Problems 4601 to 4700

Table 2.95: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

4601	$x^{2} y^{''} + (\frac{1}{2} x + x^{2}) y^{'} + x y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.685

4602	$x^{2} y^{''} + (- x^{2} + x) y^{'} - (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.846

4603	$x^{2} y^{''} + 2 y^{'} x - (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.645

4604	$x y^{''} - 2 y^{'} x - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.383

4605	$x y^{''} + 2 y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.699

4606	$x^{2} y^{''} - x^{2} y^{'} + 2 (x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.382

4607	$x y^{''} + y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.518

4608	$y^{'} = a f (x)$	[_quadrature]	✓	0.286

4609	$y^{'} = x + \sin (x) + y$	[[_linear, ‘class A‘]]	✓	1.591

4610	$y^{'} = x^{2} + 3 \cosh (x) + 2 y$	[[_linear, ‘class A‘]]	✓	1.811

4611	$y^{'} = a + b x + c y$	[[_linear, ‘class A‘]]	✓	0.914

4612	$y^{'} = a \cos (b x + c) + k y$	[[_linear, ‘class A‘]]	✓	1.745

4613	$y^{'} = a \sin (b x + c) + k y$	[[_linear, ‘class A‘]]	✓	1.747

4614	$y^{'} = a + b e^{k x} + c y$	[[_linear, ‘class A‘]]	✓	1.423

4615	$y^{'} = x (x^{2} - y)$	[_linear]	✓	1.296

4616	$y^{'} = x (e^{- x^{2}} + a y)$	[_linear]	✓	1.413

4617	$y^{'} = x^{2} (a x^{3} + b y)$	[_linear]	✓	2.132

4618	$y^{'} = a x^{n} y$	[_separable]	✓	1.524

4619	$y^{'} = \sin (x) \cos (x) + \cos (x) y$	[_linear]	✓	1.958

4620	$y^{'} = e^{\sin (x)} + \cos (x) y$	[_linear]	✓	1.802

4621	$y^{'} = \cot (x) y$	[_separable]	✓	1.431

4622	$y^{'} = 1 - \cot (x) y$	[_linear]	✓	1.299

4623	$y^{'} = x \csc (x) - \cot (x) y$	[_linear]	✓	1.785

4624	$y^{'} = (2 \csc (2 x) + \cot (x)) y$	[_separable]	✓	3.324

4625	$y^{'} = \sec (x) - \cot (x) y$	[_linear]	✓	1.825

4626	$y^{'} = e^{x} \sin (x) + \cot (x) y$	[_linear]	✓	2.255

4627	$y^{'} + \csc (x) + 2 \cot (x) y = 0$	[_linear]	✓	1.679

4628	$y^{'} = 4 \csc (x) x \sec {(x)}^{2} - 2 y \cot (2 x)$	[_linear]	✓	14.796

4629	$y^{'} = 2 \cot {(x)}^{2} \cos (2 x) - 2 y \csc (2 x)$	[_linear]	✓	3.358

4630	$y^{'} = 4 \csc (x) x (\sin {(x)}^{3} + y)$	[_linear]	✓	4.332

4631	$y^{'} = 4 \csc (x) x (1 - \tan {(x)}^{2} + y)$	[_linear]	✓	3.933

4632	$y^{'} = y \sec (x)$	[_separable]	✓	1.563

4633	$y^{'} + \tan (x) = (1 - y) \sec (x)$	[_linear]	✓	2.132

4634	$y^{'} = y \tan (x)$	[_separable]	✓	1.291

4635	$y^{'} = \cos (x) + y \tan (x)$	[_linear]	✓	1.862

4636	$y^{'} = \cos (x) - y \tan (x)$	[_linear]	✓	1.730

4637	$y^{'} = \sec (x) - y \tan (x)$	[_linear]	✓	1.614

4638	$y^{'} = \sin (2 x) + y \tan (x)$	[_linear]	✓	1.959

4639	$y^{'} = \sin (2 x) - y \tan (x)$	[_linear]	✓	1.945

4640	$y^{'} = \sin (x) + 2 y \tan (x)$	[_linear]	✓	1.885

4641	$y^{'} = 2 + 2 \sec (2 x) + 2 y \tan (2 x)$	[_linear]	✓	4.991

4642	$y^{'} = \csc (x) + 3 y \tan (x)$	[_linear]	✓	1.794

4643	$y^{'} = (a + \cos (\ln (x)) + \sin (\ln (x))) y$	[_separable]	✓	2.200

4644	$y^{'} = 6 e^{2 x} - y \tanh (x)$	[_linear]	✓	2.112

4645	$y^{'} = f (x) f^{'} (x) + f^{'} (x) y$	[_linear]	✓	0.692

4646	$y^{'} = f (x) + g (x) y$	[_linear]	✓	1.129

4647	$y^{'} = x^{2} - y^{2}$	[_Riccati]	✓	1.439

4648	$y^{'} + f {(x)}^{2} = f^{'} (x) + y^{2}$	[_Riccati]	✓	1.278

4649	$y^{'} + 1 - x = y (x + y)$	[_Riccati]	✓	1.572

4650	$y^{'} = {(x + y)}^{2}$	[[_homogeneous, ‘class C‘], _Riccati]	✓	1.514

4651	$y^{'} = {(x - y)}^{2}$	[[_homogeneous, ‘class C‘], _Riccati]	✓	1.794

4652	$y^{'} = 3 - 3 x + 3 y + {(x - y)}^{2}$	[[_homogeneous, ‘class C‘], _Riccati]	✓	3.449

