Problems 13101 to 13200

Table 2.265: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

13101	$x^{'''} - x^{'} - 8 x = 0$	[[_3rd_order, _missing_x]]	✓	0.096

13102	$x^{'''} + x^{''} = 2 e^{t} + 3 t^{2}$	[[_3rd_order, _missing_y]]	✓	0.119

13103	$x^{'''} - 8 x = 0$	[[_3rd_order, _missing_x]]	✓	0.060

13104	$x^{'''} + x^{''} - x^{'} - 4 x = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.371

13105	$x^{'} + 5 x = Heaviside (t - 2)$ i.c.	[[_linear, ‘class A‘]]	✓	0.609

13106	$x^{'} + x = \sin (2 t)$ i.c.	[[_linear, ‘class A‘]]	✓	0.520

13107	$x^{''} - x^{'} - 6 x = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.318

13108	$x^{''} - 2 x^{'} + 2 x = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.325

13109	$x^{''} - 2 x^{'} + 2 x = e^{- t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.326

13110	$x^{''} - x^{'} = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.174

13111	$x^{''} + \frac{2 x^{'}}{5} + 2 x = 1 - Heaviside (t - 5)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	4.338

13112	$x^{''} + 9 x = \sin (3 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.384

13113	$x^{''} - 2 x = 1$ i.c.	[[_2nd_order, _missing_x]]	✓	0.331

13114	$x^{'} = 2 x + Heaviside (t - 1)$ i.c.	[[_linear, ‘class A‘]]	✓	0.561

13115	$x^{''} + 4 x = \cos (2 t) Heaviside (2 π - t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.842

13116	$x^{'} = x - 2 Heaviside (t - 1)$ i.c.	[[_linear, ‘class A‘]]	✓	0.613

13117	$x^{'} = - x + Heaviside (t - 1) - Heaviside (t - 2)$ i.c.	[[_linear, ‘class A‘]]	✓	0.774

13118	$x^{''} + π^{2} x = π^{2} Heaviside (- t + 1)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.935

13119	$x^{''} - 4 x = 1 - Heaviside (t - 1)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.882

13120	$x^{''} + 3 x^{'} + 2 x = e^{- 4 t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.317

13121	$x^{'} + 3 x = δ (t - 1) + Heaviside (- 4 + t)$ i.c.	[[_linear, ‘class A‘]]	✓	0.791

13122	$x^{''} - x = δ (t - 5)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.532

13123	$x^{''} + x = δ (t - 2)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.545

13124	$x^{''} + 4 x = δ (t - 2) - δ (t - 5)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.674

13125	$x^{''} + x = 3 δ (t - 2 π)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.643

13126	$y^{''} + y^{'} + y = δ (t - 1)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.006

13127	$x^{''} + 4 x = \frac{(t - 5) Heaviside (t - 5)}{5} + (2 - \frac{t}{5}) Heaviside (t - 10)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.169

13128	$[\begin{matrix} x^{'} = - 3 y \\ y^{'} = 2 x \end{matrix}]$	system_of_ODEs	✓	0.533

13129	$[\begin{matrix} x^{'} = - 2 y \\ y^{'} = - 4 x \end{matrix}]$	system_of_ODEs	✓	0.524

13130	$[\begin{matrix} x^{'} = - 3 x \\ y^{'} = 2 y \end{matrix}]$	system_of_ODEs	✓	0.411

13131	$[\begin{matrix} x^{'} = 4 y \\ y^{'} = 2 y \end{matrix}]$	system_of_ODEs	✓	0.416

13132	$[\begin{matrix} x^{'} = x \\ y^{'} = x + 2 y \end{matrix}]$	system_of_ODEs	✓	0.439

13133	$[\begin{matrix} x^{'} = x - y \\ y^{'} = x + y \end{matrix}]$	system_of_ODEs	✓	0.482

13134	$[\begin{matrix} x^{'} = x + 2 y \\ y^{'} = x \end{matrix}]$	system_of_ODEs	✓	0.445

13135	$[\begin{matrix} x^{'} = - x - 2 y \\ y^{'} = 2 x - y \end{matrix}]$	system_of_ODEs	✓	0.508

13136	$[\begin{matrix} x^{'} = - 2 x - 3 y \\ y^{'} = - x + 4 y \end{matrix}]$	system_of_ODEs	✓	0.615

