Problems 1901 to 2000

Table 2.41: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

1901	$(x^{2} - x + 1) y^{''} - (1 - 4 x) y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.687

1902	$(x + 2) y^{''} + (x + 2) y^{'} + y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.609

1903	$x^{2} y^{''} - (6 - 7 x) y^{'} + 8 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.649

1904	$(2 x^{2} + x + 1) y^{''} + (1 + 7 x) y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.724

1905	$(3 + x) y^{''} + (2 x + 1) y^{'} - (2 - x) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.646

1906	$y^{''} + 3 y^{'} x + (2 x^{2} + 4) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.462

1907	$(2 + 4 x) y^{''} - 4 y^{'} - (6 + 4 x) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.541

1908	$(2 x + 1) y^{''} - (- 2 x + 1) y^{'} - (3 - 2 x) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.599

1909	$(5 + 2 x) y^{''} - y^{'} + (5 + x) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.606

1910	$(x + 4) y^{''} - (4 + 2 x) y^{'} + (6 + x) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.643

1911	$(3 x + 2) y^{''} - y^{'} x + 2 x y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.536

1912	$(2 x + 3) y^{''} + 3 y^{'} - x y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.572

1913	$(2 x + 3) y^{''} - 3 y^{'} - (x + 2) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.618

1914	$(10 - 2 x) y^{''} + (x + 1) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.516

1915	$(7 + x) y^{''} + (8 + 2 x) y^{'} + (5 + x) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.585

1916	$(6 + 4 x) y^{''} + (2 x + 1) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.530

1917	$(β x^{2} + α x + 1) y^{''} + (δ x + γ) y^{'} + ϵ y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.488

1918	$(2 x^{2} + 3 x + 1) y^{''} + (6 + 8 x) y^{'} + 4 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.571

1919	$(6 x^{2} - 5 x + 1) y^{''} - (10 - 24 x) y^{'} + 12 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.585

1920	$(4 x^{2} - 4 x + 1) y^{''} - (8 - 16 x) y^{'} + 8 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.538

1921	$(x^{2} + 4 x + 4) y^{''} + (8 + 4 x) y^{'} + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.517

1922	$(3 x^{2} + 8 x + 4) y^{''} + (16 + 12 x) y^{'} + 6 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.613

1923	$y^{''} + 2 y^{'} x + (2 x^{2} + 3) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.522

1924	$y^{''} - 3 y^{'} x + (2 x^{2} + 5) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.520

1925	$y^{''} + 5 y^{'} x - (- x^{2} + 3) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.544

1926	$y^{''} - 2 y^{'} x - (3 x^{2} + 2) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.504

1927	$y^{''} + 3 y^{'} x + (4 x^{2} + 2) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.436

1928	$2 y^{''} + 5 y^{'} x + (2 x^{2} + 4) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.522

1929	$3 y^{''} + 2 y^{'} x + (- x^{2} + 4) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.548

1930	$y^{''} + 4 y^{'} x + (4 x^{2} + 2) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.447

1931	$y^{''} + 4 y^{'} x + (4 x^{2} + 2) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.428

1932	$(x + 1) y^{''} + x^{2} y^{'} + (2 x + 1) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.567

1933	$y^{''} + (x^{2} + 2 x + 1) y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.548

1934	$(x^{2} + 1) y^{''} + (x^{2} + 2) y^{'} + x y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.628

1935	$(x + 1) y^{''} + (2 x^{2} - 3 x + 1) y^{'} - (x - 4) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.681

1936	$y^{''} + (3 x^{2} + 12 x + 13) y^{'} + (5 + 2 x) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.556

1937	$(3 x^{2} + 2 x + 1) y^{''} + (- x^{2} + 2) y^{'} + (x + 1) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.654

1938	$(x^{2} + 4 x + 3) y^{''} - (- x^{2} + 4 x + 5) y^{'} - (x + 2) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.606

1939	$(x^{2} + 2 x + 1) y^{''} + (1 - x) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.526

