Problems 1801 to 1900

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


#	ODE	CAS classiﬁcation	Solved?	time (sec)

1801	$(2 x + 1) (y^{'} + y^{2}) - 2 y - 2 x - 3 = 0$	[_rational, _Riccati]	✓	2.950

1802	$(3 x - 1) (y^{'} + y^{2}) - (3 x + 2) y - 6 x + 8 = 0$	[_rational, _Riccati]	✓	3.164

1803	$x^{2} (y^{'} + y^{2}) + x y + x^{2} - \frac{1}{4} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	1.724

1804	$x^{2} (y^{'} + y^{2}) - 7 x y + 7 = 0$	[[_homogeneous, ‘class G‘], _rational, _Riccati]	✓	2.258

1805	$y^{''} + 9 y = \tan (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.137

1806	$y^{''} + 4 y = \sin (2 x) \sec {(2 x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.349

1807	$y^{''} - 3 y^{'} + 2 y = \frac{4}{1 + e^{- x}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.613

1808	$y^{''} - 2 y^{'} + 2 y = 3 e^{x} \sec (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.842

1809	$y^{''} - 2 y^{'} + y = 14 x^{3 / 2} e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.640

1810	$y^{''} - y = \frac{4 e^{- x}}{1 - e^{- 2 x}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.718

1811	$x^{2} y^{''} + y^{'} x - y = 2 x^{2} + 2$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.673

1812	$x y^{''} + (2 - 2 x) y^{'} + (x - 2) y = e^{2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.714

1813	$4 x^{2} y^{''} + (- 8 x^{2} + 4 x) y^{'} + (4 x^{2} - 4 x - 1) y = 4 \sqrt{x} e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.730

1814	$y^{''} + 4 y^{'} x + (4 x^{2} + 2) y = 4 e^{- x (x + 2)}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.740

1815	$x^{2} y^{''} - 4 y^{'} x + 6 y = x^{5 / 2}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.512

1816	$x^{2} y^{''} - 3 y^{'} x + 3 y = 2 x^{4} \sin (x)$	[[_2nd_order, _with_linear_symmetries]]	✓	6.389

1817	$(2 x + 1) y^{''} - 2 y^{'} - (2 x + 3) y = {(2 x + 1)}^{2} e^{- x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.582

1818	$2 x y^{''} + 2 y^{'} + 2 y = \sin (\sqrt{x})$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.656

1819	$x y^{''} - (2 x + 2) y^{'} + (x + 2) y = 6 x^{3} e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.548

1820	$x^{2} y^{''} - (2 a - 1) x y^{'} + a^{2} y = x^{a + 1}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.571

1821	$x^{2} y^{''} - 2 y^{'} x + (x^{2} + 2) y = x^{3} \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.984

1822	$x y^{''} - y^{'} - 4 x^{3} y = 8 x^{5}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.294

1823	$\sin (x) y^{''} + (2 \sin (x) - \cos (x)) y^{'} + (\sin (x) - \cos (x)) y = e^{- x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✗	3.054

1824	$4 x^{2} y^{''} - 4 y^{'} x + (- 16 x^{2} + 3) y = 8 x^{5 / 2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.093

1825	$4 x^{2} y^{''} - 4 y^{'} x + (4 x^{2} + 3) y = x^{7 / 2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.045

1826	$x^{2} y^{''} - 2 y^{'} x - (x^{2} - 2) y = 3 x^{4}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.035

1827	$x^{2} y^{''} - 2 x (x + 1) y^{'} + (x^{2} + 2 x + 2) y = x^{3} e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.666

1828	$x^{2} y^{''} - y^{'} x - 3 y = x^{3 / 2}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.322

1829	$x^{2} y^{''} - x (x + 4) y^{'} + 2 (3 + x) y = x^{4} e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.949

1830	$x^{2} y^{''} - 2 x (x + 2) y^{'} + (x^{2} + 4 x + 6) y = 2 x e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.688

