Problems 2901 to 3000

Table 2.61: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

2901	$x - y + 1 + (x - y - 1) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.814

2902	$x + 2 y + (3 x + 6 y + 3) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.911

2903	$x + 2 y + 2 = (2 x + y - 1) y^{'}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.827

2904	$3 x - y + 1 + (x - 3 y - 5) y^{'} = 0$ i.c.	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	5.488

2905	$6 x - 3 y + 6 + (2 x - y + 5) y^{'} = 0$ i.c.	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.196

2906	$2 x + 3 y + 2 + (y - x) y^{'} = 0$ i.c.	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	228.711

2907	$x + y + 4 = (2 x + 2 y - 1) y^{'}$ i.c.	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.236

2908	$2 x + 3 y - 1 + (2 x + 3 y + 2) y^{'} = 0$ i.c.	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.167

2909	$3 x - y + 2 + (x + 2 y + 1) y^{'} = 0$ i.c.	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	5.668

2910	$3 x + 2 y + 3 - (x + 2 y - 1) y^{'} = 0$ i.c.	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	6.563

2911	$x - 2 y + 3 + (1 - x + 2 y) y^{'} = 0$ i.c.	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.148

2912	$2 x + y + (4 x + 2 y + 1) y^{'} = 0$ i.c.	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.266

2913	$2 x + y + (4 x - 2 y + 1) y^{'} = 0$ i.c.	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	93.877

2914	$x + y + (x - 2 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.839

2915	$3 x + y + (x + 3 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.761

2916	$a_{1} x + b_{1} y + c_{1} + (b_{1} x + b_{2} y + c_{2}) y^{'} = 0$	[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	5.191

2917	$x (6 x y + 5) + (2 x^{3} + 3 y) y^{'} = 0$	[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.494

2918	$3 x^{2} y + x y^{2} + e^{x} + (x^{3} + x^{2} y + \sin (y)) y^{'} = 0$	[_exact]	✓	2.227

2919	$2 x y - (x^{2} + y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.288

2920	$\cos (x) y - 2 \sin (y) = (2 x \cos (y) - \sin (x)) y^{'}$	[_exact]	✓	10.380

2921	$\frac{2 x y - 1}{y} + \frac{(x + 3 y) y^{'}}{y^{2}} = 0$	[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.189

2922	$y e^{x} - 2 x + e^{x} y^{'} = 0$	[[_linear, ‘class A‘]]	✓	1.487

2923	$3 y \sin (x) - \cos (y) + (x \sin (y) - 3 \cos (x)) y^{'} = 0$	[_exact]	✓	41.390

2924	$x y^{2} + 2 y + (2 y^{3} - x^{2} y + 2 x) y^{'} = 0$	[_rational]	✗	1.455

2925	$\frac{2}{y} - \frac{y}{x^{2}} + (\frac{1}{x} - \frac{2 x}{y^{2}}) y^{'} = 0$	[_separable]	✓	1.592

2926	$\frac{x y + 1}{y} + \frac{(- x + 2 y) y^{'}}{y^{2}} = 0$	[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.867

2927	$\frac{y (2 + x^{3} y)}{x^{3}} = \frac{(1 - 2 x^{3} y) y^{'}}{x^{2}}$	[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.773

2928	$y^{2} \csc {(x)}^{2} + 6 x y - 2 = (2 \cot (x) y - 3 x^{2}) y^{'}$	[_exact, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	49.587

2929	$\frac{2 y}{x^{3}} + \frac{2 x}{y^{2}} = (\frac{1}{x^{2}} + \frac{2 x^{2}}{y^{3}}) y^{'}$	[[_homogeneous, ‘class G‘], _exact, _rational]	✓	2.454

2930	$\cos (y) - (x \sin (y) - y^{2}) y^{'} = 0$	[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	6.000

2931	$2 y \sin (x y) + (2 x \sin (x y) + y^{3}) y^{'} = 0$	[_exact]	✓	45.312

2932	$\frac{x \cos (\frac{x}{y})}{y} + \sin (\frac{x}{y}) + \cos (x) - \frac{x^{2} \cos (\frac{x}{y}) y^{'}}{y^{2}} = 0$	[_exact]	✓	6.291