13137	$[\begin{matrix} x^{'} = - 3 y \\ y^{'} = - 2 x + y \end{matrix}]$	system_of_ODEs	✓	0.475

13138	$[\begin{matrix} x^{'} = - 2 x \\ y^{'} = x \end{matrix}]$	system_of_ODEs	✓	0.405

13139	$[\begin{matrix} x^{'} = - 2 x - y \\ y^{'} = - 4 y \end{matrix}]$	system_of_ODEs	✓	0.444

13140	$[\begin{matrix} x^{'} = x - 2 y \\ y^{'} = - 2 x + 4 y \end{matrix}]$	system_of_ODEs	✓	0.450

13141	$[\begin{matrix} x^{'} = - 6 y \\ y^{'} = 6 y \end{matrix}]$	system_of_ODEs	✓	0.416

13142	$[\begin{matrix} x^{'} = 2 x + 3 y \\ y^{'} = - x - 14 \end{matrix}]$	system_of_ODEs	✓	1.237

13143	$[\begin{matrix} x^{'} = 3 y - 3 x \\ y^{'} = x + 2 y - 1 \end{matrix}]$	system_of_ODEs	✓	0.969

13144	$[\begin{matrix} x^{'} = y - x \\ y^{'} = - 3 y \end{matrix}]$	system_of_ODEs	✓	0.449

13145	$[\begin{matrix} x^{'} = x \\ y^{'} = 3 x - 4 y \end{matrix}]$	system_of_ODEs	✓	0.448

13146	$[\begin{matrix} x^{'} = y - x \\ y^{'} = x - 2 y \end{matrix}]$	system_of_ODEs	✓	0.591

13147	$[\begin{matrix} x^{'} = x + y \\ y^{'} = 3 y - 3 x \end{matrix}]$	system_of_ODEs	✓	0.707

13148	$[\begin{matrix} x^{'} = x - 2 y \\ y^{'} = 3 x - 4 y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.574

13149	$[\begin{matrix} x^{'} = 5 x - y \\ y^{'} = 3 x + y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.582

13150	$[\begin{matrix} x^{'} = - 3 x + y \\ y^{'} = - 3 y \end{matrix}]$	system_of_ODEs	✓	0.351

13151	$[\begin{matrix} x^{'} = x - y \\ y^{'} = x + 3 y \end{matrix}]$	system_of_ODEs	✓	0.440

13152	$[\begin{matrix} x^{'} = x + 2 y \\ y^{'} = 3 x + 2 y \end{matrix}]$	system_of_ODEs	✓	0.454

13153	$[\begin{matrix} x^{'} = - 3 x + 4 y \\ y^{'} = - 3 y \end{matrix}]$	system_of_ODEs	✓	0.406

13154	$[\begin{matrix} x^{'} = 2 x + 2 y \\ y^{'} = 6 x + 3 y \end{matrix}]$	system_of_ODEs	✓	0.470

13155	$[\begin{matrix} x^{'} = - 5 x + 3 y \\ y^{'} = 2 x - 10 y \end{matrix}]$	system_of_ODEs	✓	0.479

13156	$[\begin{matrix} x^{'} = 2 x \\ y^{'} = 2 y \end{matrix}]$	system_of_ODEs	✓	0.305

13157	$[\begin{matrix} x^{'} = 3 x - 2 y \\ y^{'} = 4 x - y \end{matrix}]$	system_of_ODEs	✓	0.542

13158	$[\begin{matrix} x^{'} = 5 x - 4 y \\ y^{'} = x + y \end{matrix}]$	system_of_ODEs	✓	0.433

13159	$[\begin{matrix} x^{'} = 9 y \\ y^{'} = - x \end{matrix}]$	system_of_ODEs	✓	0.498

13160	$[\begin{matrix} x^{'} = 2 x + y \\ y^{'} = - x \end{matrix}]$ i.c.	system_of_ODEs	✓	0.540

13161	$[\begin{matrix} x^{'} = x - 2 y \\ y^{'} = - 2 x + 4 y \end{matrix}]$	system_of_ODEs	✓	0.446

13162	$[\begin{matrix} x^{'} = 3 x - y + 1 \\ y^{'} = x + y + 2 \end{matrix}]$ i.c.	system_of_ODEs	✓	0.667

13163	$[\begin{matrix} x^{'} = - 5 x + 3 y + e^{- t} \\ y^{'} = 2 x - 10 y \end{matrix}]$	system_of_ODEs	✓	0.509

