Problems 19101 to 19200

Table 2.385: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

19101	$y^{''} + 9 y = \cos (2 x) + \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	4.615

19102	$y^{''} + a^{2} y = \cos (a x) + \cos (b x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	4.671

19103	$y^{''} + 4 y = e^{x} + \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	4.637

19104	$y^{'''} + 3 y^{''} - y^{'} - 12 y = \cos (4 x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.211

19105	$y^{''} - 4 y = 2 \sin (\frac{x}{2})$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.529

19106	$y^{''} + y = \sin (3 x) - \cos {(\frac{x}{2})}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	3.395

19107	$y^{'''} - 4 y^{''} + 5 y^{'} - 2 = 0$	[[_3rd_order, _missing_x]]	✓	0.088

19108	$y^{'''} - y^{''} - y^{'} + y = x$	[[_3rd_order, _with_linear_symmetries]]	✓	0.092

19109	$y^{'''} - y^{''} - 6 y^{'} = x^{2} + 1$	[[_3rd_order, _missing_y]]	✓	0.101

19110	$y^{'''} + 2 y^{''} + y^{'} = e^{2 x} + x^{2} + x$	[[_3rd_order, _missing_y]]	✓	0.123

19111	$y^{'''} - 3 y^{'} + 2 y = e^{x}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.102

19112	$y^{''} - 2 y^{'} + 5 y = e^{2 x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	28.595

19113	$y^{''} - 2 y^{'} + 4 y = e^{x} \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	66.583

19114	$y^{''} - y = \cosh (x) \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.938

19115	$y^{'''} - 7 y^{'} - 6 y = e^{2 x} (x + 1)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.119

19116	$y^{''''} + y^{''} + y = a x^{2} + b e^{- x} \sin (2 x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	1.047

19117	$y^{''} + 4 y^{'} - 12 y = (- 1 + x) e^{2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.251

19118	$y^{''} + 2 y^{'} + y = x \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.546

19119	$y^{''''} + 2 y^{''} + y = x^{2} \cos (x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.923

19120	$y^{''''} - y = x \sin (x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.620

19121	$y^{''} - 2 y^{'} + y = x e^{x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.495

19122	$y^{''} - 4 y^{'} + 4 y = 8 x^{2} e^{2 x} \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	36.977

19123	$y^{''} + y = e^{- x} + \cos (x) + x^{3} + e^{x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	8.203

19124	$y^{''''} + y^{''} + y = e^{- \frac{x}{2}} \cos (\frac{\sqrt{3} x}{2})$	[[_high_order, _linear, _nonhomogeneous]]	✓	1.063

19125	$y^{(6)} - 2 y^{(5)} + 3 y^{''''} - 4 y^{'''} + 3 y^{''} - 2 y^{'} + y = \sin {(\frac{x}{2})}^{2} + e^{x}$	[[_high_order, _linear, _nonhomogeneous]]	✓	1.507

19126	$y^{''''} + y^{''} + 16 y = 16 x^{2} + 256$	[[_high_order, _with_linear_symmetries]]	✓	0.244

19127	$y^{''} + y = 3 \cos {(x)}^{2} + 2 \sin {(x)}^{3}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	4.111

19128	$y^{''''} + 10 y^{''} + 9 y = 96 \sin (2 x) \cos (x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.905

19129	$y^{(5)} - 13 y^{'''} + 26 y^{''} + 82 y^{'} + 104 y = 0$	[[_high_order, _missing_x]]	✓	0.073

19130	$y^{''} + 2 y^{'} + 10 y + 37 \sin (3 x) = 0$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	18.756

19131	$y^{''''} + 2 y^{''} + y = 24 x \cos (x)$ i.c.	[[_high_order, _linear, _nonhomogeneous]]	✓	0.790

