2.2.79 Problems 7801 to 7900

Table 2.159: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

7801

\[ {}x \left (x^{2}-4\right ) y^{\prime } = 1 \]
i.c.

[_quadrature]

0.826

7802

\[ {}\left (x +1\right ) \left (x^{2}+1\right ) y^{\prime } = 2 x^{2}+x \]
i.c.

[_quadrature]

1.296

7803

\[ {}y^{\prime } = 2 x y+1 \]

[_linear]

1.116

7804

\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

0.827

7805

\[ {}y^{\prime } = \frac {2 x y^{2}}{1-x^{2} y} \]

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

1.768

7806

\[ {}2 y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+2 y = 0 \]

[[_3rd_order, _missing_x]]

0.054

7807

\[ {}x^{5} y^{\prime }+y^{5} = 0 \]

[_separable]

8.090

7808

\[ {}y^{\prime } = 4 x y \]

[_separable]

1.644

7809

\[ {}y^{\prime }+\tan \left (x \right ) y = 0 \]

[_separable]

1.756

7810

\[ {}\left (x^{2}+1\right ) y^{\prime }+1+y^{2} = 0 \]

[_separable]

2.250

7811

\[ {}y \ln \left (y\right )-x y^{\prime } = 0 \]

[_separable]

1.983

7812

\[ {}x y^{\prime } = \left (-4 x^{2}+1\right ) \tan \left (y\right ) \]

[_separable]

2.027

7813

\[ {}y^{\prime } \sin \left (y\right ) = x^{2} \]

[_separable]

1.504

7814

\[ {}y^{\prime }-\tan \left (x \right ) y = 0 \]

[_separable]

1.811

7815

\[ {}x y y^{\prime } = y-1 \]

[_separable]

1.611

7816

\[ {}x y^{2}-x^{2} y^{\prime } = 0 \]

[_separable]

1.576

7817

\[ {}y y^{\prime } = x +1 \]
i.c.

[_separable]

3.462

7818

\[ {}x^{2} y^{\prime } = y \]
i.c.

[_separable]

2.237

7819

\[ {}\frac {y^{\prime }}{x^{2}+1} = \frac {x}{y} \]
i.c.

[_separable]

2.204

7820

\[ {}y^{2} y^{\prime } = x +2 \]
i.c.

[_separable]

3.232

7821

\[ {}y^{\prime } = y^{2} x^{2} \]
i.c.

[_separable]

2.659

7822

\[ {}y^{\prime } \left (y+1\right ) = -x^{2}+1 \]
i.c.

[_separable]

2.071

7823

\[ {}\frac {y^{\prime \prime }}{y^{\prime }} = x^{2} \]

[[_2nd_order, _missing_y]]

0.786

7824

\[ {}y^{\prime \prime } y^{\prime } = x \left (x +1\right ) \]

[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]]

1.427

7825

\[ {}y^{\prime }-x y = 0 \]

[_separable]

0.221

7826

\[ {}y^{\prime }+x y = x \]

[_separable]

0.240

7827

\[ {}y^{\prime }+y = \frac {1}{1+{\mathrm e}^{2 x}} \]

[_linear]

0.258

7828

\[ {}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}+x^{2} \]

[[_linear, ‘class A‘]]

0.247

7829

\[ {}2 y-x^{3} = x y^{\prime } \]

[_linear]

0.222

7830

\[ {}y^{\prime }+2 x y = 0 \]

[_separable]

0.215

7831

\[ {}x y^{\prime }-3 y = x^{4} \]

[_linear]

0.205

7832

\[ {}\left (x^{2}+1\right ) y^{\prime }+2 x y = \cot \left (x \right ) \]

[_linear]

0.247

7833

\[ {}y^{\prime }+y \cot \left (x \right ) = 2 x \csc \left (x \right ) \]

[_linear]

0.278

7834

\[ {}y-x +x y \cot \left (x \right )+x y^{\prime } = 0 \]

[_linear]

0.297

7835

\[ {}y^{\prime }-x y = 0 \]
i.c.

[_separable]

0.361

7836

\[ {}y^{\prime }-2 x y = 6 x \,{\mathrm e}^{x^{2}} \]
i.c.

[_linear]

0.464

7837

\[ {}x \ln \left (x \right ) y^{\prime }+y = 3 x^{3} \]
i.c.

