Problems 8101 to 8200

Table 2.165: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

8101	$(x^{2} + 1) y^{''} + 2 x y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.389

8102	$y^{''} + x y^{'} + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.369

8103	$y^{''} + y^{'} - x y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.380

8104	$y^{''} + y^{'} - x y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.383

8105	$y^{''} + (p + \frac{1}{2} - \frac{x^{2}}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.482

8106	$y^{''} + x y = 0$	[[_Emden, _Fowler]]	✓	0.322

8107	$(- x^{2} + 1) y^{''} - x y^{'} + p^{2} y = 0$	[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.684

8108	$y^{''} - 2 x y^{'} + 2 p y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.487

8109	$x^{3} (- 1 + x) y^{''} - 2 (- 1 + x) y^{'} + 3 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.105

8110	$x^{2} (x^{2} - 1) y^{''} - x (1 - x) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.253

8111	$x^{2} y^{''} + (2 - x) y^{'} = 0$	[[_2nd_order, _missing_y]]	✗	0.141

8112	$(3 x + 1) x y^{''} - (x + 1) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.602

8113	$y^{''} + y \sin (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.654

8114	$x y^{''} + y \sin (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.999

8115	$x^{2} y^{''} + y \sin (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.196

8116	$x^{3} y^{''} + y \sin (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.587

8117	$x^{4} y^{''} + y \sin (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.109

8118	$x^{3} y^{''} + (\cos (2 x) - 1) y^{'} + 2 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.774

8119	$4 x^{2} y^{''} + (2 x^{4} - 5 x) y^{'} + (3 x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.840

8120	$x^{2} y^{''} + 3 x y^{'} + 4 x y = 0$	[[_Emden, _Fowler]]	✓	1.306

8121	$x^{3} y^{''} - 4 x^{2} y^{'} + 3 x y = 0$	[[_Emden, _Fowler]]	✓	0.619

8122	$4 x y^{''} + 3 y^{'} + y = 0$	[[_Emden, _Fowler]]	✓	0.799

8123	$2 x y^{''} + (3 - x) y^{'} - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.756

8124	$2 x y^{''} + (x + 1) y^{'} + 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.835

8125	$2 x^{2} y^{''} + x y^{'} - (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.852

8126	$x^{2} y^{''} + x y^{'} + x^{2} y = 0$	[_Lienard]	✓	0.474

8127	$y^{''} + \frac{y^{'}}{x^{2}} - \frac{y}{x^{3}} = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✗	0.096

8128	$x^{2} y^{''} + (3 x - 1) y^{'} + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✗	0.126

8129	$x^{2} y^{''} - 3 x y^{'} + (4 x + 4) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.726

8130	$4 x^{2} y^{''} - 8 x^{2} y^{'} + (4 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.824

8131	$x y^{''} + 2 y^{'} + x y = 0$	[_Lienard]	✓	0.659

8132	$x^{2} y^{''} - x^{2} y^{'} + (x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.857

8133	$x y^{''} - y^{'} + 4 x^{3} y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.605

8134	${(- 1 + x)}^{2} y^{''} - 3 (- 1 + x) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.633

8135	$3 {(x + 1)}^{2} y^{''} - (x + 1) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.634

8136	$x^{2} y^{''} + x y^{'} + (x^{2} - 1) y = 0$	[_Bessel]	✓	1.228

8137	$x^{2} y^{''} + x y^{'} + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.724

8138	$x (1 - x) y^{''} + (\frac{3}{2} - 2 x) y^{'} + 2 y = 0$	[_Jacobi]	✓	0.951

8139	$(2 x^{2} + 2 x) y^{''} + (1 + 5 x) y^{'} + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.635

8140	$(x^{2} - 1) y^{''} + (5 x + 4) y^{'} + 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.927

8141	$(x^{2} - x - 6) y^{''} + (5 + 3 x) y^{'} + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.881

8142	$(- x^{2} + 1) y^{''} - x y^{'} + p^{2} y = 0$	[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.388

8143	$(1 - e^{x}) y^{''} + \frac{y^{'}}{2} + y e^{x} = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.041

8144	$y^{''} + 2 x y = x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.364

8145	$y^{''} - x y^{'} + y = x$	[[_2nd_order, _with_linear_symmetries]]	✓	0.377

8146	$y^{''} + y^{'} + y = x^{3} - x$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.533

8147	$2 y^{''} + x y^{'} + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.383

8148	$(x^{2} + 4) y^{''} - y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.584

8149	$(x^{2} + 1) y^{''} - x y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.386

8150	$y^{''} - (x + 1) y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.455

8151	$(- 1 + x) y^{''} + (x + 1) y^{'} + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.562

8152	$(x^{2} + 1) x^{2} y^{''} - x y^{'} + (x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.776

8153	$x^{2} y^{''} + x y^{'} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.719

8154	$x y^{''} - 4 y^{'} + x y = 0$	[_Lienard]	✓	0.665

8155	$4 x^{2} y^{''} + 4 x^{2} y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.746

8156	$2 x y^{''} + (1 - x) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.818

8157	$x y^{''} - (- 1 + x) y^{'} + 2 y = 0$	[_Laguerre]	✓	0.688

8158	$x^{2} y^{''} + x (1 - x) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.726

8159	$x y^{''} + (x + 1) y^{'} + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.642

8160	$x^{3} y^{'''} + 2 x^{2} y^{''} + (x^{2} + x) y^{'} + x y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.026

8161	$x^{3} y^{'''} + x^{2} y^{''} - 3 x y^{'} + (- 1 + x) y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.026