2933	$y e^{x y} + 2 x y + (x e^{x y} + x^{2}) y^{'} = 0$	[_exact]	✓	2.320

2934	$\frac{x^{2} + 3 y^{2}}{x (3 x^{2} + 4 y^{2})} + \frac{(2 x^{2} + y^{2}) y^{'}}{y (3 x^{2} + 4 y^{2})} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	42.801

2935	$\frac{x^{2} - y^{2}}{x (2 x^{2} + y^{2})} + \frac{(x^{2} + 2 y^{2}) y^{'}}{y (2 x^{2} + y^{2})} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	46.623

2936	$\frac{2 x^{2}}{x^{2} + y^{2}} + \ln (x^{2} + y^{2}) + \frac{2 x y y^{'}}{x^{2} + y^{2}} = 0$	[_exact]	✓	2.034

2937	$y^{'} x + \ln (x) - y = 0$	[_linear]	✓	0.966

2938	$x y + (y + x^{2}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.758

2939	$(x - 2 x y) y^{'} + 2 y = 0$	[_separable]	✓	2.017

2940	$x^{2} y + y^{2} + x^{3} y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	1.885

2941	$x y^{3} - 1 + x^{2} y^{2} y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	3.099

2942	$(x^{3} y^{3} - 1) y^{'} + x^{2} y^{4} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	2.228

2943	$y (y - x^{2}) + x^{3} y^{'} = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	1.761

2944	$y + x y^{2} + (x - x^{2} y) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.999

2945	$(x - x \sqrt{x^{2} - y^{2}}) y^{'} - y = 0$	[‘y=_G(x,y’)‘]	✗	3.783

2946	$2 x y + (y - x^{2}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.617

2947	$y = x (x^{2} y - 1) y^{'}$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	12.327

2948	$e^{x} y^{'} = 2 x y^{2} + y e^{x}$	[_Bernoulli]	✓	2.338

2949	$(x^{2} + y^{2} + x) y^{'} = y$	[_rational]	✓	1.158

2950	$(2 x + 3 x^{2} y) y^{'} + y + 2 x y^{2} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.808

2951	$2 x^{2} y y^{'} + x^{4} e^{x} - 2 x y^{2} = 0$	[[_homogeneous, ‘class D‘], _Bernoulli]	✓	2.180

2952	$y (1 - x^{4} y^{2}) + y^{'} x = 0$ i.c.	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	2.840

2953	$(x^{2} - 1) y + x (x^{2} + 1) y^{'} = 0$ i.c.	[_separable]	✓	1.651

2954	$x^{2} y^{2} - y + (2 x^{3} y + x) y^{'} = 0$ i.c.	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.455

2955	$(x^{2} + y^{2} - 2 y) y^{'} = 2 x$ i.c.	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.469

2956	$y - x^{2} \sqrt{x^{2} - y^{2}} - y^{'} x = 0$ i.c.	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	38.302

2957	$y (x + y^{2}) + x (x - y^{2}) y^{'} = 0$ i.c.	[[_homogeneous, ‘class G‘], _rational]	✓	3.403

2958	$y^{'} x + 2 y = x^{2}$	[_linear]	✓	1.404

2959	$y^{'} - x y = e^{\frac{x^{2}}{2}} \cos (x)$	[_linear]	✓	1.860

2960	$y^{'} + 2 x y = 2 x e^{- x^{2}}$	[_linear]	✓	2.390

2961	$y^{'} = y + 3 x^{2} e^{x}$	[[_linear, ‘class A‘]]	✓	1.655

2962	$x^{'} + x = e^{- y}$	[[_linear, ‘class A‘]]	✓	0.904

2963	$y x^{'} + (1 + y) x = e^{y}$	[_linear]	✓	1.423

2964	$y + (2 x - 3 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.612

2965	$y^{'} x - 2 x^{4} - 2 y = 0$	[_linear]	✓	1.564

2966	$1 = (e^{y} + x) y^{'}$	[[_1st_order, _with_exponential_symmetries]]	✓	1.232

