2.2.275 Problems 27401 to 27500

Table 2.567: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

27401

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

[_dAlembert]

60.549

27402

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

13.472

27403

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

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

4.543

27404

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

1.839

27405

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

20.111

27406

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

1.017

27407

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

[_linear]

3.883

27408

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

[_separable]

8.821

27409

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

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

13.151

27410

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

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

7.076

27411

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

[_separable]

11.781

27412

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

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

15.375

27413

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

[_quadrature]

0.865

27414

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

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

9.477

27415

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

[_separable]

5.506

27416

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.679

27417

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

[[_1st_order, _with_linear_symmetries]]

5.517

27418

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

[_separable]

7.136

27419

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

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

1.913

27420

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

[_separable]

6.932

27421

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

[[_1st_order, _with_exponential_symmetries]]

4.648

27422

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

1.047

27423

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

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

90.806

27424

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

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

1.656

27425

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

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

24.808

27426

\begin{align*} 2 y y^{\prime } x^{3}+3 y^{2} x^{2}+7&=0 \\ \end{align*}

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

9.790

27427

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

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

46.026

27428

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

[_separable]

4.285

27429

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

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

10.490

27430

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

[_separable]

13.983

27431

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

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

13.457

27432

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

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

17.766

27433

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

[_linear]

3.132

27434

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

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

4.126

27435

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

[_separable]

13.075

27436

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

[_Bernoulli]

6.747

27437

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

[_separable]

11.102

27438

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

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

10.555

27439

\begin{align*} 3 {y^{\prime }}^{3}-y^{\prime } x +1&=0 \\ \end{align*}

[_quadrature]

3.181

27440

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

[_Bernoulli]

14.270

27441

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

[_exact]

4.612

27442

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

[_rational, _dAlembert]

4.268

27443

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

[_linear]

3.159

27444

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

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

49.671

27445

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

20.691

27446

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

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

10.709

27447

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

[_Bernoulli]

6.905

27448

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

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

4.510

27449

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

[[_1st_order, _with_linear_symmetries]]

1.247

27450

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

[_Bernoulli]

10.710

27451

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

[_Bernoulli]

6.981

27452

\begin{align*} \left (4 y x -3\right ) y^{\prime }+y^{2}&=1 \\ \end{align*}

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

37.430

27453

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

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

42.611

27454

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

[_Bernoulli]

11.186

27455

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

[_quadrature]

97.660

27456

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

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

31.366

27457

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

[[_homogeneous, ‘class C‘], _Riccati]

13.587

27458

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

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

13.055

27459

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

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

4.631

27460

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

[_Bernoulli]

8.912

27461

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

[[_homogeneous, ‘class G‘]]

16.423

27462

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

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

8.422

27463

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

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

8.065

27464

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

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

31.881

27465

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

[_quadrature]

2.760

27466

\begin{align*} \left (2 x^{2} y-3 y^{2}\right ) y^{\prime }&=6 x^{2}-2 x y^{2}+1 \\ \end{align*}

[_exact, _rational]

4.434

27467

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

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

36.697

27468

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

[_Bernoulli]

7.901

27469

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

[_dAlembert]

2.585

27470

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

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

8.764

27471

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

[_linear]

3.992

27472

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

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

11.310

27473

\begin{align*} y^{2}+x^{2} {y^{\prime }}^{5}&=x y \left ({y^{\prime }}^{2}+{y^{\prime }}^{3}\right ) \\ \end{align*}

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

2.404

27474

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

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

7.355

27475

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

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

20.391

27476

\begin{align*} 2 x^{2} y+2 \sqrt {1+y^{2} x^{4}}+x^{3} y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘]]

19.690

27477

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

[_rational, _Bernoulli]

7.647

27478

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

[_dAlembert]

66.413

27479

\begin{align*} 2 x +3 y-1+\left (4 x +6 y-5\right ) y^{\prime }&=0 \\ \end{align*}

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

16.928

27480

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

[_rational]

4.682

27481

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

[_quadrature]

5.075

27482

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

[_Bernoulli]

9.400

27483

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

[[_homogeneous, ‘class G‘]]

19.451

27484

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

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

11.582

27485

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

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

5.954

27486

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

[[_homogeneous, ‘class G‘], _Clairaut]

4.459

27487

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

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

3.575

27488

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

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

5.711

27489

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

[_linear]

3.945

27490

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

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

64.536

27491

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

[_rational, _Bernoulli]

6.001

27492

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

[_rational, _dAlembert]

133.638

27493

\begin{align*} \left (2 x +y+5\right ) y^{\prime }&=3 x +6 \\ \end{align*}

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

259.418

27494

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

[‘y=_G(x,y’)‘]

9.492

27495

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

[[_homogeneous, ‘class G‘]]

230.046

27496

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

[_rational, _Bernoulli]

5.797

27497

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

[[_1st_order, _with_linear_symmetries]]

3.543

27498

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

[[_homogeneous, ‘class G‘]]

233.819

27499

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

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

16.171

27500

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

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

49.469