8162	$x^{3} y^{'''} - 2 x^{2} y^{''} + (x^{2} + 2 x) y^{'} - x y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.026

8163	$x^{3} y^{'''} + (2 x^{3} - x^{2}) y^{''} - x y^{'} + y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.026

8164	$x^{3} y^{''} + x^{2} y^{'} + y = 0$	[[_Emden, _Fowler]]	✓	0.696

8165	$9 {(- 2 + x)}^{2} (x - 3) y^{''} + 6 x (- 2 + x) y^{'} + 16 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.182

8166	$(- x^{2} + 1) y^{''} - 2 x y^{'} + p (p + 1) y = 0$	[_Gegenbauer]	✓	1.028

8167	$y^{''} + 5 y^{'} + 6 y = 5 e^{3 t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.337

8168	$y^{''} + y^{'} - 6 y = t$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.324

8169	$y^{''} - y = t^{2}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.231

8170	$L i^{'} + R i = E_{0} Heaviside (t)$ i.c.	[[_linear, ‘class A‘]]	✓	0.171

8171	$L i^{'} + R i = E_{0} δ (t)$ i.c.	[[_linear, ‘class A‘]]	✓	0.094

8172	$L i^{'} + R i = E_{0} \sin (ω t)$ i.c.	[[_linear, ‘class A‘]]	✓	0.320

8173	$y^{''} + 3 y^{'} - 5 y = 1$ i.c.	[[_2nd_order, _missing_x]]	✓	0.416

8174	$y^{''} + 3 y^{'} - 2 y = - 6 e^{- t + π}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.800

8175	$y^{''} + 2 y^{'} - y = t e^{- t}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.318

8176	$y^{''} - y^{'} + y = 3 e^{- t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.482

8177	$y^{''} - 5 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓	0.177

8178	$y^{''} + 3 y^{'} + 3 y = 2$	[[_2nd_order, _missing_x]]	✓	0.330

8179	$y^{''} + y^{'} + 2 y = t$	[[_2nd_order, _with_linear_symmetries]]	✓	0.346

8180	$y^{''} - 7 y^{'} + 12 y = t e^{2 t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.186

8181	$i^{''} + 2 i^{'} + 3 i = {\begin{array}{cc} 30 & 0 < t < 2 π \\ 0 & 2 π \leq t \leq 5 π \\ 10 & 5 π < t < \infty \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✗	15.331

8182	$[\begin{matrix} x^{'} = x + 3 y \\ y^{'} = 3 x + y \end{matrix}]$	system_of_ODEs	✓	0.438

8183	$[\begin{matrix} x^{'} = x + 3 y \\ y^{'} = 3 x + y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.554

8184	$[\begin{matrix} x^{'} = x + 2 y \\ y^{'} = 3 x + 2 y \end{matrix}]$	system_of_ODEs	✓	0.451

8185	$[\begin{matrix} x^{'} = x + 2 y + t - 1 \\ y^{'} = 3 x + 2 y - 5 t - 2 \end{matrix}]$	system_of_ODEs	✓	0.497

8186	$[\begin{matrix} x^{'} = x + y \\ y^{'} = y \end{matrix}]$	system_of_ODEs	✓	0.329

8187	$[\begin{matrix} x^{'} = x \\ y^{'} = y \end{matrix}]$	system_of_ODEs	✓	0.285

8188	$[\begin{matrix} x^{'} = - 3 x + 4 y \\ y^{'} = - 2 x + 3 y \end{matrix}]$	system_of_ODEs	✓	0.441

8189	$[\begin{matrix} x^{'} = 4 x - 2 y \\ y^{'} = 5 x + 2 y \end{matrix}]$	system_of_ODEs	✓	0.556

8190	$[\begin{matrix} x^{'} = 5 x + 4 y \\ y^{'} = y - x \end{matrix}]$	system_of_ODEs	✓	0.438

8191	$[\begin{matrix} x^{'} = 4 x - 3 y \\ y^{'} = 8 x - 6 y \end{matrix}]$	system_of_ODEs	✓	0.443

8192	$[\begin{matrix} x^{'} = 2 x \\ y^{'} = 3 y \end{matrix}]$	system_of_ODEs	✓	0.399

8193	$[\begin{matrix} x^{'} = - 4 x - y \\ y^{'} = x - 2 y \end{matrix}]$	system_of_ODEs	✓	0.424

8194	$[\begin{matrix} x^{'} = 7 x + 6 y \\ y^{'} = 2 x + 6 y \end{matrix}]$	system_of_ODEs	✓	0.455

8195	$[\begin{matrix} x^{'} = x - 2 y \\ y^{'} = 4 x + 5 y \end{matrix}]$	system_of_ODEs	✓	0.553

8196	$[\begin{matrix} x^{'} = x + y - 5 t + 2 \\ y^{'} = 4 x - 2 y - 8 t - 8 \end{matrix}]$	system_of_ODEs	✓	0.512

8197	$[\begin{matrix} x^{'} = 3 x - 4 y \\ y^{'} = 4 x - 7 y \end{matrix}]$	system_of_ODEs	✓	0.468

8198	$[\begin{matrix} x^{'} = x + y \\ y^{'} = 4 x + y \end{matrix}]$	system_of_ODEs	✓	0.440

8199	$[\begin{matrix} x^{'} = - 3 x + \sqrt{2} y \\ y^{'} = \sqrt{2} x - 2 y \end{matrix}]$	system_of_ODEs	✓	0.512

8200	$[\begin{matrix} x^{'} = 5 x + 3 y \\ y^{'} = - 6 x - 4 y \end{matrix}]$	system_of_ODEs	✓	0.452

2.2.82 Problems 8101 to 8200