[_linear]

0.230

7838

\[ {}y^{\prime }-\frac {y}{x} = x^{2} \]
i.c.

[_linear]

0.328

7839

\[ {}y^{\prime }+4 y = {\mathrm e}^{-x} \]
i.c.

[[_linear, ‘class A‘]]

0.373

7840

\[ {}x^{2} y^{\prime }+x y = 2 x \]
i.c.

[_separable]

0.417

7841

\[ {}x y^{\prime }+y = x^{4} y^{3} \]

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

3.322

7842

\[ {}x y^{2} y^{\prime }+y^{3} = x \cos \left (x \right ) \]

[_Bernoulli]

39.554

7843

\[ {}x y^{\prime }+y = x y^{2} \]

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

1.573

7844

\[ {}y^{\prime }+x y = x y^{4} \]

[_separable]

3.000

7845

\[ {}\left ({\mathrm e}^{y}-2 x y\right ) y^{\prime } = y^{2} \]

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

1.243

7846

\[ {}y-x y^{\prime } = y^{\prime } y^{2} {\mathrm e}^{y} \]

[[_1st_order, _with_linear_symmetries]]

1.290

7847

\[ {}x y^{\prime }+2 = x^{3} \left (y-1\right ) y^{\prime } \]

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

2.461

7848

\[ {}x y^{\prime } = 2 x^{2} y+y \ln \left (x \right ) \]

[_separable]

2.085

7849

\[ {}y^{\prime } \sin \left (2 x \right ) = 2 y+2 \cos \left (x \right ) \]

[_linear]

3.322

7850

\[ {}\left (x +\frac {2}{y}\right ) y^{\prime }+y = 0 \]

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

1.689

7851

\[ {}\sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (y\right )^{2} y^{\prime } = 0 \]

[‘y=_G(x,y’)‘]

39.764

7852

\[ {}y-x^{3}+\left (x +y^{3}\right ) y^{\prime } = 0 \]

[_exact, _rational]

1.251

7853

\[ {}2 y^{2}-4 x +5 = \left (4-2 y+4 x y\right ) y^{\prime } \]

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

1.557

7854

\[ {}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0 \]

[_separable]

2.197

7855

\[ {}\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime } = 0 \]

[_separable]

3.329

7856

\[ {}\left (\sin \left (x \right ) \sin \left (y\right )-x \,{\mathrm e}^{y}\right ) y^{\prime } = {\mathrm e}^{y}+\cos \left (x \right ) \cos \left (y\right ) \]

[_exact]

36.119

7857

\[ {}-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}} = 0 \]

[_separable]

0.317

7858

\[ {}1+y+\left (1-x \right ) y^{\prime } = 0 \]

[_separable]

1.787

7859

\[ {}2 x y^{3}+\cos \left (x \right ) y+\left (3 y^{2} x^{2}+\sin \left (x \right )\right ) y^{\prime } = 0 \]

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

41.713

7860

\[ {}\frac {y}{1-y^{2} x^{2}}+\frac {x y^{\prime }}{1-y^{2} x^{2}} = 1 \]

[_exact, _rational, _Riccati]

1.638

7861

\[ {}2 x y^{4}+\sin \left (y\right )+\left (4 x^{2} y^{3}+x \cos \left (y\right )\right ) y^{\prime } = 0 \]

[_exact]

2.993

7862

\[ {}\frac {x y^{\prime }+y}{1-y^{2} x^{2}}+x = 0 \]

[_exact, _rational, _Riccati]

1.637

7863

\[ {}2 x \left (1+\sqrt {x^{2}-y}\right ) = \sqrt {x^{2}-y}\, y^{\prime } \]

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

5.405

7864

\[ {}x \ln \left (y\right )+x y+\left (y \ln \left (x \right )+x y\right ) y^{\prime } = 0 \]

[_separable]

1.971

7865

\[ {}{\mathrm e}^{y^{2}}-\csc \left (y\right ) \csc \left (x \right )^{2}+\left (2 x y \,{\mathrm e}^{y^{2}}-\csc \left (y\right ) \cot \left (y\right ) \cot \left (x \right )\right ) y^{\prime } = 0 \]

[_exact]

56.211

7866

\[ {}1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime } = 0 \]

