2.2.226 Problems 22501 to 22600

Table 2.465: 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]

0.263

22502

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.157

22503

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

[_Clairaut]

1.409

22504

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

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

1.117

22505

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

[_quadrature]

0.979

22506

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

[_quadrature]

0.593

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)]‘]]

0.508

22508

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

[_separable]

2.227

22509

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

[_quadrature]

0.087

22510

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

[_quadrature]

0.080

22511

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

[_linear]

1.658

22512

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

[_separable]

2.412

22513

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

[_quadrature]

0.156

22514

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

[_separable]

1.657

22515

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

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

4.006

22516

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

[[_linear, ‘class A‘]]

2.316

22517

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

[_linear]

1.428

22518

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

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

3.764

22519

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

[[_linear, ‘class A‘]]

0.694

22520

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

[_linear]

1.920

22521

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

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

1.887

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‘]]

3.100

22523

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

[[_linear, ‘class A‘]]

1.456

22524

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

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

1.840

22525

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

[_rational, _Bernoulli]

2.142

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‘]]

1.977

22527

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

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

2.317

22528

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

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

0.375

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’)‘]

28.130

22530

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

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

4.066

22531

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

[_linear]

2.947

22532

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

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

5.146

22533

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

[[_linear, ‘class A‘]]

2.788

22534

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

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

1.362

22535

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

[_linear]

2.873

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]‘]]

5.813

22537

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

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

3.858

22538

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

[_separable]

2.957

22539

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

[_linear]

1.180

22540

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

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

3.231

22541

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

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

2.141

22542

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

[[_2nd_order, _missing_y]]

1.082

22543

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

[_separable]

2.116

22544

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

[_separable]

3.249

22545

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

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

4.086

22546

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

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

5.336

22547

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

[_linear]

2.899

22548

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

[_separable]

2.187

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]

2.590

22550

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

[_quadrature]

0.654

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‘]]

5.626

22552

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

[[_linear, ‘class A‘]]

1.168

22553

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

[_linear]

2.831

22554

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

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

4.799

22555

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

[_separable]

2.587

22556

\begin{align*} \left (3 y \cos \left (x \right )+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‘]]

36.920

22557

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

[_separable]

4.297

22558

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

[[_linear, ‘class A‘]]

0.995

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‘]]

66.686

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]

1.729

22561

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

[[_linear, ‘class A‘]]

0.755

22562

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

[_separable]

1.566

22563

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

[[_linear, ‘class A‘]]

1.580

22564

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

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

1.109

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]]

0.449

22566

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

[_separable]

2.570

22567

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

[_linear]

1.712

22568

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

[_separable]

2.558

22569

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

[_linear]

2.563

22570

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

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

3.700

22571

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

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

1.963

22572

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

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

3.508

22573

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

[_linear]

1.968

22574

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

[[_2nd_order, _missing_y]]

0.722

22575

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

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

0.439

22576

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

[[_1st_order, _with_exponential_symmetries]]

1.531

22577

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

[[_linear, ‘class A‘]]

1.038

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]]

0.275

22579

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

[[_3rd_order, _quadrature]]

0.105

22580

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

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

5.577

22581

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

[_linear]

2.851

22582

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

[_separable]

1.003

22583

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

[_quadrature]

1.065

22584

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

[[_linear, ‘class A‘]]

1.949

22585

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

[_linear]

1.559

22586

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

[_separable]

2.766

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‘]]

3.785

22588

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

[_Bernoulli]

1.112

22589

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

[_linear]

1.104

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]]

0.729

22591

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

[[_homogeneous, ‘class C‘], _Riccati]

1.174

22592

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

[_separable]

2.507

22593

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

[_Bernoulli]

2.950

22594

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

[_separable]

13.725

22595

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

[_separable]

2.491

22596

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

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

1.183

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)]‘]]

6.598

22598

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

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

1.357

22599

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

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

1.054

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]]

0.146