1831	$x^{2} y^{''} - 4 y^{'} x + (x^{2} + 6) y = x^{4}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.904

1832	$(x - 1) y^{''} - y^{'} x + y = 2 {(x - 1)}^{2} e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.965

1833	$4 x^{2} y^{''} - 4 x (x + 1) y^{'} + (2 x + 3) y = x^{5 / 2} e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.975

1834	$(3 x - 1) y^{''} - (3 x + 2) y^{'} - (6 x - 8) y = {(3 x - 1)}^{2} e^{2 x}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.883

1835	${(x - 1)}^{2} y^{''} - 2 (x - 1) y^{'} + 2 y = {(x - 1)}^{2}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	1.469

1836	${(x - 1)}^{2} y^{''} - (x^{2} - 1) y^{'} + (x + 1) y = {(x - 1)}^{3} e^{x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	1.030

1837	${(x - 1)}^{2} y^{''} + 4 y^{'} x + 2 y = 2 x$ i.c.	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.793

1838	$x^{2} y^{''} + 2 y^{'} x - 2 y = - 2 x^{2}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	1.500

1839	$(x + 1) (2 x + 3) y^{''} + 2 (x + 2) y^{'} - 2 y = {(2 x + 3)}^{2}$ i.c.	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.613

1840	$(x + 2) y^{''} + y^{'} x + 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.486

1841	$(3 x^{2} + 1) y^{''} + 3 x^{2} y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.586

1842	$(2 x^{2} + 1) y^{''} + (2 - 3 x) y^{'} + 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.581

1843	$(x^{2} + 1) y^{''} + (2 - x) y^{'} + 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.546

1844	$(3 x^{2} + 1) y^{''} - 2 y^{'} x + 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.504

1845	$x y^{''} + (4 + 2 x) y^{'} + (x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.641

1846	$x^{2} y^{''} + 2 y^{'} x - 3 x y = 0$	[[_Emden, _Fowler]]	✓	0.606

1847	$(2 - x) y^{''} + 2 y = 0$ i.c.	[[_Emden, _Fowler]]	✓	0.428

1848	$(x + 1) y^{''} + 2 {(x - 1)}^{2} y^{'} + 3 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.607

1849	$x^{2} (1 - x) y^{''} + x (x + 4) y^{'} + (2 - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.493

1850	$x^{2} (x + 1) y^{''} + x (2 x + 1) y^{'} - (6 x + 4) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.454

1851	$x^{2} (x + 1) y^{''} - x (- x^{2} - 6 x + 1) y^{'} + (x^{2} + 6 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.884

1852	$x^{2} (3 x + 1) y^{''} + x (x^{2} + 12 x + 2) y^{'} + 2 x (3 + x) y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.834

1853	$x^{2} (2 x^{2} + 1) y^{''} + x (2 x^{2} + 4) y^{'} + 2 (- x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.923

1854	$x^{2} (x^{2} + 2) y^{''} + 2 x (x^{2} + 5) y^{'} + 2 (- x^{2} + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.457

1855	$(x^{2} + 1) y^{''} + 6 y^{'} x + 6 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.458

1856	$(x^{2} + 1) y^{''} + 2 y^{'} x - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.393

1857	$(x^{2} + 1) y^{''} - 8 y^{'} x + 20 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.453

1858	$(- x^{2} + 1) y^{''} - 8 y^{'} x - 12 y = 0$	[_Gegenbauer]	✓	0.515

1859	$(2 x^{2} + 1) y^{''} + 7 y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.473

1860	$(x^{2} + 1) y^{''} + 2 y^{'} x + \frac{y}{4} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.506

1861	$(- x^{2} + 1) y^{''} - 5 y^{'} x - 4 y = 0$	[_Gegenbauer]	✓	0.497

1862	$(x^{2} + 1) y^{''} - 10 y^{'} x + 28 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.509