1940	$(- 2 x^{2} + x) y^{''} + (- x^{2} + 3 x + 1) y^{'} + (x + 2) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.624

1941	$(2 x^{2} - 11 x + 16) y^{''} + (x^{2} - 6 x + 10) y^{'} - (2 - x) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.628

1942	$2 x^{2} (x^{2} + x + 1) y^{''} + x (11 x^{2} + 11 x + 9) y^{'} + (7 x^{2} + 10 x + 6) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.941

1943	$(3 + x) x^{2} y^{''} + 5 x (x + 1) y^{'} - (1 - 4 x) y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.838

1944	$x^{2} (- x^{2} + 2) y^{''} - x (4 x^{2} + 3) y^{'} + (2 x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.885

1945	$2 x^{2} (x^{2} + x + 1) y^{''} + x (5 x^{2} + 3 x + 3) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.113

1946	$3 x^{2} y^{''} + 2 x (- 2 x^{2} + x + 1) y^{'} + (- 8 x^{2} + 2 x) y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.748

1947	$x^{2} (x^{2} + 3 x + 3) y^{''} + x (7 x^{2} + 8 x + 5) y^{'} - (- 9 x^{2} - 2 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.976

1948	$4 x^{2} y^{''} + x (4 x^{2} + 2 x + 7) y^{'} - (- 7 x^{2} - 4 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.943

1949	$12 x^{2} (x + 1) y^{''} + x (3 x^{2} + 35 x + 11) y^{'} - (- 5 x^{2} - 10 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.829

1950	$x^{2} (10 x^{2} + x + 5) y^{''} + x (48 x^{2} + 3 x + 4) y^{'} + (36 x^{2} + x) y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.863

1951	$8 x^{2} y^{''} - 2 x (- x^{2} - 4 x + 3) y^{'} + (x^{2} + 6 x + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.895

1952	$18 x^{2} (x + 1) y^{''} + 3 x (x^{2} + 11 x + 5) y^{'} - (- 5 x^{2} - 2 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.854

1953	$x (x^{2} + x + 3) y^{''} + (- x^{2} + x + 4) y^{'} + x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.868

1954	$10 x^{2} (2 x^{2} + x + 1) y^{''} + x (66 x^{2} + 13 x + 13) y^{'} - (10 x^{2} + 4 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.956

1955	$2 x^{2} y^{''} + x (2 x + 3) y^{'} - (1 - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.786

1956	$(3 + x) x^{2} y^{''} + x (5 + 4 x) y^{'} - (- 2 x + 1) y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.910

1957	$2 x^{2} y^{''} + x (5 + x) y^{'} - (2 - 3 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.716

1958	$3 x^{2} y^{''} + x (x + 1) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.724

1959	$2 x^{2} y^{''} - y^{'} x + (- 2 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.751

1960	$9 x^{2} y^{''} + 9 y^{'} x - (3 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.794

1961	$3 x^{2} y^{''} + x (x + 1) y^{'} - (3 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.805

1962	$2 (3 + x) x^{2} y^{''} + x (1 + 5 x) y^{'} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.872

1963	$x^{2} (x + 4) y^{''} - x (1 - 3 x) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.788

1964	$2 x^{2} y^{''} + 5 y^{'} x + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.885

1965	$x^{2} (4 x + 3) y^{''} + x (5 + 18 x) y^{'} - (1 - 12 x) y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.864

1966	$6 x^{2} y^{''} + x (10 - x) y^{'} - (x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.760

1967	$x^{2} (8 + x) y^{''} + x (3 x + 2) y^{'} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.883

1968	$x^{2} (4 x + 3) y^{''} + x (11 + 4 x) y^{'} - (4 x + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.948

1969	$2 x^{2} (3 x + 2) y^{''} + x (4 + 11 x) y^{'} - (1 - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.927

1970	$x^{2} (x + 2) y^{''} + 5 x (1 - x) y^{'} - (2 - 8 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.912

1971	$x^{2} (6 + x) y^{''} + x (11 + 4 x) y^{'} + (2 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.954

