Problems 13301 to 13400

Table 2.269: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

13301	$y^{'} + y = {\begin{array}{cc} 1 & 0 \leq x < 2 \\ 0 & 0 < x \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓	0.745

13302	$(x + 2) y^{'} + y = {\begin{array}{cc} 2 x & 0 \leq x \leq 2 \\ 4 & 2 < x \end{array}$ i.c.	[_linear]	✓	0.804

13303	$x y + x^{2} y^{'} = \frac{y^{3}}{x}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	158.105

13304	$5 x y + 4 y^{2} + 1 + (x^{2} + 2 x y) y^{'} = 0$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.686

13305	$2 x + \tan (y) + (x - x^{2} \tan (y)) y^{'} = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	2.582

13306	$(x + 1) y^{2} + y + (1 + 2 x y) y^{'} = 0$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.441

13307	$2 x y^{2} + y + (2 y^{3} - x) y^{'} = 0$	[_rational]	✓	2.418

13308	$4 x y^{2} + 6 y + (5 x^{2} y + 8 x) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.254

13309	$8 x^{2} y^{3} - 2 y^{4} + (5 x^{3} y^{2} - 8 x y^{3}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.856

13310	$5 x + 2 y + 1 + (2 x + y + 1) y^{'} = 0$	[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.789

13311	$3 x - y + 1 - (6 x - 2 y - 3) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.967

13312	$x - 2 y - 3 + (2 x + y - 1) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.491

13313	$10 x - 4 y + 12 - (x + 5 y + 3) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.230

13314	$6 x + 4 y + 1 + (4 x + 2 y + 2) y^{'} = 0$ i.c.	[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.566

13315	$3 x - y - 6 + (x + y + 2) y^{'} = 0$ i.c.	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	19.995

13316	$2 x + 3 y + 1 + (4 x + 6 y + 1) y^{'} = 0$ i.c.	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.138

13317	$(x + y + 1) y^{'} + 1 + 4 x + 3 y = 0$ i.c.	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.073

13318	$y^{''} + 5 y^{'} + 6 y = e^{x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.674

13319	$y^{''} + 5 y^{'} + 6 y = e^{x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.655

13320	$y^{''} + y^{'} x + x^{2} y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✗	0.821

13321	$y^{''} - 4 y^{'} + 3 y = 0$	[[_2nd_order, _missing_x]]	✓	0.321

13322	$y^{''} - 2 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.603

13323	$x^{2} y^{''} - 2 y^{'} x + 2 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.778

13324	$x^{2} y^{''} + y^{'} x - 4 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.147

13325	$y^{''} - 5 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓	0.360

13326	$y^{'''} - 6 y^{''} + 5 y^{'} + 12 y = 0$	[[_3rd_order, _missing_x]]	✓	0.081

13327	$x^{3} y^{'''} - 4 x^{2} y^{''} + 8 y^{'} x - 8 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓	0.141

13328	$x^{2} y^{''} - 4 y^{'} x + 4 y = 0$	[[_Emden, _Fowler]]	✓	0.133

13329	${(x + 1)}^{2} y^{''} - 3 (x + 1) y^{'} + 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.137

13330	$(x^{2} - 1) y^{''} - 2 y^{'} x + 2 y = 0$	[_Gegenbauer]	✓	0.154

13331	$(x^{2} - x + 1) y^{''} - (x^{2} + x) y^{'} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.148

13332	$(2 x + 1) y^{''} - 4 (x + 1) y^{'} + 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.169

13333	$(x^{3} - x^{2}) y^{''} - (x^{3} + 2 x^{2} - 2 x) y^{'} + (2 x^{2} + 2 x - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.175

13334	$y^{''} - 3 y^{'} + 2 y = 4 x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.470

13335	$y^{''} - 5 y^{'} + 6 y = 2 - 12 x + 6 e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.544

13336	$y^{''} - 5 y^{'} + 6 y = 0$	[[_2nd_order, _missing_x]]	✓	0.346

13337	$y^{''} - 2 y^{'} - 3 y = 0$	[[_2nd_order, _missing_x]]	✓	0.330

13338	$4 y^{''} - 12 y^{'} + 5 y = 0$	[[_2nd_order, _missing_x]]	✓	0.333

13339	$3 y^{''} - 14 y^{'} - 5 y = 0$	[[_2nd_order, _missing_x]]	✓	0.345

13340	$y^{'''} - 3 y^{''} - y^{'} + 3 y = 0$	[[_3rd_order, _missing_x]]	✓	0.077

13341	$y^{'''} - 6 y^{''} + 5 y^{'} + 12 y = 0$	[[_3rd_order, _missing_x]]	✓	0.076

13342	$y^{''} - 8 y^{'} + 16 y = 0$	[[_2nd_order, _missing_x]]	✓	0.349

13343	$4 y^{''} + 4 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.466

13344	$y^{''} - 4 y^{'} + 13 y = 0$	[[_2nd_order, _missing_x]]	✓	0.515

13345	$y^{''} + 6 y^{'} + 25 y = 0$	[[_2nd_order, _missing_x]]	✓	0.498

13346	$y^{''} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	1.442

13347	$4 y^{''} + y = 0$	[[_2nd_order, _missing_x]]	✓	1.472

13348	$y^{'''} - 5 y^{''} + 7 y^{'} - 3 y = 0$	[[_3rd_order, _missing_x]]	✓	0.076

13349	$4 y^{'''} + 4 y^{''} - 7 y^{'} + 2 y = 0$	[[_3rd_order, _missing_x]]	✓	0.080

