Problems 3001 to 3100

Table 2.63: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

3001	$2 y = (x^{2} y^{4} + x) y^{'}$ i.c.	[[_homogeneous, ‘class G‘], _rational]	✓	2.823

3002	$1 + x y (x y^{2} + 1) y^{'} = 0$ i.c.	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	3.203

3003	$(- x^{2} + 1) y^{'} + x y = x (- x^{2} + 1) \sqrt{y}$ i.c.	[_rational, _Bernoulli]	✗	1.497

3004	$(1 - x) y^{'} - 1 - y = 0$	[_separable]	✓	1.629

3005	$y^{2} + (x^{2} + x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	7.349

3006	$2 x + y - (x - 2 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.660

3007	$x \ln (x) y^{'} + y - x = 0$	[_linear]	✓	1.297

3008	$x - 2 y + 1 + (- 2 + y) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.182

3009	$2 x y - 2 x y^{3} + x^{3} + (x^{2} + y^{2} - 3 x^{2} y^{2}) y^{'} = 0$	[_exact, _rational]	✓	1.873

3010	$2 e^{x} - t^{2} + t e^{x} x^{'} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	1.639

3011	$6 + 2 y = x y^{'} y$	[_separable]	✓	2.348

3012	$x - 3 y = (3 y - x + 2) y^{'}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.062

3013	$y \sin (x) - 2 \cos (y) + \tan (x) - (\cos (x) - 2 x \sin (y) + \sin (y)) y^{'} = 0$	[_exact]	✓	45.133

3014	$x^{2} y - (x^{3} + y^{3}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	142.283

3015	$y - y^{'} x = 2 y^{'} + 2 y^{2}$	[_separable]	✓	1.939

3016	$\tan (y) = (3 x + 4) y^{'}$	[_separable]	✓	2.823

3017	$y^{'} + y \ln (y) \tan (x) = 2 y$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	2.927

3018	$2 x y + y^{4} + (x y^{3} - 2 x^{2}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	2.319

3019	$y + (3 x - 2 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	80.458

3020	$r^{'} = r \cot (θ)$	[_separable]	✓	1.448

3021	$(3 x + 4 y) y^{'} + 2 x + y = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.488

3022	$2 x^{3} - y^{3} - 3 x + 3 x y^{2} y^{'} = 0$	[_rational, _Bernoulli]	✓	2.141

3023	$y^{'} x - y - \sqrt{x^{2} + y^{2}} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.550

3024	$y^{'} = \cos (y) \cos {(x)}^{2}$	[_separable]	✓	2.927

3025	$x + y + (2 x + 3 y - 1) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.014

3026	$1 + e^{\frac{x}{y}} + e^{\frac{x}{y}} (1 - \frac{x}{y}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _dAlembert]	✓	4.699

3027	$y^{'} + x + \cot (x) y = 0$	[_linear]	✓	1.539

3028	$3 x - 6 = x y^{'} y$	[_separable]	✓	1.786

3029	$x - 2 x y + e^{y} + (y - x^{2} + x e^{y}) y^{'} = 0$	[_exact]	✓	1.976

3030	$2 y^{'} x - y + \frac{x^{2}}{y^{2}} = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	2.703

3031	$y^{'} x + y (1 + y^{2}) = 0$	[_separable]	✓	5.462

3032	$y \sqrt{x^{2} + y^{2}} + x y = x^{2} y^{'}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	23.713

3033	$3 e^{x} \tan (y) = (1 - e^{x}) \sec {(y)}^{2} y^{'}$	[_separable]	✓	3.324

3034	$\sec {(y)}^{2} y^{'} = \tan (y) + 2 x e^{x}$	[‘y=_G(x,y’)‘]	✓	3.170

3035	$2 x \tan (y) + 3 y^{2} + x^{2} + (x^{2} \sec {(y)}^{2} + 6 x y - y^{2}) y^{'} = 0$	[_exact]	✓	57.628

3036	$y \cos (\frac{x}{y}) - (y + x \cos (\frac{x}{y})) y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	8.341

3037	$y (3 x^{2} + y) - x (x^{2} - y) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.336

3038	$x + (2 x + 3 y + 2) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓	2.496

