2.2.19 Problems 1801 to 1900

Table 2.39: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

1801

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

[_rational, _Riccati]

3.090

1802

\[ {}\left (3 x -1\right ) \left (y^{\prime }+y^{2}\right )-\left (3 x +2\right ) y-6 x +8 = 0 \]

[_rational, _Riccati]

3.385

1803

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

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

1.484

1804

\[ {}x^{2} \left (y^{\prime }+y^{2}\right )-7 x y+7 = 0 \]

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

2.687

1805

\[ {}y^{\prime \prime }+9 y = \tan \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

5.500

1806

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

[[_2nd_order, _linear, _nonhomogeneous]]

4.358

1807

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \frac {4}{1+{\mathrm e}^{-x}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.880

1808

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 3 \,{\mathrm e}^{x} \sec \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

28.747

1809

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 14 x^{{3}/{2}} {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.310

1810

\[ {}y^{\prime \prime }-y = \frac {4 \,{\mathrm e}^{-x}}{1-{\mathrm e}^{-2 x}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.366

1811

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1.687

1812

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.772

1813

\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 4 \sqrt {x}\, {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.835

1814

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.704

1815

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{{5}/{2}} \]

[[_2nd_order, _with_linear_symmetries]]

1.571

1816

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

[[_2nd_order, _with_linear_symmetries]]

7.398

1817

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.076

1818

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.728

1819

\[ {}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y = 6 x^{3} {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.811

1820

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

[[_2nd_order, _with_linear_symmetries]]

1.595

1821

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

[[_2nd_order, _linear, _nonhomogeneous]]

6.249

1822

\[ {}x y^{\prime \prime }-y^{\prime }-4 x^{3} y = 8 x^{5} \]

[[_2nd_order, _linear, _nonhomogeneous]]

7.569

1823

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.855

1824

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 8 x^{{5}/{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.641

1825

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}+3\right ) y = x^{{7}/{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3.699

1826

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.624

1827

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.800

1828

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1.404

1829

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.392

1830

\[ {}x^{2} y^{\prime \prime }-2 x \left (x +2\right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y = 2 x \,{\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.682

1831

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y = x^{4} \]

[[_2nd_order, _linear, _nonhomogeneous]]

2.693

1832

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

[[_2nd_order, _with_linear_symmetries]]

1.454

1833

\[ {}4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y = x^{{5}/{2}} {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.420

1834

\[ {}\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y = \left (3 x -1\right )^{2} {\mathrm e}^{2 x} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.456

1835

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

[[_2nd_order, _with_linear_symmetries]]

1.575

1836

\[ {}\left (-1+x \right )^{2} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+\left (x +1\right ) y = \left (-1+x \right )^{3} {\mathrm e}^{x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

1.405

1837

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

2.771

1838

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

[[_2nd_order, _with_linear_symmetries]]

1.747

1839

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

2.075

1840

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

[[_2nd_order, _with_linear_symmetries]]

0.391

1841

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

[[_2nd_order, _with_linear_symmetries]]

0.447

1842

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

[[_2nd_order, _with_linear_symmetries]]

0.504

1843

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

[[_2nd_order, _with_linear_symmetries]]

0.440

1844

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

[[_2nd_order, _with_linear_symmetries]]

0.389

1845

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

[[_2nd_order, _with_linear_symmetries]]

0.484

1846

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

[[_Emden, _Fowler]]

0.487

1847

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

[[_Emden, _Fowler]]

0.340

1848

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

[[_2nd_order, _with_linear_symmetries]]

0.435

1849

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

[[_2nd_order, _with_linear_symmetries]]

1.481

1850

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (4+6 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1.388

1851

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (-x^{2}-6 x +1\right ) y^{\prime }+\left (x^{2}+6 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.766

1852

\[ {}x^{2} \left (1+3 x \right ) y^{\prime \prime }+x \left (x^{2}+12 x +2\right ) y^{\prime }+2 x \left (x +3\right ) y = 0 \]