13164	$[\begin{matrix} x^{'} = y \\ y^{'} = - x + \cos (w t) \end{matrix}]$	system_of_ODEs	✓	0.778

13165	$[\begin{matrix} x^{'} = 3 x + 2 y + 3 \\ y^{'} = 7 x + 5 y + 2 t \end{matrix}]$	system_of_ODEs	✓	0.914

13166	$[\begin{matrix} x^{'} = x - 3 y \\ y^{'} = 3 x + 7 y \end{matrix}]$	system_of_ODEs	✓	0.436

13167	$y^{'} + y = x + 1$	[[_linear, ‘class A‘]]	✓	1.514

13168	$y^{''} - 7 y^{'} + 12 y = 0$	[[_2nd_order, _missing_x]]	✓	0.846

13169	$y^{''} - 3 y^{'} + 2 y = 4 x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.148

13170	$(x^{2} + 1) y^{''} + 4 x y^{'} + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.870

13171	$2 x y y^{'} + x^{2} + y^{2} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]	✓	58.829

13172	$x y^{'} + y = x^{3} y^{3}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	3.405

13173	$y^{'} + 3 y = 3 x^{2} e^{- 3 x}$	[[_linear, ‘class A‘]]	✓	1.882

13174	$y^{'} + 4 x y = 8 x$	[_separable]	✓	1.505

13175	$y^{''} - 2 y^{'} - 8 y = 0$	[[_2nd_order, _missing_x]]	✓	0.845

13176	$y^{'''} - 2 y^{''} - 4 y^{'} + 8 y = 0$	[[_3rd_order, _missing_x]]	✓	0.054

13177	$y^{'''} - 3 y^{''} - 4 y^{'} + 12 y = 0$	[[_3rd_order, _missing_x]]	✓	0.063

13178	$x^{3} y^{'''} + 2 x^{2} y^{''} - 10 x y^{'} - 8 y = 0$	[[_3rd_order, _fully, _exact, _linear]]	✓	0.116

13179	$y^{'} + 2 y = 6 e^{x} + 4 x e^{- 2 x}$	[[_linear, ‘class A‘]]	✓	1.707

13180	$y^{''} - 4 y^{'} + 4 y = - 8 \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.437

13181	${y^{'}}^{2} - 4 y = 0$	[_quadrature]	✓	0.371

13182	$y^{''} + y^{'} - 6 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.430

13183	$y^{'} + y = 2 x e^{- x}$ i.c.	[[_linear, ‘class A‘]]	✓	2.069

13184	$y^{'} + y = 2 x e^{- x}$ i.c.	[[_linear, ‘class A‘]]	✓	2.169

13185	$y^{''} - y^{'} - 12 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.417

13186	$y^{''} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✗	1.638

13187	$y^{''} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✗	1.634

13188	$y^{''} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.464

13189	$x^{3} y^{'''} - 3 x^{2} y^{''} + 6 x y^{'} - 6 y = 0$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓	0.179

13190	$y^{'} = x^{2} \sin (y)$ i.c.	[_separable]	✓	3.608

13191	$y^{'} = \frac{y^{2}}{- 2 + x}$ i.c.	[_separable]	✓	2.594

13192	$y^{'} = y^{1 / 3}$ i.c.	[_quadrature]	✓	2.236

13193	$3 x + 2 y + (2 x + y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.781

13194	$y^{2} + 3 + (2 x y - 4) y^{'} = 0$	[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.563

13195	$2 x y + 1 + (x^{2} + 4 y) y^{'} = 0$	[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.307

13196	$3 x^{2} y + 2 - (x^{3} + y) y^{'} = 0$	[_rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✗	1.213

13197	$6 x y + 2 y^{2} - 5 + (3 x^{2} + 4 x y - 6) y^{'} = 0$	[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.757

13198	$y \sec {(x)}^{2} + \sec (x) \tan (x) + (\tan (x) + 2 y) y^{'} = 0$	[_exact, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	12.647

13199	$\frac{x}{y^{2}} + x + (\frac{x^{2}}{y^{3}} + y) y^{'} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	2.036

13200	$\frac{(2 s - 1) s^{'}}{t} + \frac{s - s^{2}}{t^{2}} = 0$	[_separable]	✓	3.924

2.2.132 Problems 13101 to 13200