19132	${y^{'}}^{2} - 7 y^{'} + 12 = 0$	[_quadrature]	✓	0.332

19133	${y^{'}}^{2} - 5 y^{'} + 6 = 0$	[_quadrature]	✓	0.331

19134	${y^{'}}^{2} - 9 y^{'} + 18 = 0$	[_quadrature]	✓	0.327

19135	${y^{'}}^{2} + 2 x y^{'} - 3 x^{2} = 0$	[_quadrature]	✓	0.391

19136	${y^{'}}^{2} + 2 y^{'} y \cot (x) = y^{2}$	[_separable]	✓	1.155

19137	${y^{'}}^{2} - 2 y^{'} \cosh (x) + 1 = 0$	[_quadrature]	✓	0.383

19138	$y^{'} (y^{'} - y) = (x + y) x$	[_quadrature]	✓	0.519

19139	$y {y^{'}}^{2} + (x - y) y^{'} - x = 0$	[_quadrature]	✓	0.473

19140	$x + y {y^{'}}^{2} = y^{'} (1 + x y)$	[_quadrature]	✓	0.434

19141	$x {y^{'}}^{2} + (y - x) y^{'} - y = 0$	[_quadrature]	✓	0.450

19142	${y^{'}}^{3} - a x^{4} = 0$	[_quadrature]	✓	0.414

19143	${y^{'}}^{2} + x y^{'} + y y^{'} + x y = 0$	[_quadrature]	✓	0.511

19144	${y^{'}}^{3} - y^{'} (y^{2} + x y + x^{2}) + x y (x + y) = 0$	[_quadrature]	✓	0.952

19145	$(y^{'} + y + x) (y + x + x y^{'}) (y^{'} + 2 x) = 0$	[_quadrature]	✓	1.021

19146	$x^{2} {y^{'}}^{3} + y (1 + x^{2} y) {y^{'}}^{2} + y^{2} y^{'} = 0$	[_quadrature]	✓	24.958

19147	$x^{2} {y^{'}}^{2} + x y y^{'} - 6 y^{2} = 0$	[_separable]	✓	1.089

19148	${y^{'}}^{3} + 2 x {y^{'}}^{2} - y^{2} {y^{'}}^{2} - 2 x y^{2} y^{'} = 0$	[_quadrature]	✓	2.307

19149	${y^{'}}^{2} {(2 - 3 y)}^{2} = 4 - 4 y$	[_quadrature]	✓	0.405

19150	$y = 3 x + a \ln (y^{'})$	[_separable]	✓	5.630

19151	${y^{'}}^{2} - y y^{'} + x = 0$	[_dAlembert]	✓	1.448

19152	$y = x + a \arctan (y^{'})$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	9.494

19153	$3 {y^{'}}^{5} - y y^{'} + 1 = 0$	[_quadrature]	✓	0.987

19154	$y = x {y^{'}}^{2} + y^{'}$	[_rational, _dAlembert]	✓	0.995

19155	$x {y^{'}}^{2} + a x = 2 y y^{'}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.310

19156	${y^{'}}^{3} + y^{'} = e^{y}$	[_quadrature]	✓	0.647

19157	$y = \sin (y^{'}) - y^{'} \cos (y^{'})$	[_quadrature]	✓	10.900

19158	$y = \sin (x) y^{'} + \cos (x)$	[_linear]	✓	2.075

19159	$y = y^{'} \tan (y^{'}) + \ln (\cos (y^{'}))$	[_dAlembert]	✓	2.230

19160	$x = y y^{'} - {y^{'}}^{2}$	[_dAlembert]	✓	1.451

19161	$(2 x - b) y^{'} = y - a y {y^{'}}^{2}$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	0.866

19162	$x = y + a \ln (y^{'})$	[_separable]	✓	4.085

19163	$y {y^{'}}^{2} + 2 x y^{'} = y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.688

19164	$x (1 + {y^{'}}^{2}) = 1$	[_quadrature]	✓	0.354

19165	$x^{2} = a^{2} (1 + {y^{'}}^{2})$	[_quadrature]	✓	0.417

19166	$y = x y^{'} + \frac{a}{y^{'}}$	[[_homogeneous, ‘class G‘], _rational, _Clairaut]	✓	0.469

19167	$y = x y^{'} + y^{'} - {y^{'}}^{3}$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.431

19168	$y = x y^{'} + a y^{'} (1 - y^{'})$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.488

19169	$y = x y^{'} + \sqrt{1 + {y^{'}}^{2}}$	[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]	✓	1.849

19170	$y = x y^{'} + \sqrt{b^{2} - a^{2} {y^{'}}^{2}}$	[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]	✓	3.287

