Problems 4701 to 4800

Table 2.97: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

4701	$y^{'} = a + b y + \sqrt{A 0 + B 0 y}$	[_quadrature]	✓	152.247

4702	$y^{'} = a x + b \sqrt{y}$	[[_homogeneous, ‘class G‘], _Chini]	✓	4.352

4703	$y^{'} + x^{3} = x \sqrt{x^{4} + 4 y}$	[[_1st_order, _with_linear_symmetries]]	✓	3.224

4704	$y^{'} + 2 y (1 - x \sqrt{y}) = 0$	[_Bernoulli]	✓	1.534

4705	$y^{'} = \sqrt{a + b y^{2}}$	[_quadrature]	✓	4.880

4706	$y^{'} = y \sqrt{a + b y}$	[_quadrature]	✓	220.984

4707	$y^{'} + (f (x) - y) g (x) \sqrt{(y - a) (y - b)} = 0$	[‘y=_G(x,y’)‘]	✗	5.096

4708	$y^{'} = \sqrt{X Y}$	[_quadrature]	✓	0.717

4709	$y^{'} = \cos (y) \cos {(x)}^{2}$	[_separable]	✓	2.949

4710	$y^{'} = \sec {(x)}^{2} \cot (y) \cos (y)$	[_separable]	✓	2.947

4711	$y^{'} = a + b \cos (A x + B y)$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	72.329

4712	$y^{'} + f (x) + g (x) \sin (a y) + h (x) \cos (a y) = 0$	[‘y=_G(x,y’)‘]	✗	5.504

4713	$y^{'} = a + b \cos (y)$	[_quadrature]	✓	39.465

4714	$y^{'} + x (\sin (2 y) - x^{2} \cos {(y)}^{2}) = 0$	[‘y=_G(x,y’)‘]	✗	5.566

4715	$y^{'} + \tan (x) \sec (x) \cos {(y)}^{2} = 0$	[_separable]	✓	2.634

4716	$y^{'} = \cot (x) \cot (y)$	[_separable]	✓	3.462

4717	$y^{'} + \cot (x) \cot (y) = 0$	[_separable]	✓	2.925

4718	$y^{'} = \sin (x) (\csc (y) - \cot (y))$	[_separable]	✓	3.156

4719	$y^{'} = \tan (x) \cot (y)$	[_separable]	✓	2.207

4720	$y^{'} + \tan (x) \cot (y) = 0$	[_separable]	✓	3.184

4721	$y^{'} + \sin (2 x) \csc (2 y) = 0$	[_separable]	✓	4.246

4722	$y^{'} = \tan (x) (\tan (y) + \sec (x) \sec (y))$	[‘y=_G(x,y’)‘]	✗	8.013

4723	$y^{'} = \cos (x) \sec {(y)}^{2}$	[_separable]	✓	2.113

4724	$y^{'} = \sec {(x)}^{2} \sec {(y)}^{3}$	[_separable]	✓	2.157

4725	$y^{'} = a + b \sin (y)$	[_quadrature]	✓	36.493

4726	$y^{'} = (1 + \cos (x) \sin (y)) \tan (y)$	[‘y=_G(x,y’)‘]	✗	7.363

4727	$y^{'} + \csc (2 x) \sin (2 y) = 0$	[_separable]	✓	5.576

4728	$y^{'} + f (x) + g (x) \tan (y) = 0$	[‘y=_G(x,y’)‘]	✗	3.226

4729	$y^{'} = \sqrt{a + b \cos (y)}$	[_quadrature]	✓	23.244

4730	$y^{'} = e^{y} + x$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	1.370

4731	$y^{'} = e^{x + y}$	[_separable]	✓	2.083

4732	$y^{'} = e^{x} (a + b e^{- y})$	[_separable]	✓	2.181

4733	$y \ln (x) \ln (y) + y^{'} = 0$	[_separable]	✓	1.727

4734	$y^{'} = x^{m - 1} y^{1 - n} f (a x^{m} + b y^{n})$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	4.128

4735	$y^{'} = a f (y)$	[_quadrature]	✓	0.755

4736	$y^{'} = f (a + b x + c y)$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	1.306

4737	$y^{'} = f (x) g (y)$	[_separable]	✓	1.199

4738	$y^{'} = \sec {(x)}^{2} + y \sec (x) Csx (x)$	[_linear]	✓	1.579

4739	$2 y^{'} = 2 \sin {(y)}^{2} \tan (y) - \sin (2 y) x$	[‘y=_G(x,y’)‘]	✗	47.083

4740	$2 y^{'} + a x = \sqrt{a^{2} x^{2} - 4 b x^{2} - 4 c y}$	[[_homogeneous, ‘class G‘]]	✓	6.413

4741	$3 y^{'} = x + \sqrt{x^{2} - 3 y}$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	5.630

