Problems 18401 to 18500

Table 2.371: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

18401	$[\begin{matrix} x^{'} = 2 x \\ y^{'} = 3 y \end{matrix}]$	system_of_ODEs	✓	0.408

18402	$[\begin{matrix} x^{'} = - x - 2 y \\ y^{'} = 4 x - 5 y \end{matrix}]$	system_of_ODEs	✓	0.565

18403	$[\begin{matrix} x^{'} = - 3 x + 4 y \\ y^{'} = - 2 x + 3 y \end{matrix}]$	system_of_ODEs	✓	0.453

18404	$[\begin{matrix} x^{'} = 5 x + 2 y \\ y^{'} = - 17 x - 5 y \end{matrix}]$	system_of_ODEs	✓	0.548

18405	$[\begin{matrix} x^{'} = - 4 x - y \\ y^{'} = x - 2 y \end{matrix}]$	system_of_ODEs	✓	0.443

18406	$[\begin{matrix} x^{'} = 4 x - 3 y \\ y^{'} = 8 x - 6 y \end{matrix}]$	system_of_ODEs	✓	0.503

18407	$[\begin{matrix} x^{'} = 4 x - 2 y \\ y^{'} = 5 x + 2 y \end{matrix}]$	system_of_ODEs	✓	0.576

18408	$x^{''} + (5 x^{4} - 9 x^{2}) x^{'} + x^{5} = 0$	[[_2nd_order, _missing_x]]	✗	2.263

18409	$x^{'} = 3 t^{2} + 4 t$ i.c.	[_quadrature]	✓	0.694

18410	$x^{'} = b e^{t}$ i.c.	[_quadrature]	✓	0.315

18411	$x^{'} = \frac{1}{t^{2} + 1}$ i.c.	[_quadrature]	✓	0.760

18412	$x^{'} = \frac{1}{\sqrt{t^{2} + 1}}$ i.c.	[_quadrature]	✓	0.773

18413	$x^{'} = \cos (t)$ i.c.	[_quadrature]	✓	0.751

18414	$x^{'} = \frac{\cos (t)}{\sin (t)}$ i.c.	[_quadrature]	✓	1.139

18415	$x^{'} = x^{2} - 3 x + 2$ i.c.	[_quadrature]	✓	1.634

18416	$x^{'} = b e^{x}$ i.c.	[_quadrature]	✓	0.943

18417	$x^{'} = {(x - 1)}^{2}$ i.c.	[_quadrature]	✓	1.176

18418	$x^{'} = \sqrt{x^{2} - 1}$ i.c.	[_quadrature]	✓	4.401

18419	$x^{'} = 2 \sqrt{x}$ i.c.	[_quadrature]	✓	1.583

18420	$x^{'} = \tan (x)$ i.c.	[_quadrature]	✓	3.045

18421	$3 t^{2} x - t x + (3 t^{3} x^{2} + t^{3} x^{4}) x^{'} = 0$	[_separable]	✓	3.939

18422	$1 + 2 x + (- t^{2} + 4) x^{'} = 0$	[_separable]	✓	1.881

18423	$x^{'} = \cos (\frac{x}{t})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	2.768

18424	$(t^{2} - x^{2}) x^{'} = t x$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	18.569

18425	$e^{3 t} x^{'} + 3 x e^{3 t} = 2 t$	[[_linear, ‘class A‘]]	✓	1.872

18426	$2 t + 3 x + (3 t - x) x^{'} = t^{2}$	[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.487

