Problems 4101 to 4200

Table 2.85: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

4101	$y^{'} - y \tan (x) = x$ i.c.	[_linear]	✓	1.619

4102	$y^{'} = e^{x - 2 y}$ i.c.	[_separable]	✓	2.474

4103	$y^{'} = \frac{x^{2} + y^{2}}{2 x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	1.684

4104	$y^{'} x = x + y$ i.c.	[_linear]	✓	1.477

4105	$e^{- y} + (x^{2} + 1) y^{'} = 0$ i.c.	[_separable]	✓	1.919

4106	$y^{'} = e^{x} \sin (x)$ i.c.	[_quadrature]	✓	0.716

4107	$y^{'} - 3 y = e^{3 x} + e^{- 3 x}$ i.c.	[[_linear, ‘class A‘]]	✓	1.965

4108	$y^{'} = x + \frac{1}{x}$ i.c.	[_quadrature]	✓	0.521

4109	$y^{'} x + 2 y = (3 x + 2) e^{3 x}$ i.c.	[_linear]	✓	1.854

4110	$2 \sin (3 x) \sin (2 y) y^{'} - 3 \cos (3 x) \cos (2 y) = 0$ i.c.	[_separable]	✓	4.854

4111	$x y^{'} y = (x + 1) (1 + y)$ i.c.	[_separable]	✓	1.807

4112	$y^{'} = \frac{2 x - y}{2 x + y}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	73.236

4113	$y^{'} = \frac{3 x - y + 1}{3 y - x + 5}$ i.c.	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	5.519

4114	$3 y - 7 x + 7 + (7 y - 3 x + 3) y^{'} = 0$ i.c.	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1218.450

4115	$x + (2 - x + 2 y) y^{'} = x y (y^{'} - 1)$	[_quadrature]	✓	0.534

4116	$\cos (x) y^{'} + y \sin (x) = 1$ i.c.	[_linear]	✓	2.190

4117	$(x + y^{2}) y^{'} + y - x^{2} = 0$ i.c.	[_exact, _rational]	✓	2.441

4118	$y^{''} + 8 y^{'} + 15 y = 0$	[[_2nd_order, _missing_x]]	✓	0.355

4119	$y^{''} + 2 y^{'} - 15 y = 0$	[[_2nd_order, _missing_x]]	✓	0.343

4120	$y^{''} + 6 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	0.364

4121	$y^{''} + 6 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	0.394

4122	$y^{''} - 3 y^{'} + 2 y = 0$	[[_2nd_order, _missing_x]]	✓	0.343

4123	$y^{''} - 4 y^{'} + 13 y = 0$	[[_2nd_order, _missing_x]]	✓	0.518

4124	$2 y^{''} + 3 y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	1.109

4125	$y^{''} + 25 y = 0$	[[_2nd_order, _missing_x]]	✓	1.461

4126	$4 y^{''} + y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.582

4127	$y^{''} = 0$	[[_2nd_order, _quadrature]]	✓	0.715

4128	$y^{''} - 6 y^{'} + 5 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.559

4129	$y^{''} - 4 y^{'} + 3 y = 1$	[[_2nd_order, _missing_x]]	✓	0.419

4130	$y^{''} + y^{'} - 2 y = - 2 x^{2} + 2 x + 2$	[[_2nd_order, _with_linear_symmetries]]	✓	0.473

4131	$y^{''} + y = x^{3} + x$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.585

4132	$y^{''} - 6 y^{'} + 9 y = e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.532

4133	$y^{''} + 2 y = x + e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.726

4134	$y^{''} + 2 y = e^{x} + 2$	[[_2nd_order, _with_linear_symmetries]]	✓	0.701

4135	$y^{''} - y = 2 e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.595

4136	$y^{''} + y = \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.657

4137	$y^{''} - y = 4 x e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.614

4138	$y^{''} - 2 y^{'} + 3 y = x^{3} + \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.899

4139	$(x^{2} + 1) y^{''} + y^{'} x - 4 y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.907

4140	$x^{2} y^{''} - 2 y^{'} x + 2 y = x^{2} + 2$	[[_2nd_order, _with_linear_symmetries]]	✓	2.108

