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]	✓	78.381

4702	$y^{'} = a x + b \sqrt{y}$	[[_homogeneous, ‘class G‘], _Chini]	✓	4.493

4703	$y^{'} + x^{3} = x \sqrt{x^{4} + 4 y}$	[[_1st_order, _with_linear_symmetries]]	✓	3.899

4704	$y^{'} + 2 y (1 - x \sqrt{y}) = 0$	[_Bernoulli]	✓	1.306

4705	$y^{'} = \sqrt{a + b y^{2}}$	[_quadrature]	✓	8.455

4706	$y^{'} = y \sqrt{a + b y}$	[_quadrature]	✓	119.475

4707	$y^{'} + (f (x) - y) g (x) \sqrt{(y - a) (y - b)} = 0$	[‘y=_G(x,y’)‘]	✗	5.625

4708	$y^{'} = \sqrt{X Y}$	[_quadrature]	✓	0.437

4709	$y^{'} = \cos {(x)}^{2} \cos (y)$	[_separable]	✓	2.479

4710	$y^{'} = \sec {(x)}^{2} \cot (y) \cos (y)$	[_separable]	✓	2.897

4711	$y^{'} = a + b \cos (A x + B y)$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	36.640

4712	$y^{'} + f (x) + g (x) \sin (a y) + h (x) \cos (a y) = 0$	[‘y=_G(x,y’)‘]	✗	6.354

4713	$y^{'} = a + b \cos (y)$	[_quadrature]	✓	37.933

4714	$y^{'} + x (\sin (2 y) - x^{2} \cos {(y)}^{2}) = 0$	[‘y=_G(x,y’)‘]	✗	5.098

4715	$y^{'} + \tan (x) \sec (x) \cos {(y)}^{2} = 0$	[_separable]	✓	2.635

4716	$y^{'} = \cot (x) \cot (y)$	[_separable]	✓	1.977

4717	$y^{'} + \cot (x) \cot (y) = 0$	[_separable]	✓	2.075

4718	$y^{'} = \sin (x) (\csc (y) - \cot (y))$	[_separable]	✓	3.218

4719	$y^{'} = \tan (x) \cot (y)$	[_separable]	✓	1.858

4720	$y^{'} + \tan (x) \cot (y) = 0$	[_separable]	✓	1.852

4721	$y^{'} + \sin (2 x) \csc (2 y) = 0$	[_separable]	✓	6.009

4722	$y^{'} = \tan (x) (\tan (y) + \sec (x) \sec (y))$	[‘y=_G(x,y’)‘]	✗	7.303

4723	$y^{'} = \cos (x) \sec {(y)}^{2}$	[_separable]	✓	2.124

4724	$y^{'} = \sec {(x)}^{2} \sec {(y)}^{3}$	[_separable]	✓	2.095

4725	$y^{'} = a + b \sin (y)$	[_quadrature]	✓	38.447

4726	$y^{'} = (1 + \cos (x) \sin (y)) \tan (y)$	unknown	✗	7.890

4727	$y^{'} + \csc (2 x) \sin (2 y) = 0$	[_separable]	✓	5.028

4728	$y^{'} + f (x) + g (x) \tan (y) = 0$	[‘y=_G(x,y’)‘]	✗	3.836

4729	$y^{'} = \sqrt{a + b \cos (y)}$	[_quadrature]	✓	11.815

4730	$y^{'} = e^{y} + x$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	1.389

4731	$y^{'} = e^{x + y}$	[_separable]	✓	2.665

4732	$y^{'} = e^{x} (a + b e^{- y})$	[_separable]	✓	1.875

4733	$y \ln (x) \ln (y) + y^{'} = 0$	[_separable]	✓	1.704

4734	$y^{'} = x^{m - 1} y^{1 - n} f (a x^{m} + b y^{n})$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	3.713

4735	$y^{'} = a f (y)$	[_quadrature]	✓	1.068

4736	$y^{'} = f (a + b x + c y)$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	1.138

4737	$y^{'} = f (x) g (y)$	[_separable]	✓	1.063

4738	$y^{'} = \sec {(x)}^{2} + y \sec (x) Csx (x)$	[_linear]	✓	1.448

4739	$2 y^{'} = 2 \sin {(y)}^{2} \tan (y) - x \sin (2 y)$	[‘y=_G(x,y’)‘]	✗	44.194

4740	$2 y^{'} + a x = \sqrt{a^{2} x^{2} - 4 b x^{2} - 4 c y}$	[[_homogeneous, ‘class G‘]]	✓	13.868

4741	$3 y^{'} = x + \sqrt{x^{2} - 3 y}$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	8.118

