Problems 7201 to 7300

Table 2.147: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

7201	$(x^{2} - 25) y^{''} + 2 y^{'} x + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.417

7202	$(x^{2} - 25) y^{''} + 2 y^{'} x + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.604

7203	$(x^{2} - 2 x + 10) y^{''} + y^{'} x - 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.542

7204	$(x^{2} - 2 x + 10) y^{''} + y^{'} x - 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.602

7205	$y^{''} - x y = 0$	[[_Emden, _Fowler]]	✓	0.310

7206	$y^{''} + x^{2} y = 0$	[[_Emden, _Fowler]]	✓	0.286

7207	$y^{''} - 2 y^{'} x + y = 0$	[_Lienard]	✓	0.378

7208	$y^{''} - y^{'} x + 2 y = 0$	[_Hermite]	✓	0.308

7209	$y^{''} + x^{2} y^{'} + x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.348

7210	$y^{''} + 2 y^{'} x + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.356

7211	$(x - 1) y^{''} + y^{'} = 0$	[[_2nd_order, _missing_y]]	✓	0.341

7212	$(x + 2) y^{''} + y^{'} x - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.338

7213	$y^{''} - (x + 1) y^{'} - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.413

7214	$(x^{2} + 1) y^{''} - 6 y = 0$	[[_Emden, _Fowler]]	✓	0.417

7215	$(x^{2} + 2) y^{''} + 3 y^{'} x - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.454

7216	$(x^{2} - 1) y^{''} + y^{'} x - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.438

7217	$(x - 1) y^{''} - y^{'} x + y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.480

7218	$(x + 1) y^{''} - (2 - x) y^{'} + y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.519

7219	$y^{''} - 2 y^{'} x + 8 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.449

7220	$(x^{2} + 1) y^{''} + 2 y^{'} x = 0$ i.c.	[[_2nd_order, _missing_y]]	✓	0.475

7221	$y^{''} + y \sin (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.506

7222	$y^{''} + e^{x} y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.607

7223	$y^{''} + y^{'} x + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.375

7224	$x^{3} y^{''} + 4 x^{2} y^{'} + 3 y = 0$	[[_Emden, _Fowler]]	✗	0.169

7225	$x {(3 + x)}^{2} y^{''} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.344

7226	${(x^{2} - 9)}^{2} y^{''} + (3 + x) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.598

7227	$y^{''} - \frac{y^{'}}{x} + \frac{y}{{(x - 1)}^{3}} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.567

7228	$(x^{3} + 4 x) y^{''} - 2 y^{'} x + 6 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.436

7229	$x^{2} {(x - 5)}^{2} y^{''} + 4 y^{'} x + (x^{2} - 25) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.212

7230	$(x^{2} + x - 6) y^{''} + (3 + x) y^{'} + (x - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.617

7231	$x {(x^{2} + 1)}^{2} y^{''} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.433

7232	$x^{3} (x^{2} - 25) {(x - 2)}^{2} y^{''} + 3 x (x - 2) y^{'} + 7 (5 + x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.192

7233	${(x^{3} - 2 x^{2} + 3 x)}^{2} y^{''} + x {(x - 3)}^{2} y^{'} - (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.005

7234	$(x^{2} - 1) y^{''} + 5 (x + 1) y^{'} + (x^{2} - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.546

7235	$x y^{''} + (3 + x) y^{'} + 7 x^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.319

7236	$x^{2} y^{''} + (\frac{5}{3} x + x^{2}) y^{'} - \frac{y}{3} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.796

7237	$x y^{''} + y^{'} + 10 y = 0$	[[_Emden, _Fowler]]	✓	0.566

7238	$2 x y^{''} - y^{'} + 2 y = 0$	[[_Emden, _Fowler]]	✓	0.647

7239	$2 x y^{''} + 5 y^{'} + x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.572

7240	$4 x y^{''} + \frac{y^{'}}{2} + y = 0$	[[_Emden, _Fowler]]	✓	0.648

7241	$2 x^{2} y^{''} - y^{'} x + (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.651

7242	$3 x y^{''} + (2 - x) y^{'} - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.683

7243	$x^{2} y^{''} - (x - \frac{2}{9}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.745

7244	$2 x y^{''} - (2 x + 3) y^{'} + y = 0$	[_Laguerre]	✓	0.697

7245	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{4}{9}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.612

7246	$9 x^{2} y^{''} + 9 x^{2} y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.738

7247	$2 x^{2} y^{''} + 3 y^{'} x + (2 x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.691