4141	$y^{''} + 2 n y^{'} + n^{2} y = A \cos (p x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.878

4142	$y^{'''} - 3 y^{''} + 2 y^{'} = 0$	[[_3rd_order, _missing_x]]	✓	0.079

4143	$y^{'''} - y^{''} - 12 y = 0$	[[_3rd_order, _missing_x]]	✓	0.127

4144	$y^{'''} - 3 y^{''} + 4 y^{'} - 2 y = 0$	[[_3rd_order, _missing_x]]	✓	0.084

4145	$y^{'''} + 2 y^{''} - 5 y^{'} - 6 y = 0$	[[_3rd_order, _missing_x]]	✓	0.077

4146	$y^{'''} - 3 y^{''} + 3 y^{'} - y = 0$	[[_3rd_order, _missing_x]]	✓	0.073

4147	$y^{'''} + 4 y^{'} = 0$	[[_3rd_order, _missing_x]]	✓	0.080

4148	$y^{''''} + 5 y^{''} + 4 y = 0$	[[_high_order, _missing_x]]	✓	0.085

4149	$y^{''''} - y^{'''} - 9 y^{''} - 11 y^{'} - 4 y = 0$	[[_high_order, _missing_x]]	✓	0.081

4150	$y^{(6)} + 9 y^{''''} + 24 y^{''} + 16 y = 0$	[[_high_order, _missing_x]]	✓	0.107

4151	$y^{'''} - y = 0$	[[_3rd_order, _missing_x]]	✓	0.091

4152	$y^{''} - 3 y^{'} + 2 y = \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.574

4153	$y^{''} + 2 y^{'} - 2 y = x^{2} + 1$	[[_2nd_order, _with_linear_symmetries]]	✓	0.584

4154	$y^{''} + \frac{y^{'}}{2} + \frac{y}{8} = \frac{\sin (x)}{8} - \frac{\cos (x)}{4}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.699

4155	$y^{''} + 3 y^{'} + 2 y = e^{x} - 2 e^{2 x} + \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.697

4156	$y^{''} - 4 y^{'} + 4 y = x^{3} e^{2 x} + x e^{2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.622

4157	$y^{''} + 3 y^{'} + 2 y = x \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.767

4158	$y^{''} - 6 y^{'} + 9 y = e^{x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.701

4159	$y^{'''} - y^{''} - 4 y^{'} + 4 y = 2 x^{2} - 4 x - 1 + 2 x^{2} e^{2 x} + 5 x e^{2 x} + e^{2 x}$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.207

4160	$y^{''''} + 10 y^{''} + 9 y = \cos (2 x + 3)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.233

4161	$y^{''} - 3 y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.579

4162	$y^{''} + 9 y = 8 \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.063

4163	$25 y^{''} - 30 y^{'} + 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.705

4164	$9 y^{''} - 6 y^{'} + y = (4 x^{2} + 24 x + 18) e^{x}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.975

4165	$x^{3} y^{'''} + x^{2} y^{''} - 2 y^{'} x + 2 y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓	0.137

4166	$[\begin{matrix} y_{1}^{'} = y_{2} \\ y_{2}^{'} = 3 y_{2} - 2 y_{1} \end{matrix}]$	system_of_ODEs	✓	0.332

4167	$[\begin{matrix} y_{1}^{'} = y_{1} + y_{2} \\ y_{2}^{'} = 3 y_{2} - y_{1} \end{matrix}]$	system_of_ODEs	✓	0.420

4168	$[\begin{matrix} y_{1}^{'} = y_{1} - y_{2} \\ y_{2}^{'} = 2 y_{1} + 3 y_{2} \end{matrix}]$	system_of_ODEs	✓	0.544

4169	$[\begin{matrix} y_{1}^{'} = 4 y_{2} \\ y_{2}^{'} = 4 y_{2} - y_{1} \end{matrix}]$	system_of_ODEs	✓	0.399

4170	$[\begin{matrix} y_{1}^{'} = y_{1} + y_{2} \\ y_{2}^{'} = y_{1} - y_{2} \end{matrix}]$	system_of_ODEs	✓	0.525

