2.2.256 Problems 25501 to 25600

Table 2.529: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

25501

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

[_separable]

5.278

25502

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

[_separable]

5.008

25503

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

[_separable]

13.158

25504

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

[_separable]

7.372

25505

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

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

26.016

25506

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

[‘x=_G(y,y’)‘]

23.996

25507

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

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

29.609

25508

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

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

21.307

25509

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

[_separable]

0.289

25510

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

[_linear]

0.466

25511

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

[[_2nd_order, _missing_x]]

0.907

25512

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

[[_2nd_order, _missing_y]]

0.260

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]]

0.524

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]]

0.304

25515

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

[[_2nd_order, _missing_x]]

4.746

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]]

46.082

25517

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

[[_2nd_order, _missing_x]]

3.230

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]]

1.742

25519

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.802

25520

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

[[_high_order, _missing_x]]

0.066

25521

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

[[_2nd_order, _with_linear_symmetries]]

0.619

25522

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

[[_2nd_order, _with_linear_symmetries]]

0.733

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]]

3.042

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]]

0.751

25525

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.769

25526

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.247

25527

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.818

25528

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

[[_2nd_order, _missing_x]]

81.775

25529

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

[[_2nd_order, _quadrature]]

1.306

25530

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

[[_2nd_order, _quadrature]]

1.237

25531

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

[[_2nd_order, _with_linear_symmetries]]

1.495

25532

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

[_quadrature]

2.276

25533

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

[[_2nd_order, _missing_x]]

4.598

25534

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

[[_2nd_order, _missing_x]]

1.613

25535

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

[[_2nd_order, _missing_x]]

0.336

25536

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

[[_high_order, _missing_x]]

0.092

25537

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

[[_2nd_order, _missing_x]]

0.371

25538

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

[[_high_order, _missing_x]]

0.102

25539

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

[[_2nd_order, _missing_x]]

1.007

25540

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

[[_2nd_order, _missing_x]]

0.409

25541

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

[[_2nd_order, _missing_x]]

0.438

25542

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

[[_high_order, _missing_x]]

0.112

25543

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

[[_2nd_order, _quadrature]]

1.438

25544

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

[[_2nd_order, _quadrature]]

2.253

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]]

2.543

25546

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.598

25547

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

[[_2nd_order, _with_linear_symmetries]]

0.669

25548

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

[[_2nd_order, _with_linear_symmetries]]

0.768

25549

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

[[_2nd_order, _with_linear_symmetries]]

0.586

25550

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

[[_2nd_order, _with_linear_symmetries]]

0.740

25551

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

[[_high_order, _with_linear_symmetries]]

1.482

25552

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

[[_2nd_order, _with_linear_symmetries]]

0.654

25553

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

[[_3rd_order, _with_linear_symmetries]]

0.432

25554

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

[[_2nd_order, _with_linear_symmetries]]

1.242

25555

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

[[_2nd_order, _with_linear_symmetries]]

1.074

25556

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

[[_2nd_order, _missing_x]]

3.692

25557

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

[[_2nd_order, _with_linear_symmetries]]

1.093

25558

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

[[_2nd_order, _missing_x]]

1.949

25559

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

[[_2nd_order, _with_linear_symmetries]]

1.730

25560

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

[[_2nd_order, _missing_x]]

1.491

25561

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

[[_2nd_order, _missing_x]]

2.852

25562

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

[[_2nd_order, _with_linear_symmetries]]

2.062

25563

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

[[_2nd_order, _missing_x]]

1.458

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]]

1.451

25565

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

[[_2nd_order, _missing_x]]

1.488

25566

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.593

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]]

0.732

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]]

0.733

25569

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

[[_2nd_order, _with_linear_symmetries]]

0.710

25570

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

[[_2nd_order, _with_linear_symmetries]]

0.701

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]]

1.069

25572

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.954

25573

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.701

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]]

3.375

25575

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.787

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]]

1.356

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]]

1.451

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]]

0.655

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]]

0.770

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]]

0.753

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]]

2.425

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]]

1.960

25583

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

[[_2nd_order, _missing_x]]

3.984

25584

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

[[_2nd_order, _missing_x]]

1.806

25585

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

[[_2nd_order, _quadrature]]

1.161

25586

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

[[_2nd_order, _with_linear_symmetries]]

0.586

25587

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

[[_2nd_order, _with_linear_symmetries]]

0.590

25588

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.627

25589

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.638

25590

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

[[_2nd_order, _with_linear_symmetries]]

0.594

25591

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

[[_2nd_order, _with_linear_symmetries]]

0.586

25592

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.627

25593

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

[[_2nd_order, _missing_y]]

1.254

25594

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

[[_2nd_order, _missing_y]]

1.291

25595

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.700

25596

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.929

25597

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

[[_2nd_order, _with_linear_symmetries]]

0.595

25598

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.600

25599

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.608

25600

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.834