18427	$x^{'} + 2 x = e^{t}$	[[_linear, ‘class A‘]]	✓	1.358

18428	$x^{'} + x \tan (t) = 0$	[_separable]	✓	1.790

18429	$x^{'} - x \tan (t) = 4 \sin (t)$	[_linear]	✓	1.965

18430	$t^{3} x^{'} + (- 3 t^{2} + 2) x = t^{3}$	[_linear]	✓	2.533

18431	$x^{'} + 2 t x + t x^{4} = 0$	[_separable]	✓	2.663

18432	$t x^{'} + x \ln (t) = t^{2}$	[_linear]	✓	1.352

18433	$t x^{'} + x g (t) = h (t)$	[_linear]	✓	1.165

18434	$t^{2} x^{''} - 6 t x^{'} + 12 x = 0$	[[_Emden, _Fowler]]	✓	0.937

18435	$x^{'} = - λ x$	[_quadrature]	✓	0.856

18436	$[\begin{matrix} x^{'} = x \\ y^{'} = x + 2 y \end{matrix}]$	system_of_ODEs	✓	0.426

18437	$t^{2} x^{''} - 2 t x^{'} + 2 x = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.024

18438	$x^{''} - 5 x^{'} + 6 x = 0$	[[_2nd_order, _missing_x]]	✓	0.842

18439	$x^{''} - 4 x^{'} + 4 x = 0$	[[_2nd_order, _missing_x]]	✓	0.963

18440	$x^{''} - 4 x^{'} + 5 x = 0$	[[_2nd_order, _missing_x]]	✓	2.105

18441	$x^{''} + 3 x^{'} = 0$	[[_2nd_order, _missing_x]]	✓	1.895

18442	$x^{''} - 3 x^{'} + 2 x = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.154

18443	$x^{''} + x = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.052

18444	$x^{''} + 2 x^{'} + x = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.323

18445	$x^{''} - 2 x^{'} + 2 x = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.143

18446	$x^{''} - x = t^{2}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	1.182

18447	$x^{''} - x = e^{t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	1.219

18448	$x^{''} + 2 x^{'} + 4 x = e^{t} \cos (2 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	67.877

18449	$x^{''} - x^{'} + x = \sin (2 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	78.315

18450	$x^{''} + 4 x^{'} + 3 x = t \sin (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.694

18451	$x^{''} + x = \cos (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	3.517

18452	$x^{2} y^{''} - \frac{x^{2} {y^{'}}^{2}}{2 y} + 4 x y^{'} + 4 y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	✗	0.133

18453	$y^{'} + c y = a$	[_quadrature]	✓	0.872

18454	$y^{''} + \frac{y^{'}}{x} + k^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.808

18455	$\cos (x) y^{'} + \sin (x) y^{''} + n y \sin (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	1.395

18456	$y^{'} = \frac{\sqrt{1 - y^{2}} \arcsin (y)}{x}$	[_separable]	✓	5.431

18457	$v^{''} = {(\frac{1}{v} + {v^{'}}^{4})}^{1 / 3}$	[[_2nd_order, _missing_x]]	✗	3.306

18458	$v^{'} + u^{2} v = \sin (u)$	[_linear]	✓	1.676

18459	$\sqrt{y^{'} + y} = {(y^{''} + 2 x)}^{1 / 4}$	[NONE]	✗	0.435

18460	$v^{'} + \frac{2 v}{u} = 3$	[_linear]	✓	2.504

18461	$\sin (x) \cos {(y)}^{2} + \cos {(x)}^{2} y^{'} = 0$	[_separable]	✓	3.977

18462	$y^{'} + \sqrt{\frac{1 - y^{2}}{- x^{2} + 1}} = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	26.539

18463	$y - x y^{'} = b (1 + x^{2} y^{'})$	[_separable]	✓	1.033

18464	$x^{'} = k (A - n x) (M - m x)$	[_quadrature]	✓	7.715

18465	$y^{'} = 1 + \frac{1}{x} - \frac{1}{y^{2} + 2} - \frac{1}{x (y^{2} + 2)}$	[_separable]	✓	1.595

18466	$y^{2} = x (y - x) y^{'}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	39.711

18467	$2 x^{2} y + y^{3} - x^{3} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	75.541

18468	$2 a x + b y + (2 c y + b x + e) y^{'} = g$	[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.614

18469	$\sec {(x)}^{2} \tan (y) y^{'} + \sec {(y)}^{2} \tan (x) = 0$	[_separable]	✓	38.659