[_exact, _Bernoulli]

0.595

7867

\[ {}\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0 \]

[_separable]

1.944

7868

\[ {}3 x^{2} \left (1+\ln \left (y\right )\right )+\left (\frac {x^{3}}{y}-2 y\right ) y^{\prime } = 0 \]

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

1.671

7869

\[ {}\frac {y-x y^{\prime }}{\left (x +y\right )^{2}}+y^{\prime } = 1 \]

[[_1st_order, _with_linear_symmetries], _exact, _rational]

1.995

7870

\[ {}\frac {4 y^{2}-2 x^{2}}{4 x y^{2}-x^{3}}+\frac {\left (8 y^{2}-x^{2}\right ) y^{\prime }}{4 y^{3}-x^{2} y} = 0 \]

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

0.915

7871

\[ {}x^{2}-2 y^{2}+x y y^{\prime } = 0 \]

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

62.566

7872

\[ {}x^{2} y^{\prime }-3 x y-2 y^{2} = 0 \]

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

3.096

7873

\[ {}x^{2} y^{\prime } = 3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+x y \]

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

10.426

7874

\[ {}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x \]

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

5.431

7875

\[ {}x y^{\prime } = y+2 x \,{\mathrm e}^{-\frac {y}{x}} \]

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

40.421

7876

\[ {}x -y-\left (x +y\right ) y^{\prime } = 0 \]

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

4.199

7877

\[ {}x y^{\prime } = 2 x -6 y \]

[_linear]

2.458

7878

\[ {}x y^{\prime } = \sqrt {x^{2}+y^{2}} \]

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

9.972

7879

\[ {}x^{2} y^{\prime } = y^{2}+2 x y \]

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

2.815

7880

\[ {}x^{3}+y^{3}-x y^{2} y^{\prime } = 0 \]

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

11.161

7881

\[ {}y^{\prime } = \frac {x +y+4}{x -y-6} \]

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

37.063

7882

\[ {}y^{\prime } = \frac {x +y+4}{x +y-6} \]

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

1.770

7883

\[ {}2 x -2 y+\left (y-1\right ) y^{\prime } = 0 \]

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

35.925

7884

\[ {}y^{\prime } = \frac {x +y-1}{x +4 y+2} \]

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

5.707

7885

\[ {}2 x +3 y-1-4 \left (x +1\right ) y^{\prime } = 0 \]

[_linear]

1.957

7886

\[ {}y^{\prime } = \frac {1-x y^{2}}{2 x^{2} y} \]

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

2.320

7887

\[ {}y^{\prime } = \frac {2+3 x y^{2}}{4 x^{2} y} \]

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

2.876

7888

\[ {}y^{\prime } = \frac {y-x y^{2}}{x +x^{2} y} \]

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

1.779

7889

\[ {}y^{\prime } = \sin \left (\frac {y}{x}\right )-\cos \left (\frac {y}{x}\right ) \]

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

4.196

7890

\[ {}{\mathrm e}^{\frac {x}{y}}-\frac {y y^{\prime }}{x} = 0 \]

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

3.292

7891

\[ {}y^{\prime } = \frac {x^{2}-x y}{y^{2} \cos \left (\frac {x}{y}\right )} \]

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

6.879

7892

\[ {}y^{\prime } = \frac {y \tan \left (\frac {y}{x}\right )}{x} \]

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

4.398

7893

\[ {}\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 x y = 0 \]

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

0.428

7894

\[ {}x y-1+\left (x^{2}-x y\right ) y^{\prime } = 0 \]

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

0.503

7895

\[ {}x y^{\prime }+y+3 x^{3} y^{4} y^{\prime } = 0 \]

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

4.007

7896

\[ {}{\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 y \csc \left (y\right )\right ) y^{\prime } = 0 \]

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

0.465

7897

\[ {}\left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime } = 0 \]

[_separable]

0.479

7898

\[ {}y+\left (x -2 x^{2} y^{3}\right ) y^{\prime } = 0 \]

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

0.373

7899

\[ {}x +3 y^{2}+2 x y y^{\prime } = 0 \]

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

0.530

7900

\[ {}y+\left (2 x -y \,{\mathrm e}^{y}\right ) y^{\prime } = 0 \]

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

0.361