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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.757

22502

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.732

22503

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

[_Clairaut]

3.120

22504

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

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

8.065

22505

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

[_quadrature]

10.281

22506

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

[_quadrature]

6.769

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)]‘]]

6.879

22508

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

[_separable]

9.889

22509

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

[_quadrature]

0.270

22510

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

[_quadrature]

0.236

22511

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

[_linear]

11.810

22512

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

[_separable]

13.102

22513

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

[_quadrature]

0.536

22514

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

[_separable]

7.330

22515

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

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

29.408

22516

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

[[_linear, ‘class A‘]]

8.148

22517

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

[_linear]

4.749

22518

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

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

13.278

22519

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

[[_linear, ‘class A‘]]

3.569

22520

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

[_linear]

6.279

22521

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

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

13.252

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‘]]

16.740

22523

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

[[_linear, ‘class A‘]]

5.457

22524

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

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

41.917

22525

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

[_rational, _Bernoulli]

6.164

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‘]]

12.047

22527

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

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

16.425

22528

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

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

6.590

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’)‘]

34.497

22530

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

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

47.430

22531

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

[_linear]

6.500

22532

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

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

50.194

22533

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

[[_linear, ‘class A‘]]

8.259

22534

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

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

12.026

22535

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

[_linear]

16.080

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]‘]]

28.161

22537

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

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

20.019

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]

6.621

22539

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

[_linear]

4.792

22540

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

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

24.705

22541

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

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

12.638

22542

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

[[_2nd_order, _missing_y]]

1.803

22543

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

[_separable]

7.935

22544

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

[_separable]

6.931

22545

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

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

18.408

22546

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

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

37.996

22547

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

[_linear]

14.392

22548

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

[_separable]

8.542

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]

5.516

22550

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

[_quadrature]

5.971

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‘]]

33.207

22552

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

[[_linear, ‘class A‘]]

4.741

22553

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

[_linear]

11.770

22554

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

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

57.296

22555

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

[_separable]

10.206

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‘]]

37.852

22557

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

[_separable]

15.060

22558

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

[[_linear, ‘class A‘]]

3.957

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‘]]

91.246

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]

12.393

22561

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

[[_linear, ‘class A‘]]

5.536

22562

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

[_separable]

10.099

22563

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

[[_linear, ‘class A‘]]

4.609

22564

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

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

12.892

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]]

3.633

22566

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

[_separable]

23.494

22567

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

[_linear]

4.437

22568

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

[_separable]

19.984

22569

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

[_linear]

7.204

22570

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

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

25.041

22571

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

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

18.254

22572

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

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

35.946

22573

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

[_linear]

16.964

22574

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

[[_2nd_order, _missing_y]]

2.834

22575

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

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

7.957

22576

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

[[_1st_order, _with_exponential_symmetries]]

7.954

22577

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

[[_linear, ‘class A‘]]

5.569

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]]

3.095

22579

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

[[_3rd_order, _quadrature]]

0.464

22580

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

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

65.322

22581

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

[_linear]

7.352

22582

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

[_separable]

9.953

22583

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

[_quadrature]

6.455

22584

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

[[_linear, ‘class A‘]]

8.955

22585

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

[_linear]

4.481

22586

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

[_separable]

15.723

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‘]]

67.201

22588

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

[_Bernoulli]

6.290

22589

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

[_linear]

4.187

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]]

2.824

22591

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

[[_homogeneous, ‘class C‘], _Riccati]

11.848

22592

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

[_separable]

15.366

22593

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

[_Bernoulli]

16.502

22594

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

[_separable]

69.458

22595

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

[_separable]

11.714

22596

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

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

13.992

22597

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

7.961

22599

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

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

7.787

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]]

0.485