7248	$x y^{''} + 2 y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.627

7249	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.674

7250	$x y^{''} - y^{'} x + y = 0$	[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.351

7251	$y^{''} + \frac{3 y^{'}}{x} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.219

7252	$x y^{''} + (1 - x) y^{'} - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.556

7253	$x y^{''} + y^{'} + y = 0$	[[_Emden, _Fowler]]	✓	0.567

7254	$x y^{''} + (x - 6) y^{'} - 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.950

7255	$x (x - 1) y^{''} + 3 y^{'} - 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.635

7256	$x^{4} y^{''} + λ y = 0$	[[_Emden, _Fowler]]	✗	0.173

7257	$x^{3} y^{''} + y = 0$	[[_Emden, _Fowler]]	✗	0.136

7258	$x^{2} y^{''} + (3 x - 1) y^{'} + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✗	0.214

7259	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{9}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.608

7260	$x^{2} y^{''} + y^{'} x + (x^{2} - 1) y = 0$	[_Bessel]	✓	1.221

7261	$4 x^{2} y^{''} + 4 y^{'} x + (4 x^{2} - 25) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.683

7262	$16 x^{2} y^{''} + 16 y^{'} x + (16 x^{2} - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.656

7263	$x y^{''} + y^{'} + x y = 0$	[_Lienard]	✓	0.516

7264	$x y^{''} + y^{'} + (x - \frac{4}{x}) y = 0$	[_Bessel]	✓	1.309

7265	$x^{2} y^{''} + y^{'} x + (9 x^{2} - 4) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.288

7266	$x^{2} y^{''} + y^{'} x + (36 x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.646

7267	$x^{2} y^{''} + y^{'} x + (25 x^{2} - \frac{4}{9}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.647

7268	$x^{2} y^{''} + y^{'} x + (2 x^{2} - 64) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.830

7269	$x y^{''} + 2 y^{'} + 4 y = 0$	[[_Emden, _Fowler]]	✓	1.240

7270	$x y^{''} + 3 y^{'} + x y = 0$	[_Lienard]	✓	1.159

7271	$x y^{''} - y^{'} + x y = 0$	[_Lienard]	✓	1.135

7272	$x y^{''} - 5 y^{'} + x y = 0$	[_Lienard]	✓	1.351

7273	$x^{2} y^{''} + (x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.644

7274	$4 x^{2} y^{''} + (16 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.604

7275	$x y^{''} + 3 y^{'} + x^{3} y = 0$	[[_Emden, _Fowler]]	✓	0.558

7276	$9 x^{2} y^{''} + 9 y^{'} x + (x^{6} - 36) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.635

7277	$y^{''} - x^{2} y = 0$	[[_Emden, _Fowler]]	✓	0.289

7278	$x y^{''} + y^{'} - 7 x^{3} y = 0$	[[_Emden, _Fowler]]	✓	0.488

7279	$y^{''} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.363

7280	$x^{2} y^{''} + 4 y^{'} x + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.657

7281	$16 x^{2} y^{''} + 32 y^{'} x + (x^{4} - 12) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.620

7282	$4 x^{2} y^{''} - 4 y^{'} x + (16 x^{4} + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.696

7283	$2 x y^{''} + y^{'} + y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.650

7284	$y^{''} - y^{'} x - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.397

7285	$(x - 1) y^{''} + 3 y = 0$	[[_Emden, _Fowler]]	✓	0.447

7286	$y^{''} - x^{2} y^{'} + x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.344

7287	$x y^{''} - (x + 2) y^{'} + 2 y = 0$	[_Laguerre]	✓	0.709

7288	$\cos (x) y^{''} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.795

7289	$y^{''} + y^{'} x + 2 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.398

7290	$(x + 2) y^{''} + 3 y = 0$ i.c.	[[_Emden, _Fowler]]	✓	0.418

7291	$(x + 1) y^{'} = y$	[_separable]	✓	0.273

7292	$y^{'} = - 2 x y$	[_separable]	✓	0.315

7293	$y^{'} x - 3 y = k$	[_separable]	✓	0.305

7294	$y^{''} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.360

7295	$y^{''} - y^{'} + x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.379

7296	$y^{''} - y^{'} + x^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.465

7297	$(- x^{2} + 1) y^{''} - 2 y^{'} x + 2 y = 0$	[_Gegenbauer]	✓	0.348

7298	$y^{''} + (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.396

7299	$y^{''} - 4 y^{'} x + (4 x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.442

7300	$y^{'} + 4 y = 1$ i.c.	[_quadrature]	✓	0.392

2.2.73 Problems 7201 to 7300