Problems 3501 to 3600

Table 2.73: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

3501	$(- z^{2} + 1) y^{''} - 3 z y^{'} + λ y = 0$	[_Gegenbauer]	✓	0.659

3502	$4 z y^{''} + 2 (1 - z) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.696

3503	$z y^{''} - 2 y^{'} + 9 z^{5} y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.622

3504	$f^{''} + 2 (z - 1) f^{'} + 4 f = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.500

3505	$z^{2} y^{''} - \frac{3 z y^{'}}{2} + (1 + z) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.851

3506	$z y^{''} - 2 y^{'} + y z = 0$	[_Lienard]	✓	0.641

3507	$y^{''} - 2 z y^{'} - 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.419

3508	$z (1 - z) y^{''} + (1 - z) y^{'} + λ y = 0$	[_Jacobi]	✓	0.936

3509	$z y^{''} + (2 z - 3) y^{'} + \frac{4 y}{z} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.716

3510	$(z^{2} + 5 z + 6) y^{''} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.554

3511	$(z^{2} + 5 z + 7) y^{''} + 2 y = 0$	[[_Emden, _Fowler]]	✓	0.562

3512	$y^{''} + \frac{y}{z^{3}} = 0$	[[_Emden, _Fowler]]	✗	0.171

3513	$z y^{''} + (1 - z) y^{'} + λ y = 0$	[_Laguerre]	✓	0.924

3514	$(- z^{2} + 1) y^{''} - z y^{'} + m^{2} y = 0$	[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.555

3515	$y^{'} = 2 x y$	[_separable]	✓	1.193

3516	$y^{'} = \frac{y^{2}}{x^{2} + 1}$	[_separable]	✓	1.420

3517	$e^{x + y} y^{'} - 1 = 0$	[_separable]	✓	2.348

3518	$y^{'} = \frac{y}{x \ln (x)}$	[_separable]	✓	1.256

3519	$y - (x - 2) y^{'} = 0$	[_separable]	✓	1.422

3520	$y^{'} = \frac{2 x (- 1 + y)}{x^{2} + 3}$	[_separable]	✓	1.327

3521	$y - y^{'} x = 3 - 2 x^{2} y^{'}$	[_separable]	✓	1.744

3522	$y^{'} = \frac{\cos (x - y)}{\sin (x) \sin (y)} - 1$	[_separable]	✓	2.678

3523	$y^{'} = \frac{x (- 1 + y^{2})}{2 (x - 2) (x - 1)}$	[_separable]	✓	3.105

3524	$y^{'} = \frac{x^{2} y - 32}{- x^{2} + 16} + 32$	[_linear]	✓	1.759

3525	$(x - a) (x - b) y^{'} - y + c = 0$	[_separable]	✓	2.391

3526	$(x^{2} + 1) y^{'} + y^{2} = - 1$ i.c.	[_separable]	✓	2.291

3527	$(- x^{2} + 1) y^{'} + x y = a x$ i.c.	[_separable]	✓	1.441

3528	$y^{'} = 1 - \frac{\sin (x + y)}{\sin (y) \cos (x)}$ i.c.	[_separable]	✓	3.481

3529	$y^{'} = y^{3} \sin (x)$	[_separable]	✓	2.526

3530	$y^{'} - y = e^{2 x}$	[[_linear, ‘class A‘]]	✓	1.088

3531	$x^{2} y^{'} - 4 x y = x^{7} \sin (x)$	[_linear]	✓	1.599

3532	$y^{'} + 2 x y = 2 x^{3}$	[_linear]	✓	1.462

3533	$y^{'} + \frac{2 x y}{x^{2} + 1} = 4 x$	[_linear]	✓	1.678

3534	$y^{'} + \frac{2 x y}{x^{2} + 1} = \frac{4}{{(x^{2} + 1)}^{2}}$	[_linear]	✓	1.840

3535	$2 \cos {(x)}^{2} y^{'} + y \sin (2 x) = 4 \cos {(x)}^{4}$	[_linear]	✓	3.730

3536	$y^{'} + \frac{y}{x \ln (x)} = 9 x^{2}$	[_linear]	✓	1.392

3537	$y^{'} - y \tan (x) = 8 \sin {(x)}^{3}$	[_linear]	✓	2.471

3538	$x^{'} t + 2 x = 4 e^{t}$	[_linear]	✓	1.302

3539	$y^{'} = \sin (x) (y \sec (x) - 2)$	[_linear]	✓	2.328

3540	$1 - y \sin (x) - \cos (x) y^{'} = 0$	[_linear]	✓	1.897

3541	$y^{'} - \frac{y}{x} = 2 x^{2} \ln (x)$	[_linear]	✓	1.147

3542	$y^{'} + α y = e^{β x}$	[[_linear, ‘class A‘]]	✓	1.202

3543	$y^{'} + \frac{m}{x} = \ln (x)$	[_quadrature]	✓	0.336

3544	$(3 x - y) y^{'} = 3 y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.952

3545	$y^{'} = \frac{{(x + y)}^{2}}{2 x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	2.140

3546	$\sin (\frac{y}{x}) (y^{'} x - y) = x \cos (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	6.512

3547	$y^{'} x = \sqrt{16 x^{2} - y^{2}} + y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	145.614

3548	$y^{'} x - y = \sqrt{9 x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.702

3549	$x (x^{2} - y^{2}) - x (x^{2} + y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.645

3550	$y^{'} x + y \ln (x) = y \ln (y)$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.814

3551	$y^{'} = \frac{y^{2} + 2 x y - 2 x^{2}}{x^{2} - x y + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	6.125