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

0.732

1853

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

[[_2nd_order, _with_linear_symmetries]]

0.725

1854

\[ {}x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1.483

1855

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+6 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.382

1856

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

[[_2nd_order, _with_linear_symmetries]]

0.347

1857

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.362

1858

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }-12 y = 0 \]

[_Gegenbauer]

0.384

1859

\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.392

1860

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

[[_2nd_order, _with_linear_symmetries]]

0.384

1861

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }-4 y = 0 \]

[_Gegenbauer]

0.391

1862

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }+28 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.378

1863

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

[[_2nd_order, _with_linear_symmetries]]

0.331

1864

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

[[_2nd_order, _with_linear_symmetries]]

0.331

1865

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

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

0.372

1866

\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }-9 x y^{\prime }-6 y = 0 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.390

1867

\[ {}\left (8 x^{2}+1\right ) y^{\prime \prime }+2 y = 0 \]
i.c.

[[_Emden, _Fowler]]

0.369

1868

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

[[_2nd_order, _missing_x]]

0.405

1869

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.358

1870

\[ {}\left (2 x^{2}-4 x +1\right ) y^{\prime \prime }+10 \left (-1+x \right ) y^{\prime }+6 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

0.442

1871

\[ {}\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (-2+x \right ) y^{\prime }+36 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.431

1872

\[ {}\left (3 x^{2}+6 x +5\right ) y^{\prime \prime }+9 \left (x +1\right ) y^{\prime }+3 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

0.435

1873

\[ {}\left (x^{2}-4\right ) y^{\prime \prime }-x y^{\prime }-3 y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

0.370

1874

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

[[_2nd_order, _with_linear_symmetries]]

0.370

1875

\[ {}\left (3 x^{2}-6 x +5\right ) y^{\prime \prime }+\left (-1+x \right ) y^{\prime }+12 y = 0 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.431

1876

\[ {}\left (4 x^{2}-24 x +37\right ) y^{\prime \prime }+y = 0 \]
i.c.

[[_Emden, _Fowler]]

0.405

1877

\[ {}\left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y = 0 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.402

1878

\[ {}\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y = 0 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.417

1879

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.376

1880

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

[[_2nd_order, _with_linear_symmetries]]

0.369

1881

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

[[_Emden, _Fowler]]

0.230

1882

\[ {}\left (-2 x^{3}+1\right ) y^{\prime \prime }-10 x^{2} y^{\prime }-8 x y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

0.414

1883

\[ {}\left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.404

1884

\[ {}\left (-2 x^{3}+1\right ) y^{\prime \prime }+6 x^{2} y^{\prime }+24 x y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

0.390

1885

\[ {}\left (-x^{3}+1\right ) y^{\prime \prime }+15 x^{2} y^{\prime }-36 x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.415

1886

\[ {}\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.425

1887

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

[[_Emden, _Fowler]]

0.290

1888

\[ {}y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.299

1889

\[ {}\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.335

1890

\[ {}\left (-x^{6}+1\right ) y^{\prime \prime }-12 x^{5} y^{\prime }-30 x^{4} y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

0.378

1891

\[ {}y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.326

1892

\[ {}\left (1+3 x \right ) y^{\prime \prime }+x y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.407

1893

\[ {}\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+8 x \right ) y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

0.437

1894

\[ {}\left (-2 x^{2}+1\right ) y^{\prime \prime }+\left (2-6 x \right ) y^{\prime }-2 y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

0.496

1895

\[ {}\left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y = 0 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.510

1896

\[ {}\left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y = 0 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.378

1897

\[ {}\left (x^{2}+3 x +3\right ) y^{\prime \prime }+\left (6+4 x \right ) y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

0.443

1898

\[ {}\left (x +4\right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.395

1899

\[ {}\left (2 x^{2}-3 x +2\right ) y^{\prime \prime }-\left (4-6 x \right ) y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

0.546

1900

\[ {}\left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y = 0 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.544