1972	$8 x^{2} y^{''} + x (x^{2} + 2) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.746

1973	$8 x^{2} (- x^{2} + 1) y^{''} + 2 x (- 13 x^{2} + 1) y^{'} + (- 9 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.750

1974	$x^{2} (x^{2} + 1) y^{''} - 2 x (- x^{2} + 2) y^{'} + 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.749

1975	$x (x^{2} + 3) y^{''} + (- x^{2} + 2) y^{'} - 8 x y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.657

1976	$4 x^{2} (- x^{2} + 1) y^{''} + x (- 19 x^{2} + 7) y^{'} - (14 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.726

1977	$3 x^{2} (- x^{2} + 2) y^{''} + x (- 11 x^{2} + 1) y^{'} + (- 5 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.801

1978	$2 x^{2} (x^{2} + 2) y^{''} - x (- 7 x^{2} + 12) y^{'} + (3 x^{2} + 7) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.762

1979	$2 x^{2} (x^{2} + 2) y^{''} + x (7 x^{2} + 4) y^{'} - (- 3 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.794

1980	$2 x^{2} (2 x^{2} + 1) y^{''} + 5 x (6 x^{2} + 1) y^{'} - (- 40 x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.689

1981	$3 x^{2} (x^{2} + 1) y^{''} + 5 x (x^{2} + 1) y^{'} - (- 5 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.760

1982	$x (x^{2} + 1) y^{''} + (7 x^{2} + 4) y^{'} + 8 x y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.687

1983	$x^{2} (x^{2} + 2) y^{''} + x (x^{2} + 3) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.685

1984	$2 x^{2} (x^{2} + 1) y^{''} + x (8 x^{2} + 3) y^{'} - (- 4 x^{2} + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.676

1985	$9 x^{2} y^{''} + 3 x (x^{2} + 3) y^{'} - (- 5 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.672

1986	$6 x^{2} y^{''} + x (6 x^{2} + 1) y^{'} + (9 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.658

1987	$x^{2} (x^{2} + 8) y^{''} + 7 x (x^{2} + 2) y^{'} - (- 9 x^{2} + 2) y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.766

1988	$9 x^{2} (x^{2} + 1) y^{''} + 3 x (13 x^{2} + 3) y^{'} - (- 25 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.756

1989	$4 x^{2} (x^{2} + 1) y^{''} + 4 x (6 x^{2} + 1) y^{'} - (- 25 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.864

1990	$8 x^{2} (2 x^{2} + 1) y^{''} + 2 x (34 x^{2} + 5) y^{'} - (- 30 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.733

1991	$2 x^{2} (x + 1) y^{''} - x (1 - 3 x) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.632

1992	$6 x^{2} (2 x^{2} + 1) y^{''} + x (50 x^{2} + 1) y^{'} + (30 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.693

1993	$28 x^{2} (1 - 3 x) y^{''} - 7 x (5 + 9 x) y^{'} + 7 (2 + 9 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.737

1994	$9 x^{2} (5 + x) y^{''} + 9 x (5 + 9 x) y^{'} - (5 - 8 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.901

1995	$8 x^{2} (- x^{2} + 2) y^{''} + 2 x (- 21 x^{2} + 10) y^{'} - (35 x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.712

1996	$4 x^{2} (x^{2} + 3 x + 1) y^{''} - 4 x (- 3 x^{2} - 3 x + 1) y^{'} + 3 (x^{2} - x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.826

1997	$3 x^{2} {(x + 1)}^{2} y^{''} - x (- 11 x^{2} - 10 x + 1) y^{'} + (5 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.682

1998	$4 x^{2} (x^{2} + 2 x + 3) y^{''} - x (- 15 x^{2} - 14 x + 3) y^{'} + (7 x^{2} + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.762

1999	$x^{2} (x^{2} - 2 x + 1) y^{''} - (3 + x) x y^{'} + (x + 4) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.808

2000	$2 x^{2} (x + 2) y^{''} + 5 x^{2} y^{'} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.844

2.2.20 Problems 1901 to 2000