3039	$y^{'} x - 5 y - x \sqrt{y} = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	3.345

3040	$x \sqrt{1 - y} - y^{'} \sqrt{- x^{2} + 1} = 0$ i.c.	[_separable]	✓	2.559

3041	$x y - y^{2} - x^{2} y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	2.782

3042	$x e^{- y^{2}} + y y^{'} = 0$ i.c.	[_separable]	✓	1.992

3043	$\frac{2 y^{3} - 2 x^{2} y^{3} - x + x y^{2} \ln (y)}{x y^{2}} + \frac{(2 y^{3} \ln (x) - x^{2} y^{3} + 2 x + x y^{2}) y^{'}}{y^{3}} = 0$ i.c.	[_exact]	✓	9.219

3044	$y^{'} x - 2 y - 2 x^{4} y^{3} = 0$ i.c.	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	3.061

3045	$(- 2 x^{2} - 3 x y) y^{'} + y^{2} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	7.098

3046	$y^{'} x = x^{4} + 4 y$ i.c.	[_linear]	✓	1.368

3047	$y^{'} x + y = x^{3} y^{6}$ i.c.	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	4.778

3048	$x^{'} = x + x^{2} e^{θ}$ i.c.	[[_1st_order, _with_linear_symmetries], _Bernoulli]	✓	1.738

3049	$x^{2} + y^{2} = 2 x y^{'} y$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	6.515

3050	$3 x y + (3 x^{2} + y^{2}) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	15.027

3051	$2 y + y^{'} = 3 e^{2 x}$ i.c.	[[_linear, ‘class A‘]]	✓	1.473

3052	$4 x y^{2} + (x^{2} + 1) y^{'} = 0$ i.c.	[_separable]	✓	2.338

3053	$x - 2 y + 3 = (x - 2 y + 1) y^{'}$ i.c.	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.188

3054	$y^{2} + (x^{3} - 2 x y) y^{'} = 0$ i.c.	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	3.354

3055	$2 x y - 2 y + 1 + x (x - 1) y^{'} = 0$ i.c.	[_linear]	✓	1.757

3056	$y^{3} + 2 x^{2} y + (- 3 x^{3} - 2 x y^{2}) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	170.447

3057	$2 (x^{2} + 1) y^{'} = (2 y^{2} - 1) x y$ i.c.	[_separable]	✓	5.811

3058	$y^{'} - y = 0$	[_quadrature]	✓	0.712

3059	$y^{''} - 4 y = 0$	[[_2nd_order, _missing_x]]	✓	1.510

3060	$y^{''} + 7 y^{'} + 12 y = 0$	[[_2nd_order, _missing_x]]	✓	0.336

3061	$y^{''} - 3 y^{'} + 2 y = 0$	[[_2nd_order, _missing_x]]	✓	0.341

3062	$y^{''} - 7 y^{'} + 6 y = 0$	[[_2nd_order, _missing_x]]	✓	0.332

3063	$2 y^{''} + 3 y^{'} - 2 y = 0$	[[_2nd_order, _missing_x]]	✓	0.339

3064	$y^{''} - 2 y^{'} - y = 0$	[[_2nd_order, _missing_x]]	✓	0.408

3065	$y^{''} - 2 y^{'} - 2 y = 0$	[[_2nd_order, _missing_x]]	✓	0.394

3066	$y^{''} - 3 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.398

3067	$2 y^{''} + 2 y^{'} - y = 0$	[[_2nd_order, _missing_x]]	✓	0.421

3068	$2 y^{'''} - y^{''} - 2 y^{'} + y = 0$	[[_3rd_order, _missing_x]]	✓	0.088

3069	$y^{'''} - 3 y^{''} - 4 y^{'} + 12 y = 0$	[[_3rd_order, _missing_x]]	✓	0.085

3070	$y^{'''} - 4 y^{''} + y^{'} + 6 y = 0$	[[_3rd_order, _missing_x]]	✓	0.094

3071	$y^{''''} - 6 y^{''} + 8 y = 0$	[[_high_order, _missing_x]]	✓	0.088

3072	$y^{'''} - 7 y^{'} + 6 y = 0$	[[_3rd_order, _missing_x]]	✓	0.083

3073	$y^{'''} - 6 y^{''} + 11 y^{'} - 6 y = 0$	[[_3rd_order, _missing_x]]	✓	0.083