18470	$x + y y^{'} = m y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	12.075

18471	$\frac{2 x}{y^{3}} + (\frac{1}{y^{2}} - \frac{3 x^{2}}{y^{4}}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	34.314

18472	$(T + \frac{1}{\sqrt{t^{2} - T^{2}}}) T^{'} = \frac{T}{t \sqrt{t^{2} - T^{2}}} - t$	[_exact]	✓	3.225

18473	$y^{'} + x y = x$	[_separable]	✓	1.483

18474	$y^{'} + \frac{y}{x} = \sin (x)$	[_linear]	✓	1.446

18475	$y^{'} + \frac{y}{x} = \frac{\sin (x)}{y^{3}}$	[_Bernoulli]	✓	35.661

18476	$p^{'} = \frac{p + a t^{3} - 2 p t^{2}}{t (- t^{2} + 1)}$	[_linear]	✓	1.175

18477	$(T \ln (t) - 1) T = t T^{'}$	[_Bernoulli]	✓	2.440

18478	$y^{'} + y \cos (x) = \frac{\sin (2 x)}{2}$	[_linear]	✓	2.412

18479	$y - \cos (x) y^{'} = y^{2} \cos (x) (1 - \sin (x))$	[_Bernoulli]	✓	6.082

18480	$x {y^{'}}^{2} - y + 2 y^{'} = 0$	[_rational, _dAlembert]	✓	0.978

18481	$2 {y^{'}}^{3} + {y^{'}}^{2} - y = 0$	[_quadrature]	✓	0.347

18482	$y^{'} = e^{z - y^{'}}$	[_quadrature]	✓	0.521

18483	$\sqrt{t^{2} + T} = T^{'}$	[[_homogeneous, ‘class G‘]]	✓	4.308

18484	$(x^{2} - 1) {y^{'}}^{2} = 1$	[_quadrature]	✓	0.352

18485	$y^{'} = {(x + y)}^{2}$	[[_homogeneous, ‘class C‘], _Riccati]	✓	1.482

18486	$θ^{''} = - p^{2} θ$	[[_2nd_order, _missing_x]]	✓	1.655

18487	$\sec {(θ)}^{2} = \frac{m s^{'}}{k}$	[_quadrature]	✓	0.350

18488	$y^{''} = \frac{m \sqrt{1 + {y^{'}}^{2}}}{k}$	[[_2nd_order, _missing_x]]	✓	2.990

18489	$ϕ^{''} = \frac{4 π n c}{\sqrt{v_{0}^{2} + \frac{2 e (ϕ - V_{0})}{m}}}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	58.454

18490	$y^{'} = x (a y^{2} + b)$	[_separable]	✓	2.460

18491	$n^{'} = (n^{2} + 1) x$	[_separable]	✓	2.016

18492	$v^{'} + \frac{2 v}{u} = 3 v$	[_separable]	✓	1.684

18493	$\sqrt{- u^{2} + 1} v^{'} = 2 u \sqrt{1 - v^{2}}$	[_separable]	✓	9.791

18494	$\sqrt{1 + v^{'}} = \frac{e^{u}}{2}$	[_quadrature]	✓	0.517

18495	$\frac{y^{'}}{x} = y \sin (x^{2} - 1) - \frac{2 y}{\sqrt{x}}$	[_separable]	✓	2.138

18496	$y^{'} = 1 + \frac{2 y}{x - y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	39.421

18497	$v^{'} + 2 v u = 2 u$	[_separable]	✓	1.485

18498	$1 + v^{2} + (u^{2} + 1) v v^{'} = 0$	[_separable]	✓	2.920

18499	$u \ln (u) v^{'} + \sin {(v)}^{2} = 1$	[_separable]	✓	3.790

18500	$4 y {y^{'}}^{3} - 2 x^{2} {y^{'}}^{2} + 4 x y y^{'} + x^{3} = 16 y^{2}$	[[_1st_order, _with_linear_symmetries]]	✓	115.909

2.2.185 Problems 18401 to 18500