13350	$y^{'''} - 6 y^{''} + 12 y^{'} - 8 y = 0$	[[_3rd_order, _missing_x]]	✓	0.081

13351	$y^{'''} + 4 y^{''} + 5 y^{'} + 6 y = 0$	[[_3rd_order, _missing_x]]	✓	0.093

13352	$y^{'''} - y^{''} + y^{'} - y = 0$	[[_3rd_order, _missing_x]]	✓	0.086

13353	$y^{''''} + 8 y^{''} + 16 y = 0$	[[_high_order, _missing_x]]	✓	0.083

13354	$y^{(5)} - 2 y^{''''} + y^{'''} = 0$	[[_high_order, _missing_x]]	✓	0.076

13355	$y^{''''} - y^{'''} - 3 y^{''} + y^{'} + 2 y = 0$	[[_high_order, _missing_x]]	✓	0.084

13356	$y^{''''} - 3 y^{'''} - 2 y^{''} + 2 y^{'} + 12 y = 0$	[[_high_order, _missing_x]]	✓	0.087

13357	$y^{''''} + 6 y^{'''} + 15 y^{''} + 20 y^{'} + 12 y = 0$	[[_high_order, _missing_x]]	✓	0.089

13358	$y^{''''} + y = 0$	[[_high_order, _missing_x]]	✓	0.097

13359	$y^{(5)} = 0$	[[_high_order, _quadrature]]	✓	0.068

13360	$y^{''} - y^{'} - 12 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.541

13361	$y^{''} + 7 y^{'} + 10 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.565

13362	$y^{''} - 6 y^{'} + 8 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.552

13363	$3 y^{''} + 4 y^{'} - 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.550

13364	$y^{''} + 6 y^{'} + 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.681

13365	$4 y^{''} - 12 y^{'} + 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.660

13366	$y^{''} + 4 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.665

13367	$9 y^{''} - 6 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.646

13368	$y^{''} - 4 y^{'} + 29 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.796

13369	$y^{''} + 6 y^{'} + 58 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.861

13370	$y^{''} + 6 y^{'} + 13 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.807

13371	$y^{''} + 2 y^{'} + 5 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.748

13372	$9 y^{''} + 6 y^{'} + 5 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.852

13373	$4 y^{''} + 4 y^{'} + 37 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.780

13374	$y^{'''} - 6 y^{''} + 11 y^{'} - 6 y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.137

13375	$y^{'''} - 2 y^{''} + 4 y^{'} - 8 y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.107

13376	$y^{'''} - 3 y^{''} + 4 y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.136

13377	$y^{'''} - 5 y^{''} + 9 y^{'} - 5 y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.102

13378	$y^{''''} + 2 y^{'''} + 6 y^{''} + 2 y^{'} + 5 y = 0$	[[_high_order, _missing_x]]	✓	0.098

13379	$y^{''''} + 3 y^{'''} + y^{''} + 13 y^{'} + 30 y = 0$	[[_high_order, _missing_x]]	✓	0.091

13380	$y^{''} - 3 y^{'} + 8 y = 4 x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.674

13381	$y^{''} - 2 y^{'} - 8 y = 4 e^{2 x} - 21 e^{- 3 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.555

13382	$y^{''} + 2 y^{'} + 5 y = 6 \sin (2 x) + 7 \cos (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.706

13383	$y^{''} + 2 y^{'} + 2 y = 10 \sin (4 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.663

13384	$y^{''} + 2 y^{'} + 4 y = \cos (4 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.739

13385	$y^{''} - 3 y^{'} - 4 y = 16 x - 12 e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.551

13386	$y^{''} + 6 y^{'} + 5 y = 2 e^{x} + 10 e^{5 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.552

13387	$y^{''} + 2 y^{'} + 10 y = 5 x e^{- 2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.657

13388	$y^{'''} + 4 y^{''} + y^{'} - 6 y = - 18 x^{2} + 1$	[[_3rd_order, _with_linear_symmetries]]	✓	0.153

13389	$y^{'''} + 2 y^{''} - 3 y^{'} - 10 y = 8 x e^{- 2 x}$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.167

13390	$y^{'''} + y^{''} + 3 y^{'} - 5 y = 5 \sin (2 x) + 10 x^{2} + 3 x + 7$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.297

13391	$4 y^{'''} - 4 y^{''} - 5 y^{'} + 3 y = 3 x^{3} - 8 x$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.159

13392	$y^{''} + y^{'} - 6 y = 10 e^{2 x} - 18 e^{3 x} - 6 x - 11$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.705

13393	$y^{''} + y^{'} - 2 y = 6 e^{- 2 x} + 3 e^{x} - 4 x^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.708

13394	$y^{'''} - 3 y^{''} + 4 y = 4 e^{x} - 18 e^{- x}$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.193

13395	$y^{'''} - 2 y^{''} - y^{'} + 2 y = 9 e^{2 x} - 8 e^{3 x}$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.181

13396	$y^{'''} + y^{'} = 2 x^{2} + 4 \sin (x)$	[[_3rd_order, _missing_y]]	✓	0.644

13397	$y^{''''} - 3 y^{'''} + 2 y^{''} = 3 e^{- x} + 6 e^{2 x} - 6 x$	[[_high_order, _missing_y]]	✓	0.211

13398	$y^{'''} - 6 y^{''} + 11 y^{'} - 6 y = x e^{x} - 4 e^{2 x} + 6 e^{4 x}$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.243

13399	$y^{'''} - 4 y^{''} + 5 y^{'} - 2 y = 3 x^{2} e^{x} - 7 e^{x}$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.193

13400	$y^{''} + y = x \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.700

2.2.134 Problems 13301 to 13400