3074	$y^{'''} - 4 y^{''} - 17 y^{'} + 60 y = 0$	[[_3rd_order, _missing_x]]	✓	0.093

3075	$y^{'''} - 9 y^{''} + 23 y^{'} - 15 y = 0$	[[_3rd_order, _missing_x]]	✓	0.077

3076	$y^{''''} + y^{'''} - 7 y^{''} - y^{'} + 6 y = 0$	[[_high_order, _missing_x]]	✓	0.078

3077	$2 y^{''''} - 3 y^{'''} - 20 y^{''} + 27 y^{'} + 18 y = 0$	[[_high_order, _missing_x]]	✓	0.086

3078	$12 y^{''''} - 4 y^{'''} - 3 y^{''} + y^{'} = 0$	[[_high_order, _missing_x]]	✓	0.090

3079	$y^{'''} - 4 y^{''} + 3 y^{'} = 0$	[[_3rd_order, _missing_x]]	✓	0.080

3080	$4 y^{'''} + 2 y^{''} - 4 y^{'} + y = 0$	[[_3rd_order, _missing_x]]	✓	0.090

3081	$y^{'''} - 5 y^{''} - 2 y^{'} + 24 y = 0$	[[_3rd_order, _missing_x]]	✓	0.087

3082	$y^{''''} + 2 y^{'''} - 7 y^{''} - 8 y^{'} + 12 y = 0$	[[_high_order, _missing_x]]	✓	0.095

3083	$y^{(5)} - 3 y^{''''} - 5 y^{'''} + 15 y^{''} + 4 y^{'} - 12 y = 0$	[[_high_order, _missing_x]]	✓	0.104

3084	$y^{(5)} + y^{''''} - 13 y^{'''} - 13 y^{''} + 36 y^{'} + 36 y = 0$	[[_high_order, _missing_x]]	✓	0.096

3085	$y^{(5)} + 3 y^{''''} - 15 y^{'''} - 19 y^{''} + 30 y^{'} = 0$	[[_high_order, _missing_x]]	✓	0.093

3086	$y^{''''} + 3 y^{''} - 4 y = 0$	[[_high_order, _missing_x]]	✓	0.088

3087	$y^{(5)} + 3 y^{'''} + 2 y^{'} = 0$	[[_high_order, _missing_x]]	✓	0.096

3088	$y^{''} - 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.398

3089	$y^{''} = 0$	[[_2nd_order, _quadrature]]	✓	0.717

3090	$2 y^{'''} + y^{''} - 4 y^{'} - 3 y = 0$	[[_3rd_order, _missing_x]]	✓	0.081

3091	$y^{'''} - 3 y^{''} + 3 y^{'} - y = 0$	[[_3rd_order, _missing_x]]	✓	0.082

3092	$y^{''''} = 0$	[[_high_order, _quadrature]]	✓	0.077

3093	$y^{'''} + y^{''} - y^{'} - y = 0$	[[_3rd_order, _missing_x]]	✓	0.090

3094	$4 y^{'''} - 3 y^{'} + y = 0$	[[_3rd_order, _missing_x]]	✓	0.082

3095	$4 y^{(5)} - 3 y^{'''} - y^{''} = 0$	[[_high_order, _missing_x]]	✓	0.087

3096	$y^{'''} - 7 y^{''} + 16 y^{'} - 12 y = 0$	[[_3rd_order, _missing_x]]	✓	0.078

3097	$4 y^{'''} - 8 y^{''} + 5 y^{'} - y = 0$	[[_3rd_order, _missing_x]]	✓	0.078

3098	$y^{''''} - y = 0$	[[_high_order, _missing_x]]	✓	0.094

3099	$y^{'''} - 8 y = 0$	[[_3rd_order, _missing_x]]	✓	0.091

3100	$y^{''} - 2 y^{'} + 3 y = 0$	[[_2nd_order, _missing_x]]	✓	0.597

2.2.31 Problems 3001 to 3100