4742	$x y^{'} = \sqrt{a^{2} - x^{2}}$	[_quadrature]	✓	0.500

4743	$x y^{'} + x + y = 0$	[_linear]	✓	2.765

4744	$x y^{'} + x^{2} - y = 0$	[_linear]	✓	1.607

4745	$x y^{'} = x^{3} - y$	[_linear]	✓	1.504

4746	$x y^{'} = 1 + x^{3} + y$	[_linear]	✓	1.365

4747	$x y^{'} = x^{m} + y$	[_linear]	✓	0.728

4748	$x y^{'} = x \sin (x) - y$	[_linear]	✓	1.415

4749	$x y^{'} = x^{2} \sin (x) + y$	[_linear]	✓	1.572

4750	$x y^{'} = x^{n} \ln (x) - y$	[_linear]	✓	1.246

4751	$x y^{'} = \sin (x) - 2 y$	[_linear]	✓	1.493

4752	$x y^{'} = a y$	[_separable]	✓	1.204

4753	$x y^{'} = 1 + x + a y$	[_linear]	✓	1.595

4754	$x y^{'} = a x + b y$	[_linear]	✓	2.328

4755	$x y^{'} = a x^{2} + b y$	[_linear]	✓	1.415

4756	$x y^{'} = a + b x^{n} + c y$	[_linear]	✓	1.297

4757	$x y^{'} + 2 + (3 - x) y = 0$	[_linear]	✓	1.290

4758	$x y^{'} + x + (a x + 2) y = 0$	[_linear]	✓	1.078

4759	$x y^{'} + (b x + a) y = 0$	[_separable]	✓	1.098

4760	$x y^{'} = x^{3} + (- 2 x^{2} + 1) y$	[_linear]	✓	1.570

4761	$x y^{'} = a x - (- b x^{2} + 1) y$	[_linear]	✓	1.145

4762	$x y^{'} + x + (- a x^{2} + 2) y = 0$	[_linear]	✓	1.188

4763	$x y^{'} + x^{2} + y^{2} = 0$	[_rational, _Riccati]	✓	1.155

4764	$x y^{'} = x^{2} + y (y + 1)$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓	1.683

4765	$x y^{'} - y + y^{2} = x^{2 / 3}$	[_rational, _Riccati]	✓	11.772

4766	$x y^{'} = a + b y^{2}$	[_separable]	✓	1.477

4767	$x y^{'} = a x^{2} + y + b y^{2}$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓	1.372

4768	$x y^{'} = a x^{2 n} + (n + b y) y$	[_rational, _Riccati]	✓	2.848

4769	$x y^{'} = a x^{n} + b y + c y^{2}$	[_rational, _Riccati]	✓	2.379

4770	$x y^{'} = k + a x^{n} + b y + c y^{2}$	[_rational, _Riccati]	✓	2.458

4771	$x y^{'} + a + x y^{2} = 0$	[_rational, [_Riccati, _special]]	✓	1.087

4772	$x y^{'} + (1 - x y) y = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	1.630

4773	$x y^{'} = (1 - x y) y$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	2.498

4774	$x y^{'} = (1 + x y) y$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	2.480

4775	$x y^{'} = a x^{3} (1 - x y) y$	[_Bernoulli]	✓	1.319

4776	$x y^{'} = x^{3} + (2 x^{2} + 1) y + x y^{2}$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓	1.975

4777	$x y^{'} = y (2 x y + 1)$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	2.384

4778	$x y^{'} + b x + (2 + y a x) y = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	2.169

4779	$x y^{'} + a 0 + a 1 x + (a 2 + a 3 x y) y = 0$	[_rational, _Riccati]	✓	6.668

4780	$x y^{'} + a x^{2} y^{2} + 2 y = b$	[_rational, _Riccati]	✓	1.514

4781	$x y^{'} + x^{m} + \frac{(n - m) y}{2} + x^{n} y^{2} = 0$	[_rational, _Riccati]	✓	2.255

4782	$x y^{'} + (a + b x^{n} y) y = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	1.760

4783	$x y^{'} = a x^{m} - b y - c x^{n} y^{2}$	[_rational, _Riccati]	✓	3.286

4784	$x y^{'} = 2 x - y + a x^{n} {(x - y)}^{2}$	[[_1st_order, _with_linear_symmetries], _rational, _Riccati]	✓	3.069

4785	$x y^{'} + (1 - a y \ln (x)) y = 0$	[_Bernoulli]	✓	2.145

4786	$x y^{'} = y + (x^{2} - y^{2}) f (x)$	[[_homogeneous, ‘class D‘], _Riccati]	✓	2.020

4787	$x y^{'} = y (1 + y^{2})$	[_separable]	✓	4.719

4788	$x y^{'} + y (1 - x y^{2}) = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	3.800

4789	$x y^{'} + y = a (x^{2} + 1) y^{3}$	[_rational, _Bernoulli]	✓	3.021

4790	$x y^{'} = a y + b (x^{2} + 1) y^{3}$	[_rational, _Bernoulli]	✓	3.674

4791	$x y^{'} + 2 y = a x^{2 k} y^{k}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	4.405

4792	$x y^{'} = 4 y - 4 \sqrt{y}$	[_separable]	✓	3.608

4793	$x y^{'} + 2 y = \sqrt{1 + y^{2}}$	[_separable]	✓	3.556

4794	$x y^{'} = y + \sqrt{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	8.355

4795	$x y^{'} = y + \sqrt{x^{2} - y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	97.385

4796	$x y^{'} = y + x \sqrt{x^{2} + y^{2}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	3.550

4797	$x y^{'} = y - x (x - y) \sqrt{x^{2} + y^{2}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	5.274

4798	$x y^{'} = y + a \sqrt{y^{2} + b^{2} x^{2}}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	11.652

4799	$x y^{'} + (\sin (y) - 3 x^{2} \cos (y)) \cos (y) = 0$	[‘y=_G(x,y’)‘]	✓	2.774

4800	$x y^{'} + x - y + x \cos (\frac{y}{x}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.326

2.2.48 Problems 4701 to 4800