4742	$y^{'} x = \sqrt{a^{2} - x^{2}}$	[_quadrature]	✓	0.643

4743	$y^{'} x + x + y = 0$	[_linear]	✓	2.342

4744	$y^{'} x + x^{2} - y = 0$	[_linear]	✓	1.190

4745	$y^{'} x = x^{3} - y$	[_linear]	✓	1.197

4746	$y^{'} x = 1 + x^{3} + y$	[_linear]	✓	0.959

4747	$y^{'} x = x^{m} + y$	[_linear]	✓	0.933

4748	$y^{'} x = x \sin (x) - y$	[_linear]	✓	1.280

4749	$y^{'} x = x^{2} \sin (x) + y$	[_linear]	✓	1.212

4750	$y^{'} x = x^{n} \ln (x) - y$	[_linear]	✓	1.368

4751	$y^{'} x = \sin (x) - 2 y$	[_linear]	✓	1.427

4752	$y^{'} x = a y$	[_separable]	✓	1.385

4753	$y^{'} x = 1 + x + a y$	[_linear]	✓	2.087

4754	$y^{'} x = a x + b y$	[_linear]	✓	3.372

4755	$y^{'} x = a x^{2} + b y$	[_linear]	✓	1.897

4756	$y^{'} x = a + b x^{n} + c y$	[_linear]	✓	1.467

4757	$y^{'} x + 2 + (3 - x) y = 0$	[_linear]	✓	1.225

4758	$y^{'} x + x + (a x + 2) y = 0$	[_linear]	✓	1.211

4759	$y^{'} x + (b x + a) y = 0$	[_separable]	✓	1.415

4760	$y^{'} x = x^{3} + (- 2 x^{2} + 1) y$	[_linear]	✓	1.344

4761	$y^{'} x = a x - (- b x^{2} + 1) y$	[_linear]	✓	1.286

4762	$y^{'} x + x + (- a x^{2} + 2) y = 0$	[_linear]	✓	1.334

4763	$y^{'} x + x^{2} + y^{2} = 0$	[_rational, _Riccati]	✓	1.330

4764	$y^{'} x = x^{2} + y (1 + y)$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓	1.500

4765	$y^{'} x - y + y^{2} = x^{2 / 3}$	[_rational, _Riccati]	✓	9.639

4766	$y^{'} x = a + b y^{2}$	[_separable]	✓	1.873

4767	$y^{'} x = a x^{2} + y + b y^{2}$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓	1.529

4768	$y^{'} x = a x^{2 n} + (n + b y) y$	[_rational, _Riccati]	✓	3.344

4769	$y^{'} x = a x^{n} + b y + c y^{2}$	[_rational, _Riccati]	✓	2.477

4770	$y^{'} x = k + a x^{n} + b y + c y^{2}$	[_rational, _Riccati]	✓	3.188

4771	$y^{'} x + a + x y^{2} = 0$	[_rational, [_Riccati, _special]]	✓	1.393

4772	$y^{'} x + (1 - x y) y = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	1.178

4773	$y^{'} x = (1 - x y) y$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	1.756

4774	$y^{'} x = (x y + 1) y$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	1.750

4775	$y^{'} x = a x^{3} (1 - x y) y$	[_Bernoulli]	✓	1.385

4776	$y^{'} x = x^{3} + (2 x^{2} + 1) y + x y^{2}$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓	2.241

4777	$y^{'} x = y (1 + 2 x y)$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	1.700

4778	$y^{'} x + b x + (2 + y a x) y = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	2.523

4779	$y^{'} x + a 0 + a 1 x + (a 2 + a 3 x y) y = 0$	[_rational, _Riccati]	✓	5.038

4780	$y^{'} x + a x^{2} y^{2} + 2 y = b$	[_rational, _Riccati]	✓	1.801

4781	$y^{'} x + x^{m} + \frac{(n - m) y}{2} + x^{n} y^{2} = 0$	[_rational, _Riccati]	✓	2.711

4782	$y^{'} x + (a + b x^{n} y) y = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	1.914

4783	$y^{'} x = a x^{m} - b y - c x^{n} y^{2}$	[_rational, _Riccati]	✓	3.622

4784	$y^{'} x = 2 x - y + a x^{n} {(x - y)}^{2}$	[[_1st_order, _with_linear_symmetries], _rational, _Riccati]	✓	3.866

4785	$y^{'} x + (1 - a y \ln (x)) y = 0$	[_Bernoulli]	✓	2.271

4786	$y^{'} x = y + (x^{2} - y^{2}) f (x)$	[[_homogeneous, ‘class D‘], _Riccati]	✓	2.415

4787	$y^{'} x = y (1 + y^{2})$	[_separable]	✓	4.020

4788	$y^{'} x + y (1 - x y^{2}) = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	3.172

4789	$y^{'} x + y = a (x^{2} + 1) y^{3}$	[_rational, _Bernoulli]	✓	3.047

4790	$y^{'} x = a y + b (x^{2} + 1) y^{3}$	[_rational, _Bernoulli]	✓	3.399

4791	$y^{'} x + 2 y = a x^{2 k} y^{k}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	4.939

4792	$y^{'} x = 4 y - 4 \sqrt{y}$	[_separable]	✓	4.553

4793	$y^{'} x + 2 y = \sqrt{1 + y^{2}}$	[_separable]	✓	2.950

4794	$y^{'} x = y + \sqrt{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.305

4795	$y^{'} x = y + \sqrt{x^{2} - y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	143.657

4796	$y^{'} x = y + x \sqrt{x^{2} + y^{2}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	3.860

4797	$y^{'} x = y - x (x - y) \sqrt{x^{2} + y^{2}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	5.776

4798	$y^{'} x = y + a \sqrt{y^{2} + b^{2} x^{2}}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	27.414

4799	$y^{'} x + (\sin (y) - 3 x^{2} \cos (y)) \cos (y) = 0$	[‘y=_G(x,y’)‘]	✓	2.759

4800	$y^{'} x + x - y + x \cos (\frac{y}{x}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	2.912

2.2.48 Problems 4701 to 4800