4653	$y^{'} = 2 x - (x^{2} + 1) y + y^{2}$	[_Riccati]	✓	2.139

4654	$y^{'} = x (x^{3} + 2) - (2 x^{2} - y) y$	[[_1st_order, _with_linear_symmetries], _Riccati]	✓	1.018

4655	$y^{'} = 1 + x (- x^{3} + 2) + (2 x^{2} - y) y$	[[_1st_order, _with_linear_symmetries], _Riccati]	✓	1.778

4656	$y^{'} = \cos (x) - (\sin (x) - y) y$	[_Riccati]	✓	3.110

4657	$y^{'} = \cos (2 x) + (\sin (2 x) + y) y$	[_Riccati]	✓	6.118

4658	$y^{'} = f (x) + x f (x) y + y^{2}$	[_Riccati]	✓	2.307

4659	$y^{'} = {(3 + x - 4 y)}^{2}$	[[_homogeneous, ‘class C‘], _Riccati]	✓	9.381

4660	$y^{'} = {(1 + 4 x + 9 y)}^{2}$	[[_homogeneous, ‘class C‘], _Riccati]	✓	87.657

4661	$y^{'} = 3 a + 3 b x + 3 b y^{2}$	[_Riccati]	✓	1.631

4662	$y^{'} = a + b y^{2}$	[_quadrature]	✓	5.247

4663	$y^{'} = a x + b y^{2}$	[[_Riccati, _special]]	✓	1.418

4664	$y^{'} = a + b x + c y^{2}$	[_Riccati]	✓	1.499

4665	$y^{'} = a x^{n - 1} + b x^{2 n} + c y^{2}$	[_Riccati]	✗	37.373

4666	$y^{'} = a x^{2} + b y^{2}$	[[_Riccati, _special]]	✓	1.721

4667	$y^{'} = a 0 + a 1 y + a 2 y^{2}$	[_quadrature]	✓	7.031

4668	$y^{'} = f (x) + a y + b y^{2}$	[_Riccati]	✗	1.587

4669	$y^{'} = 1 + a (x - y) y$	[_Riccati]	✓	2.025

4670	$y^{'} = f (x) + g (x) y + a y^{2}$	[_Riccati]	✗	1.982

4671	$y^{'} = x y (3 + y)$	[_separable]	✓	2.010

4672	$y^{'} = 1 - x - x^{3} + (2 x^{2} + 1) y - x y^{2}$	[_Riccati]	✓	2.467

4673	$y^{'} = x (2 + x^{2} y - y^{2})$	[_Riccati]	✓	1.844

4674	$y^{'} = x + (- 2 x + 1) y - (1 - x) y^{2}$	[_Riccati]	✓	2.440

4675	$y^{'} = a x y^{2}$	[_separable]	✓	1.693

4676	$y^{'} = x^{n} (a + b y^{2})$	[_separable]	✓	3.818

4677	$y^{'} = a x^{m} + b x^{n} y^{2}$	[_Riccati]	✓	2.372

4678	$y^{'} = (a + b y \cos (k x)) y$	[_Bernoulli]	✓	2.317

4679	$y^{'} = \sin (x) (2 \sec {(x)}^{2} - y)$	[_linear]	✓	2.676

4680	$y^{'} + 4 \csc (x) = (3 - \cot (x)) y + \sin (x) y^{2}$	[_Riccati]	✓	6.227

4681	$y^{'} = y \sec (x) + {(\sin (x) - 1)}^{2}$	[_linear]	✓	3.166

4682	$y^{'} + \tan (x) (1 - y^{2}) = 0$	[_separable]	✓	3.267

4683	$y^{'} = f (x) + g (x) y + h (x) y^{2}$	[_Riccati]	✗	2.679

4684	$y^{'} = (a + b y + c y^{2}) f (x)$	[_separable]	✓	4.412

4685	$y^{'} + (a x + y) y^{2} = 0$	[_Abel]	✗	1.114

4686	$y^{'} = (a e^{x} + y) y^{2}$	[_Abel]	✗	1.693

4687	$y^{'} + 3 a (2 x + y) y^{2} = 0$	[_Abel]	✗	1.229

4688	$y^{'} = y (a + b y^{2})$	[_quadrature]	✓	6.310

4689	$y^{'} = a 0 + a 1 y + a 2 y^{2} + a 3 y^{3}$	[_quadrature]	✓	140.813

4690	$y^{'} = x y^{3}$	[_separable]	✓	3.269

4691	$y^{'} + y (1 - x y^{2}) = 0$	[_Bernoulli]	✓	2.714

4692	$y^{'} = (a + b x y) y^{2}$	[[_homogeneous, ‘class G‘], _Abel]	✓	2.449

4693	$y^{'} + 2 x y (1 + a x y^{2}) = 0$	[_Bernoulli]	✓	1.494

4694	$y^{'} + (\tan (x) + y^{2} \sec (x)) y = 0$	[_Bernoulli]	✓	3.001

4695	$y^{'} + y^{3} \sec (x) \tan (x) = 0$	[_separable]	✓	3.522

4696	$y^{'} = f 0 (x) + f 1 (x) y + f 2 (x) y^{2} + f 3 (x) y^{3}$	[_Abel]	✗	5.667

4697	$y^{'} = a x^{\frac{n}{1 - n}} + b y^{n}$	[[_homogeneous, ‘class G‘], _Chini]	✓	3.352

4698	$y^{'} = f (x) y + g (x) y^{k}$	[_Bernoulli]	✓	1.835

4699	$y^{'} = f (x) + g (x) y + h (x) y^{n}$	[_Chini]	✗	2.902

4700	$y^{'} = \sqrt{\| y \|}$	[_quadrature]	✓	3.169

2.2.47 Problems 4601 to 4700