2.2.226 Problems 22501 to 22600

Table 2.469: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

22501

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.671

22502

\begin{align*} y&=y^{\prime } x +1+4 {y^{\prime }}^{2} \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.601

22503

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

[_Clairaut]

2.282

22504

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

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

5.619

22505

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

[_quadrature]

7.581

22506

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

[_quadrature]

4.931

22507

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

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

5.182

22508

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

[_separable]

7.306

22509

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

[_quadrature]

0.120

22510

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

[_quadrature]

0.111

22511

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

[_linear]

8.875

22512

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

[_separable]

9.951

22513

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

[_quadrature]

0.387

22514

\begin{align*} s^{2} t s^{\prime }+t^{2}+4&=0 \\ \end{align*}

[_separable]

5.760

22515

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

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

22.029

22516

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

[[_linear, ‘class A‘]]

6.374

22517

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

[_linear]

3.772

22518

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

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

10.229

22519

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

[[_linear, ‘class A‘]]

2.781

22520

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

[_linear]

4.947

22521

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

[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

9.940

22522

\begin{align*} r^{2} \sin \left (t \right )&=\left (2 r \cos \left (t \right )+10\right ) r^{\prime } \\ \end{align*}

[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]

12.270

22523

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

[[_linear, ‘class A‘]]

4.537

22524

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

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

9.405

22525

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

[_rational, _Bernoulli]

4.843

22526

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

[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

8.968

22527

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

[[_homogeneous, ‘class G‘], _rational]

12.504

22528

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

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

4.841

22529

\begin{align*} \tan \left (y\right )-\tan \left (y\right )^{2} \cos \left (x \right )-x \sec \left (y\right )^{2} y^{\prime }&=0 \\ \end{align*}

[‘y=_G(x,y’)‘]

36.327

22530

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

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

40.125

22531

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

[_linear]

5.377

22532

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

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

63.412

22533

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

[[_linear, ‘class A‘]]

6.093

22534

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

[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]

8.764

22535

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

[_linear]

11.753

22536

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

[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

22.993

22537

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

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

15.196

22538

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

[_separable]

5.023

22539

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

[_linear]

3.188

22540

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

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

17.425

22541

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

[[_homogeneous, ‘class G‘], _rational]

9.121

22542

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

[[_2nd_order, _missing_y]]

1.174

22543

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

[_separable]

6.263

22544

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

[_separable]

5.416

22545

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

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

14.044

22546

\begin{align*} s^{\prime }&=\sqrt {\frac {1-t}{1-s}} \\ s \left (1\right ) &= 0 \\ \end{align*}

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

34.981

22547

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

[_linear]

10.930

22548

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

[_separable]

6.293

22549

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

[_exact]

4.528

22550

\begin{align*} n^{\prime }&=-a n \\ n \left (0\right ) &= n_{0} \\ \end{align*}

[_quadrature]

4.549

22551

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

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

24.984

22552

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

[[_linear, ‘class A‘]]

3.648

22553

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

[_linear]

8.147

22554

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

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

49.942

22555

\begin{align*} q^{\prime }&=\frac {p \,{\mathrm e}^{p^{2}-q^{2}}}{q} \\ \end{align*}

[_separable]

7.729

22556

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

[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]

37.820

22557

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

[_separable]

11.513

22558

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

[[_linear, ‘class A‘]]

3.191

22559

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

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

88.298

22560

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

[_separable]

9.210

22561

\begin{align*} u^{\prime }&=-a \left (u-100 t \right ) \\ u \left (0\right ) &= 0 \\ \end{align*}

[[_linear, ‘class A‘]]

4.116

22562

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

[_separable]

7.447

22563

\begin{align*} i^{\prime }+3 i&=10 \sin \left (t \right ) \\ i \left (0\right ) &= 0 \\ \end{align*}

[[_linear, ‘class A‘]]

3.625

22564

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

[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]

9.326

22565

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

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

2.097

22566

\begin{align*} x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\ \end{align*}

[_separable]

18.058

22567

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

[_linear]

3.480

22568

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

[_separable]

14.652

22569

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

[_linear]

5.712

22570

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

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

18.525

22571

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

[[_homogeneous, ‘class G‘], _rational]

13.887

22572

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

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

31.458

22573

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

[_linear]

11.676

22574

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

[[_2nd_order, _missing_y]]

1.634

22575

\begin{align*} i^{\prime }&=\frac {i t^{2}}{t^{3}-i^{3}} \\ \end{align*}

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

5.454

22576

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

[[_1st_order, _with_exponential_symmetries]]

5.717

22577

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

[[_linear, ‘class A‘]]

3.925

22578

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

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

2.050

22579

\begin{align*} x^{4} y^{\prime \prime \prime }+1&=0 \\ \end{align*}

[[_3rd_order, _quadrature]]

0.286

22580

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

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

52.950

22581

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

[_linear]

5.221

22582

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

[_separable]

7.029

22583

\begin{align*} r^{3} r^{\prime }&=\sqrt {a^{8}-r^{8}} \\ \end{align*}

[_quadrature]

4.370

22584

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

[[_linear, ‘class A‘]]

6.421

22585

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

[_linear]

3.520

22586

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

[_separable]

10.316

22587

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

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

53.916

22588

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

[_Bernoulli]

4.347

22589

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

[_linear]

2.940

22590

\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{r}&=4-4 r \\ u \left (1\right ) &= 15 \\ u^{\prime }\left (1\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_y]]

1.847

22591

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

[[_homogeneous, ‘class C‘], _Riccati]

8.024

22592

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

[_separable]

10.895

22593

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

[_Bernoulli]

11.382

22594

\begin{align*} y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\ \end{align*}

[_separable]

54.088

22595

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

[_separable]

8.475

22596

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

[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]

9.396

22597

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

[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]

39.455

22598

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

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

5.473

22599

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

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

5.450

22600

\begin{align*} y^{\prime \prime \prime \prime }&=2 y^{\prime \prime \prime }+24 x \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}

[[_high_order, _missing_y]]

0.296