2.2.256 Problems 25501 to 25600

Table 2.525: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

25501

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

[_separable]

2.143

25502

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

[_separable]

2.113

25503

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

[_separable]

5.298

25504

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

[_separable]

2.559

25505

\begin{align*} y^{\prime }&=\frac {-3 t^{2}-2 y^{2}}{4 t y+6 y^{2}} \\ \end{align*}

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

12.593

25506

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

[‘x=_G(y,y’)‘]

30.301

25507

\begin{align*} y^{\prime }&=\frac {4 t -y}{t -6 y} \\ \end{align*}

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

4.990

25508

\begin{align*} y^{\prime }&=-\frac {3 t^{2}+2 y^{2}}{4 t y+6 y^{2}} \\ \end{align*}

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

10.343

25509

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

[_separable]

0.132

25510

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

[_linear]

0.267

25511

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

[[_2nd_order, _missing_x]]

0.348

25512

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

[[_2nd_order, _missing_y]]

0.221

25513

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

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]

0.375

25514

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

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]

0.375

25515

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

[[_2nd_order, _missing_x]]

1.921

25516

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

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

49.859

25517

\begin{align*} y^{\prime \prime }&=-9 y \\ \end{align*}

[[_2nd_order, _missing_x]]

1.943

25518

\begin{align*} y^{\prime \prime }&=-9 y \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.810

25519

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.558

25520

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

[[_high_order, _missing_x]]

0.074

25521

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

[[_2nd_order, _with_linear_symmetries]]

0.414

25522

\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{i \omega t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.505

25523

\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]]

1.481

25524

\begin{align*} y^{\prime \prime }+100 y&=\cos \left (\omega t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.583

25525

\begin{align*} y^{\prime \prime }+100 y&=\cos \left (\omega t \right )-\sin \left (\omega t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.595

25526

\begin{align*} m y^{\prime \prime }+k y&=\delta \left (-t +T \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.837

25527

\begin{align*} m y^{\prime \prime }+k y&=f \left (t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.614

25528

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

[[_2nd_order, _missing_x]]

12.042

25529

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

[[_2nd_order, _quadrature]]

0.526

25530

\begin{align*} y^{\prime \prime }&={\mathrm e}^{i \omega t} \\ \end{align*}

[[_2nd_order, _quadrature]]

0.599

25531

\begin{align*} m y^{\prime \prime }-k y&={\mathrm e}^{i \omega t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.614

25532

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

[_quadrature]

0.354

25533

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

[[_2nd_order, _missing_x]]

0.660

25534

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

[[_2nd_order, _missing_x]]

0.204

25535

\begin{align*} 2 y^{\prime \prime }+8 y^{\prime }+6 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.155

25536

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

[[_high_order, _missing_x]]

0.055

25537

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

[[_2nd_order, _missing_x]]

0.200

25538

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

[[_high_order, _missing_x]]

0.057

25539

\begin{align*} 4 y^{\prime \prime }+B y^{\prime }+16 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.241

25540

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

[[_2nd_order, _missing_x]]

0.188

25541

\begin{align*} y^{\prime \prime }-2 y^{\prime }+10 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.191

25542

\begin{align*} y^{\left (8\right )}&=y \\ \end{align*}

[[_high_order, _missing_x]]

0.073

25543

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

[[_2nd_order, _quadrature]]

0.750

25544

\begin{align*} y^{\prime \prime }&=\operatorname {Direct}_{t} \\ \end{align*}

[[_2nd_order, _quadrature]]

0.838

25545

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

[[_2nd_order, _missing_x]]

0.617

25546

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.271

25547

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

[[_2nd_order, _with_linear_symmetries]]

0.312

25548

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

[[_2nd_order, _with_linear_symmetries]]

0.418

25549

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

[[_2nd_order, _with_linear_symmetries]]

0.260

25550

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

[[_2nd_order, _with_linear_symmetries]]

0.532

25551

\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }+y&={\mathrm e}^{i \omega t} \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.553

25552

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

[[_2nd_order, _with_linear_symmetries]]

0.328

25553

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

[[_3rd_order, _with_linear_symmetries]]

0.299

25554

\begin{align*} y^{\prime \prime }+c y&={\mathrm e}^{i \omega t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.575

25555

\begin{align*} y^{\prime \prime }+5 y^{\prime }+c y&={\mathrm e}^{i \omega t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.605

25556

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

[[_2nd_order, _missing_x]]

0.690

25557

\begin{align*} y^{\prime \prime }+k y&={\mathrm e}^{i \omega t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.546

25558

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

[[_2nd_order, _missing_x]]

0.352

25559

\begin{align*} m y^{\prime \prime }+b y^{\prime }+k y&={\mathrm e}^{c t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.406

25560

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

[[_2nd_order, _missing_x]]

0.292

25561

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

[[_2nd_order, _missing_x]]

0.504

25562

\begin{align*} y^{\prime \prime }+\omega _{n}^{2} y&={\mathrm e}^{i \omega t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.915

25563

\begin{align*} y^{\prime \prime }+2 z \omega _{n} y^{\prime }+\omega _{n}^{2} y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.301

25564

\begin{align*} y^{\prime \prime }+2 z \omega _{n} y^{\prime }+\omega _{n}^{2} y&={\mathrm e}^{c t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.350

25565

\begin{align*} y^{\prime \prime }+b y^{\prime }+c y&=f \\ \end{align*}

[[_2nd_order, _missing_x]]

0.364

25566

\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=5 \cos \left (\omega t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.301

25567

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.370

25568

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.407

25569

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

[[_2nd_order, _with_linear_symmetries]]

0.278

25570

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

[[_2nd_order, _with_linear_symmetries]]

0.504

25571

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

[[_2nd_order, _missing_x]]

0.314

25572

\begin{align*} m y^{\prime \prime }+k y&=\cos \left (\sqrt {\frac {k}{m}}\, t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.996

25573

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.045

25574

\begin{align*} 4 a y^{\prime \prime }+b y^{\prime }+\frac {c y}{4}&=f \left (t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.033

25575

\begin{align*} g^{\prime \prime }-3 g^{\prime }+2 g&=\delta \left (t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.342

25576

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.449

25577

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.495

25578

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

[[_2nd_order, _missing_x]]

0.335

25579

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

[[_2nd_order, _missing_x]]

0.361

25580

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

[[_2nd_order, _missing_x]]

0.418

25581

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

[[_2nd_order, _missing_x]]

0.554

25582

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

[[_2nd_order, _with_linear_symmetries]]

0.548

25583

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

[[_2nd_order, _missing_x]]

0.612

25584

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

[[_2nd_order, _missing_x]]

0.752

25585

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

[[_2nd_order, _quadrature]]

0.639

25586

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

[[_2nd_order, _with_linear_symmetries]]

0.250

25587

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

[[_2nd_order, _with_linear_symmetries]]

0.276

25588

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.314

25589

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.299

25590

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

[[_2nd_order, _with_linear_symmetries]]

0.264

25591

\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{2 t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.274

25592

\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{2 t} t \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.294

25593

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

[[_2nd_order, _missing_y]]

0.757

25594

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

[[_2nd_order, _missing_y]]

0.778

25595

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.330

25596

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.357

25597

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

[[_2nd_order, _with_linear_symmetries]]

0.274

25598

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.282

25599

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.276

25600

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.323