499

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.714

17500

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.684