2967	$y^{2} x^{'} + (y^{2} + 2 y) x = 1$	[_linear]	✓	2.205

2968	$y^{'} x = 5 y + x + 1$	[_linear]	✓	1.536

2969	$x^{2} y^{'} + y - 2 x y - 2 x^{2} = 0$	[_linear]	✓	1.646

2970	$2 y + (x + 1) y^{'} = \frac{e^{x}}{x + 1}$	[_linear]	✓	1.764

2971	$\cos {(y)}^{2} + (x - \tan (y)) y^{'} = 0$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	4.735

2972	$2 y = (y^{4} + x) y^{'}$	[[_homogeneous, ‘class G‘], _rational]	✓	2.309

2973	$\cos (θ) r^{'} = 2 + 2 r \sin (θ)$	[_linear]	✓	2.121

2974	$\sin (θ) r^{'} + 1 + r \tan (θ) = \cos (θ)$	[_linear]	✓	5.710

2975	$y x^{'} = 2 y e^{3 y} + x (3 y + 2)$	[_linear]	✓	2.016

2976	$y^{2} + 1 + (2 x y - y^{2}) y^{'} = 0$ i.c.	[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	2.047

2977	$y^{'} + \cot (x) y - \sec (x) = 0$	[_linear]	✓	1.834

2978	$y + y^{3} + 4 (x y^{2} - 1) y^{'} = 0$ i.c.	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.940

2979	$2 y - x y - 3 + y^{'} x = 0$ i.c.	[_linear]	✓	1.492

2980	$y + 2 (x - 2 y^{2}) y^{'} = 0$ i.c.	[[_homogeneous, ‘class G‘], _rational]	✓	3.753

2981	$(x^{2} - 1) y^{'} + {(x^{2} - 1)}^{2} + 4 y = 0$ i.c.	[_linear]	✓	1.690

2982	$3 y^{2} y^{'} - x y^{3} = e^{\frac{x^{2}}{2}} \cos (x)$	[_Bernoulli]	✓	4.373

2983	$y^{3} y^{'} + x y^{4} = x e^{- x^{2}}$	[_Bernoulli]	✓	3.487

2984	$\cosh (y) y^{'} + \sinh (y) - e^{- x} = 0$	[‘y=_G(x,y’)‘]	✓	2.441

2985	$\sin (θ) θ^{'} + \cos (θ) - t e^{- t} = 0$	[‘y=_G(x,y’)‘]	✓	2.753

2986	$x y^{'} y = x^{2} - y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	3.707

2987	$y^{'} - x y = \sqrt{y} x e^{x^{2}}$	[_Bernoulli]	✓	2.070

2988	$t x^{'} + x (1 - x^{2} t^{4}) = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	3.035

2989	$x^{2} y^{'} + y^{2} = x y$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	1.868

2990	$\csc (y) \cot (y) y^{'} = \csc (y) + e^{x}$	[‘y=_G(x,y’)‘]	✓	2.791

2991	$y^{'} - x y = \frac{x}{y}$	[_separable]	✓	1.954

2992	$y^{'} x + y = y^{2} x^{2} \cos (x)$	[_Bernoulli]	✓	3.270

2993	$r^{'} + (r - \frac{1}{r}) θ = 0$	[_separable]	✓	2.010

2994	$y^{'} x + 2 y = 3 x^{3} y^{4 / 3}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	5.286

2995	$3 y^{'} + \frac{2 y}{x + 1} = \frac{x}{y^{2}}$	[_rational, _Bernoulli]	✓	2.750

2996	$y^{'} \cos (y) + (\sin (y) - 1) \cos (x) = 0$	[_separable]	✓	43.027

2997	$(x \tan {(y)}^{2} + x) y^{'} = 2 x^{2} + \tan (y)$	[‘y=_G(x,y’)‘]	✓	2.045

2998	$y^{'} + \cos (x) y = y^{3} \sin (x)$	[_Bernoulli]	✓	3.248

2999	$y + y^{'} = y^{2} e^{- t}$ i.c.	[[_1st_order, _with_linear_symmetries], _Bernoulli]	✓	2.539

3000	$y^{'} = x (1 - e^{2 y - x^{2}})$ i.c.	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	2.126

2.2.30 Problems 2901 to 3000