19171	$(y - x y^{'}) (y^{'} - 1) = y^{'}$	[[_1st_order, _with_linear_symmetries], _rational, _dAlembert]	✓	0.600

19172	$x {y^{'}}^{2} - y y^{'} + a = 0$	[[_homogeneous, ‘class G‘], _rational, _Clairaut]	✓	0.441

19173	$y = y^{'} (x - b) + \frac{a}{y^{'}}$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.543

19174	$y = x y^{'} + {y^{'}}^{3}$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.409

19175	$4 y {y^{'}}^{2} + 2 x y^{'} - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.497

19176	$y {y^{'}}^{2} + 2 x y^{'} - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.682

19177	$x + \frac{y^{'}}{\sqrt{1 + {y^{'}}^{2}}} = a$	[_quadrature]	✓	0.527

19178	$x^{2} {y^{'}}^{2} - 2 x y y^{'} + 2 y^{2} = x^{2}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.539

19179	$y = x y^{'} + x \sqrt{1 + {y^{'}}^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	8.857

19180	$x + y^{'} y (2 {y^{'}}^{2} + 3) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	6.994

19181	$y = \frac{2 a {y^{'}}^{2}}{{(1 + {y^{'}}^{2})}^{2}}$	[_quadrature]	✓	1.056

19182	${(- y + x y^{'})}^{2} = a (1 + {y^{'}}^{2}) {(x^{2} + y^{2})}^{3 / 2}$	[[_1st_order, _with_linear_symmetries]]	✓	55.843

19183	$4 x {y^{'}}^{2} + 4 y y^{'} = y^{4}$	[[_homogeneous, ‘class G‘]]	✓	2.389

19184	$2 {y^{'}}^{3} - (2 x + 4 \sin (x) - \cos (x)) {y^{'}}^{2} - (x \cos (x) - 4 x \sin (x) + \sin (2 x)) y^{'} + x \sin (2 x) = 0$	[_quadrature]	✓	1.029

19185	${(- y + x y^{'})}^{2} = {y^{'}}^{2} - \frac{2 y y^{'}}{x} + 1$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	12.612

19186	$y - x y^{'} = x + y y^{'}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	37.942

19187	$a^{2} y {y^{'}}^{2} - 4 x y^{'} + y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.779

19188	$x^{2} (y - x y^{'}) = y {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries]]	✓	2.825

19189	$({y^{'}}^{2} - \frac{1}{a^{2} - x^{2}}) (y^{'} - \sqrt{\frac{y}{x}}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	2.093

19190	${y^{'}}^{2} (- a^{2} + x^{2}) - 2 x y y^{'} + y^{2} + a^{4} = 0$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	1.250

19191	$x + y y^{'} = a {y^{'}}^{2}$	[_dAlembert]	✓	46.297

19192	$x y {y^{'}}^{2} + y^{'} (3 x^{2} - 2 y^{2}) - 6 x y = 0$	[_separable]	✓	1.405

19193	$2 y = x y^{'} + \frac{a}{y^{'}}$	[[_homogeneous, ‘class G‘], _rational, _dAlembert]	✓	0.660

19194	$y = a y^{'} + \sqrt{1 + {y^{'}}^{2}}$	[_quadrature]	✓	2.000

19195	$(a {y^{'}}^{2} - b) x y + (b x^{2} - a y^{2} + c) y^{'} = 0$	[_rational]	✓	166.756

19196	$y = a y^{'} + b {y^{'}}^{2}$	[_quadrature]	✓	0.515

19197	${y^{'}}^{3} - (y + 2 x - e^{x - y}) {y^{'}}^{2} + (2 x y - 2 x e^{x - y} - y e^{x - y}) y^{'} + 2 x y e^{x - y} = 0$	[_quadrature]	✓	1.616

19198	$(1 + 6 y^{2} - 3 x^{2} y) y^{'} = 3 x y^{2} - x^{2}$	[_exact, _rational]	✓	1.585

19199	$(x^{2} + 1) {y^{'}}^{2} - 2 x y y^{'} + y^{2} = 1$	[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]	✓	0.658

19200	$(x^{3} y^{3} + y^{2} x^{2} + x y + 1) y + (x^{3} y^{3} - y^{2} x^{2} - x y + 1) x y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	2.162

2.2.192 Problems 19101 to 19200