3552	$2 x y^{'} y - 2 y^{2} - x^{2} e^{- \frac{y^{2}}{x^{2}}} = 0$	[[_homogeneous, ‘class A‘]]	✓	4.777

3553	$x^{2} y^{'} = y^{2} + 3 x y + x^{2}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	1.760

3554	$y y^{'} = \sqrt{x^{2} + y^{2}} - x$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	6.901

3555	$2 x (2 x + y) y^{'} = y (4 x - y)$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	3.923

3556	$y^{'} x = x \tan (\frac{y}{x}) + y$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.932

3557	$y^{'} = \frac{x \sqrt{x^{2} + y^{2}} + y^{2}}{x y}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	31.187

3558	$y^{''} - 25 y = 0$	[[_2nd_order, _missing_x]]	✓	1.590

3559	$y^{''} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓	1.431

3560	$y^{''} + y^{'} - 2 y = 0$	[[_2nd_order, _missing_x]]	✓	0.361

3561	$y^{'} = - y^{2}$	[_quadrature]	✓	1.505

3562	$y^{'} = \frac{y}{2 x}$	[_separable]	✓	1.598

3563	$y^{''} + 2 y^{'} + 5 y = 0$	[[_2nd_order, _missing_x]]	✓	0.591

3564	$y^{''} - 9 y = 0$	[[_2nd_order, _missing_x]]	✓	1.601

3565	$x^{2} y^{''} + 5 y^{'} x + 3 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.218

3566	$x^{2} y^{''} - 3 y^{'} x + 4 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.984

3567	$x^{2} y^{''} - 3 y^{'} x + 13 y = 0$	[[_Emden, _Fowler]]	✓	1.064

3568	$2 x^{2} y^{''} - y^{'} x + y = 9 x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.467

3569	$x^{2} y^{''} - 4 y^{'} x + 6 y = x^{4} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	7.378

3570	$y^{''} - (a + b) y^{'} + b y a = 0$	[[_2nd_order, _missing_x]]	✓	0.812

3571	$y^{''} - 2 a y^{'} + a^{2} y = 0$	[[_2nd_order, _missing_x]]	✓	0.390

3572	$y^{''} - 2 a y^{'} + (a^{2} + b^{2}) y = 0$	[[_2nd_order, _missing_x]]	✓	0.535

3573	$y^{''} - y^{'} - 6 y = 0$	[[_2nd_order, _missing_x]]	✓	0.351

3574	$y^{''} + 6 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	0.392

3575	$x^{2} y^{''} + y^{'} x - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.290

3576	$x^{2} y^{''} + 5 y^{'} x + 4 y = 0$	[[_Emden, _Fowler]]	✓	0.998

3577	$y^{'} = \frac{e^{x} - \sin (y)}{x \cos (y)}$	[‘y=_G(x,y’)‘]	✓	2.352

3578	$y^{'} = \frac{1 - y^{2}}{2 x y + 2}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.614

3579	$y^{'} = \frac{(1 - y e^{x y}) e^{- x y}}{x}$ i.c.	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	1.712

3580	$y^{'} = \frac{x^{2} (1 - y^{2}) + y e^{\frac{y}{x}}}{x (e^{\frac{y}{x}} + 2 x^{2} y)}$	[‘y=_G(x,y’)‘]	✓	47.456

3581	$y^{'} = \frac{\cos (x) - 2 x y^{2}}{2 x^{2} y}$ i.c.	[_Bernoulli]	✓	43.771

3582	$y^{'} = \sin (x)$	[_quadrature]	✓	0.379

3583	$y^{'} = \frac{1}{x^{2 / 3}}$	[_quadrature]	✓	0.347

3584	$y^{''} = x e^{x}$	[[_2nd_order, _quadrature]]	✓	0.916

3585	$y^{''} = x^{n}$	[[_2nd_order, _quadrature]]	✓	1.076

3586	$y^{'} = x^{2} \ln (x)$ i.c.	[_quadrature]	✓	0.565

3587	$y^{''} = \cos (x)$ i.c.	[[_2nd_order, _quadrature]]	✓	2.995

3588	$y^{'''} = 6 x$ i.c.	[[_3rd_order, _quadrature]]	✓	0.206

3589	$y^{''} = x e^{x}$ i.c.	[[_2nd_order, _quadrature]]	✓	1.409

3590	$y^{''} + y^{'} - 6 y = 0$	[[_2nd_order, _missing_x]]	✓	0.353

3591	$x^{2} y^{''} - y^{'} x - 8 y = 0$	[[_Emden, _Fowler]]	✓	0.713

3592	$x^{2} y^{''} - 3 y^{'} x + 4 y = x^{2} \ln (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.543

3593	$y^{'} = 2 x y$	[_separable]	✓	1.186

3594	$y^{'} = \frac{y^{2}}{x^{2} + 1}$	[_separable]	✓	1.409

3595	$e^{x + y} y^{'} - 1 = 0$	[_separable]	✓	2.370

3596	$y^{'} = \frac{y}{x \ln (x)}$	[_separable]	✓	1.225

3597	$y - (x - 1) y^{'} = 0$	[_separable]	✓	1.441

3598	$y^{'} = \frac{2 x (- 1 + y)}{x^{2} + 3}$	[_separable]	✓	1.297

3599	$y - y^{'} x = 3 - 2 x^{2} y^{'}$	[_separable]	✓	1.560

3600	$y^{'} = \frac{\cos (x - y)}{\sin (x) \sin (y)} - 1$	[_separable]	✓	2.581

2.2.36 Problems 3501 to 3600