2.2.215 Problems 21401 to 21500

Table 2.447: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

21401

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

[_separable]

5.855

21402

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

[‘y=_G(x,y’)‘]

5.343

21403

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

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

18.795

21404

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

[_linear]

4.217

21405

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

[_linear]

3.654

21406

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

[_separable]

5.376

21407

\begin{align*} y^{\prime }+\left (b x +a \right ) y&=f \left (x \right ) \\ y \left (0\right ) &= y_{0} \\ \end{align*}

[_linear]

4.293

21408

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

[_quadrature]

2.474

21409

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

[_linear]

6.700

21410

\begin{align*} y^{\prime }-3 y&=6 \\ \end{align*}

[_quadrature]

1.671

21411

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

[_separable]

5.109

21412

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

[_separable]

7.315

21413

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

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

11.022

21414

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

[_rational]

5.300

21415

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

[_separable]

0.293

21416

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

[_quadrature]

3.789

21417

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

[‘y=_G(x,y’)‘]

3.723

21418

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

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

7.417

21419

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

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

10.441

21420

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

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

26.128

21421

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

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

29.859

21422

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

[‘y=_G(x,y’)‘]

5.592

21423

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

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

17.450

21424

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

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

10.450

21425

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

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

90.392

21426

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

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

10.890

21427

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

[_separable]

5.230

21428

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

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

31.317

21429

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

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

30.898

21430

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

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

29.921

21431

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

[_quadrature]

4.520

21432

\begin{align*} y^{\prime }+q \left (x \right ) y&=0 \\ y \left (\textit {x\_0} \right ) &= y_{0} \\ \end{align*}

[_separable]

6.516

21433

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

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

32.639

21434

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

[_quadrature]

2.411

21435

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

[[_linear, ‘class A‘]]

2.592

21436

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

[_linear]

7.746

21437

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

[[_linear, ‘class A‘]]

2.881

21438

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

[_linear]

7.063

21439

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

[_separable]

6.343

21440

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

[_linear]

5.661

21441

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

[[_linear, ‘class A‘]]

3.040

21442

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

[_separable]

5.323

21443

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

[_linear]

3.545

21444

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

[_linear]

4.080

21445

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

[_linear]

7.333

21446

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

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

3.746

21447

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

[_quadrature]

2.631

21448

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

[[_linear, ‘class A‘]]

3.576

21449

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

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

90.994

21450

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

[_linear]

3.237

21451

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

[_rational]

20.517

21452

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

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

15.003

21453

\begin{align*} 6 y^{2}-x \left (2 x^{3}+y\right ) y^{\prime }&=0 \\ \end{align*}

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

83.277

21454

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

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

5.401

21455

\begin{align*} y^{\prime }-\frac {3 y}{x}&=x^{4} y^{{1}/{3}} \\ \end{align*}

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

22.167

21456

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

[_Bernoulli]

8.954

21457

\begin{align*} y \left (6 y^{2}-x -1\right )+2 y^{\prime } x&=0 \\ \end{align*}

[_rational, _Bernoulli]

7.944

21458

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

[_separable]

9.565

21459

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

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

2.322

21460

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

[[_2nd_order, _with_linear_symmetries]]

0.911

21461

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

[_rational, _Riccati]

178.212

21462

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

[_rational, _Riccati]

108.092

21463

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

[_Riccati]

5.473

21464

\begin{align*} y^{\prime }&={\mathrm e}^{2 x}+\left (2+\frac {5 \,{\mathrm e}^{x}}{2}\right ) y+y^{2} \\ \end{align*}

[_Riccati]

96.223

21465

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

[[_homogeneous, ‘class C‘], _Riccati]

9.763

21466

\begin{align*} y^{\prime }&=1+x +x^{2} \cos \left (x \right )-\left (1+4 \cos \left (x \right ) x \right ) y+2 y^{2} \cos \left (x \right ) \\ \end{align*}

[_Riccati]

137.664

21467

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

[_quadrature]

2.527

21468

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

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

0.912

21469

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

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

0.805

21470

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

1.013

21471

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

[_quadrature]

1.669

21472

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

[_quadrature]

12.188

21473

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

[_quadrature]

11.513

21474

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

[[_2nd_order, _missing_y]]

0.800

21475

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

[[_2nd_order, _missing_x]]

0.342

21476

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

[[_3rd_order, _missing_x]]

0.111

21477

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

[[_2nd_order, _missing_x]]

5.187

21478

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

[[_2nd_order, _with_linear_symmetries]]

0.704

21479

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.184

21480

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

[[_2nd_order, _missing_x]]

4.934

21481

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

[[_2nd_order, _missing_x]]

3.444

21482

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

[[_2nd_order, _missing_x]]

0.343

21483

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

[[_2nd_order, _missing_x]]

0.487

21484

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

[[_2nd_order, _quadrature]]

0.989

21485

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

[[_2nd_order, _missing_x]]

0.477

21486

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

[[_2nd_order, _missing_x]]

0.477

21487

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

[[_2nd_order, _missing_x]]

0.398

21488

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

[[_2nd_order, _missing_x]]

2.233

21489

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

[[_2nd_order, _missing_x]]

2.435

21490

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

[[_2nd_order, _missing_x]]

0.424

21491

\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.385

21492

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

[[_2nd_order, _missing_x]]

0.514

21493

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

[[_2nd_order, _missing_x]]

0.618

21494

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.682

21495

\begin{align*} y^{\prime \prime }-2 y^{\prime }+10 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.611

21496

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.517

21497

\begin{align*} y^{\prime \prime }+16 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

[[_2nd_order, _missing_x]]

2.605

21498

\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ y \left (0\right ) &= -3 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.625

21499

\begin{align*} y^{\prime \prime }-\frac {6 y^{\prime }}{5}+\frac {9 y}{25}&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.740

21500

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.107