1863	$y^{''} + y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.382

1864	$y^{''} + 2 y^{'} x + 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.362

1865	$(x^{2} + 1) y^{''} + y^{'} x + y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.516

1866	$(2 x^{2} + 1) y^{''} - 9 y^{'} x - 6 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.544

1867	$(8 x^{2} + 1) y^{''} + 2 y = 0$ i.c.	[[_Emden, _Fowler]]	✓	0.527

1868	$y^{''} - y = 0$	[[_2nd_order, _missing_x]]	✓	0.365

1869	$y^{''} - (x - 3) y^{'} - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.441

1870	$(2 x^{2} - 4 x + 1) y^{''} + 10 (x - 1) y^{'} + 6 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.562

1871	$(2 x^{2} - 8 x + 11) y^{''} - 16 (x - 2) y^{'} + 36 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.548

1872	$(3 x^{2} + 6 x + 5) y^{''} + 9 (x + 1) y^{'} + 3 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.593

1873	$(x^{2} - 4) y^{''} - y^{'} x - 3 y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.520

1874	$y^{''} + (x - 3) y^{'} + 3 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.487

1875	$(3 x^{2} - 6 x + 5) y^{''} + (x - 1) y^{'} + 12 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.612

1876	$(4 x^{2} - 24 x + 37) y^{''} + y = 0$ i.c.	[[_Emden, _Fowler]]	✓	0.611

1877	$(x^{2} - 8 x + 14) y^{''} - 8 (x - 4) y^{'} + 20 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.602

1878	$(2 x^{2} + 4 x + 5) y^{''} - 20 (x + 1) y^{'} + 60 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.607

1879	$(x^{2} + 1) y^{''} + 4 y^{'} x + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.501

1880	$y^{''} - 2 y^{'} x + 2 α y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.473

1881	$y^{''} - x y = 0$	[[_Emden, _Fowler]]	✓	0.359

1882	$(- 2 x^{3} + 1) y^{''} - 10 x^{2} y^{'} - 8 x y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.506

1883	$(x^{3} + 1) y^{''} + 7 x^{2} y^{'} + 9 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.479

1884	$(- 2 x^{3} + 1) y^{''} + 6 x^{2} y^{'} + 24 x y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.514

1885	$(- x^{3} + 1) y^{''} + 15 x^{2} y^{'} - 36 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.505

1886	$(2 x^{5} + 1) y^{''} + 14 x^{4} y^{'} + 10 x^{3} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.559

1887	$y^{''} + x^{2} y = 0$	[[_Emden, _Fowler]]	✓	0.330

1888	$y^{''} + x^{6} y^{'} + 7 x^{5} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.344

1889	$(x^{8} + 1) y^{''} - 16 x^{7} y^{'} + 72 x^{6} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.449

1890	$(- x^{6} + 1) y^{''} - 12 x^{5} y^{'} - 30 y x^{4} = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.475

1891	$y^{''} + x^{5} y^{'} + 6 y x^{4} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.362

1892	$(3 x + 1) y^{''} + y^{'} x + 2 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.547

1893	$(2 x^{2} + x + 1) y^{''} + (2 + 8 x) y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.611

1894	$(- 2 x^{2} + 1) y^{''} + (2 - 6 x) y^{'} - 2 y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.657

1895	$(3 x^{2} + x + 1) y^{''} + (2 + 15 x) y^{'} + 12 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.712

1896	$(x + 2) y^{''} + (x + 1) y^{'} + 3 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.563

1897	$(x^{2} + 3 x + 3) y^{''} + (6 + 4 x) y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.646

1898	$(x + 4) y^{''} + (x + 2) y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.498

1899	$(2 x^{2} - 3 x + 2) y^{''} - (4 - 6 x) y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.713

1900	$(2 x^{2} + 3 x) y^{''} + 10 (x + 1) y^{'} + 8 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.622

2.2.19 Problems 1801 to 1900