4171	$[\begin{matrix} y_{1}^{'} = y_{2} \\ y_{2}^{'} = y_{1} \end{matrix}]$	system_of_ODEs	✓	0.335

4172	$[\begin{matrix} y_{1}^{'} = y_{2} - y_{1} \\ y_{2}^{'} = 3 y_{1} - 4 y_{2} \end{matrix}]$	system_of_ODEs	✓	0.599

4173	$[\begin{matrix} 2 y_{1}^{'} = y_{1} + y_{2} \\ 2 y_{2}^{'} = 5 y_{2} - 3 y_{1} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.503

4174	$[\begin{matrix} y_{1}^{'} = - 2 y_{2} \\ y_{2}^{'} = y_{1} + 2 y_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.569

4175	$[\begin{matrix} y_{1}^{'} = 1 \\ y_{2}^{'} = 2 y_{1} \end{matrix}]$	system_of_ODEs	✓	0.378

4176	$[\begin{matrix} 2 y_{1}^{'} + y_{2}^{'} - 4 y_{1} - y_{2} = e^{x} \\ y_{1}^{'} + 3 y_{1} + y_{2} = 0 \end{matrix}]$	system_of_ODEs	✓	0.783

4177	$[\begin{matrix} y_{1}^{'} = y_{2} \\ y_{2}^{'} = - y_{1} + y_{3} \\ y_{3}^{'} = - y_{2} \end{matrix}]$	system_of_ODEs	✓	0.695

4178	$y^{''} + \frac{y}{x^{2}} = 0$	[[_Emden, _Fowler]]	✓	0.502

4179	$y^{''} - \frac{(- 3 x^{2} + x) y^{'}}{2 x^{3} + 2 x^{2}} + \frac{y}{2 x^{3} + 2 x^{2}} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.688

4180	$y^{''} + (1 - \frac{1}{x}) y^{'} - \frac{y}{x} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.652

4181	$y^{''} + \frac{2 y^{'}}{x} + y = 0$	[_Lienard]	✓	0.625

4182	$y^{''} - 2 y^{'} + (\frac{1}{4 x^{2}} - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.820

4183	$y^{''} - \frac{(x^{2} + 4 x + 2) ((1 - x) y^{'} + y)}{x (- x^{2} + 2)} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.874

4184	$y^{''} - \frac{3 y^{'}}{x (1 - x)} + \frac{2 y}{x (1 - x)} = 0$	[_Jacobi, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.705

4185	$y^{''} + \frac{(1 - x) y^{'}}{2 x} - \frac{y}{4 x} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.686

4186	$y^{''} - \frac{y^{'}}{2 x} + \frac{y}{4 x} = 0$	[[_Emden, _Fowler]]	✓	0.714

4187	$y^{''} - \frac{y^{'}}{x} + (1 + \frac{1}{x^{2}}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.609

4188	$y^{''} + \frac{(1 - 5 x) y^{'}}{- x^{2} + x} - \frac{4 y}{- x^{2} + x} = 0$	[_Jacobi]	✓	0.632

4189	$y^{''} + \frac{(x - 1) y^{'}}{x (x + 1)} - \frac{y}{x (x + 1)} = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.661

4190	$y y^{'} = x$	[_separable]	✓	3.705

4191	$y^{'} - y = x^{3}$	[[_linear, ‘class A‘]]	✓	1.288

4192	$y^{'} + \cot (x) y = x$	[_linear]	✓	1.481

4193	$y^{'} + \cot (x) y = \tan (x)$	[_linear]	✓	1.671

4194	$y^{'} + y \tan (x) = \cot (x)$	[_linear]	✓	1.659

4195	$y^{'} + y \ln (x) = x^{- x}$	[_linear]	✓	1.382

4196	$y^{'} x + y = x$	[_linear]	✓	2.323

4197	$y^{'} x - y = x^{3}$	[_linear]	✓	1.374

4198	$y^{'} x + n y = x^{n}$	[_linear]	✓	1.230

4199	$y^{'} x - n y = x^{n}$	[_linear]	✓	1.040

4200	$(x^{3} + x) y^{'} + y = x$	[_linear]	✓	2.723

2.2.42 Problems 4101 to 4200