Problems 13701 to 13800

Table 2.277: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

13701	$x^{'''} - 6 x^{''} + 11 x^{'} - 6 x = e^{- t}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.117

13702	$y^{'''} - 3 y^{''} + 2 y = \sin (x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.121

13703	$x^{''''} - 4 x^{'''} + 8 x^{''} - 8 x^{'} + 4 x = \sin (t)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.156

13704	$x^{''''} - 5 x^{''} + 4 x = e^{t}$	[[_high_order, _with_linear_symmetries]]	✓	0.105

13705	$t^{2} y^{''} - (t^{2} + 2 t) y^{'} + (t + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.098

13706	$(- 1 + x) y^{''} - x y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.101

13707	$(t \cos (t) - \sin (t)) x^{''} - x^{'} t \sin (t) - x \sin (t) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.306

13708	$(- t^{2} + t) x^{''} + (- t^{2} + 2) x^{'} + (2 - t) x = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.112

13709	$y^{''} - x y^{'} + y = 0$	[_Hermite]	✓	0.103

13710	$\tan (t) x^{''} - 3 x^{'} + (\tan (t) + 3 \cot (t)) x = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.093

13711	$y^{''} - y^{'} - 6 y = e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.106

13712	$x^{''} - x = \frac{1}{t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.188

13713	$y^{''} + 4 y = \cot (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	5.555

13714	$t^{2} x^{''} - 2 x = t^{3}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	0.858

13715	$x^{''} - 4 x^{'} = \tan (t)$	[[_2nd_order, _missing_y]]	✓	2.916

13716	$(\tan {(x)}^{2} - 1) y^{''} - 4 \tan {(x)}^{3} y^{'} + 2 y \sec {(x)}^{4} = (\tan {(x)}^{2} - 1) (1 - 2 \sin {(x)}^{2})$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.416

13717	$x^{2} y^{''} - 4 x y^{'} + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	2.377

13718	$4 x^{2} y^{''} + y = 0$ i.c.	[[_Emden, _Fowler]]	✓	0.776

13719	$t^{2} x^{''} - 5 t x^{'} + 10 x = 0$ i.c.	[[_Emden, _Fowler]]	✓	4.034

13720	$t^{2} x^{''} + t x^{'} - x = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.573

13721	$x^{2} z^{''} + 3 x z^{'} + 4 z = 0$ i.c.	[[_Emden, _Fowler]]	✓	3.876

13722	$x^{2} y^{''} - x y^{'} - 3 y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.704

13723	$4 t^{2} x^{''} + 8 t x^{'} + 5 x = 0$ i.c.	[[_Emden, _Fowler]]	✓	3.580

13724	$x^{2} y^{''} - 5 x y^{'} + 5 y = 0$ i.c.	[[_Emden, _Fowler]]	✓	1.867

13725	$3 x^{2} z^{''} + 5 x z^{'} - z = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.645

13726	$t^{2} x^{''} + 3 t x^{'} + 13 x = 0$ i.c.	[[_Emden, _Fowler]]	✓	5.295

13727	$a y^{''} + (b - a) y^{'} + c y = 0$	[[_2nd_order, _missing_x]]	✓	17.266

13728	$(- x^{2} + 1) y^{''} - 2 x y^{'} + n (n + 1) y = 0$	[_Gegenbauer]	✓	0.648

13729	$y^{''} - x y^{'} + y = 0$	[_Hermite]	✓	0.309

13730	$(x^{2} + 1) y^{''} + y = 0$	[[_Emden, _Fowler]]	✓	0.365

13731	$2 x y^{''} + y^{'} - 2 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.704

13732	$y^{''} - 2 x y^{'} - 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.342

13733	$y^{''} - 2 x y^{'} + 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.331

13734	$x (1 - x) y^{''} - 3 x y^{'} - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.280

13735	$x^{2} y^{''} + x y^{'} - x^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.426

13736	$x^{2} y^{''} + x y^{'} + (x^{2} - 1) y = 0$	[_Bessel]	✓	1.123

13737	$x^{2} y^{''} + x y^{'} + (- n^{2} + x^{2}) y = 0$	[_Bessel]	✓	0.647

13738	$[\begin{matrix} x^{'} = 4 x - y \\ y^{'} = 2 x + y + t^{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.660

13739	$[\begin{matrix} x^{'} = x - 4 y + \cos (2 t) \\ y^{'} = x + y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.880

13740	$[\begin{matrix} x^{'} = 2 x + 2 y \\ y^{'} = 6 x + 3 y + e^{t} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.646

13741	$[\begin{matrix} x^{'} = 5 x - 4 y + e^{3 t} \\ y^{'} = x + y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.583

13742	$[\begin{matrix} x^{'} = 2 x + 5 y \\ y^{'} = - 2 x + \cos (3 t) \end{matrix}]$ i.c.	system_of_ODEs	✓	1.224

13743	$[\begin{matrix} x^{'} = x + y + e^{- t} \\ y^{'} = 4 x - 2 y + e^{2 t} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.709

13744	$[\begin{matrix} x^{'} = 8 x + 14 y \\ y^{'} = 7 x + y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.633

13745	$[\begin{array}{cc} 2 & 2 \\ 0 & - 4 \end{array}]$	Eigenvectors	✓	0.127

13746	$[\begin{array}{cc} 7 & - 2 \\ 26 & - 1 \end{array}]$	Eigenvectors	✓	0.237

13747	$[\begin{array}{cc} 9 & 2 \\ 2 & 6 \end{array}]$	Eigenvectors	✓	0.128

13748	$[\begin{array}{cc} 7 & 1 \\ - 4 & 11 \end{array}]$	Eigenvectors	✓	0.090

13749	$[\begin{array}{cc} 2 & - 3 \\ 3 & 2 \end{array}]$	Eigenvectors	✓	0.151

13750	$[\begin{array}{cc} 6 & 0 \\ 0 & - 13 \end{array}]$	Eigenvectors	✓	0.109

13751	$[\begin{array}{cc} 4 & - 2 \\ 1 & 2 \end{array}]$	Eigenvectors	✓	0.168

13752	$[\begin{array}{cc} 3 & - 1 \\ 1 & 1 \end{array}]$	Eigenvectors	✓	0.084

13753	$[\begin{array}{cc} - 7 & 6 \\ 12 & - 1 \end{array}]$	Eigenvectors	✓	0.124

13754	$[\begin{matrix} x^{'} = 8 x + 14 y \\ y^{'} = 7 x + y \end{matrix}]$	system_of_ODEs	✓	0.506

13755	$[\begin{matrix} x^{'} = 2 x \\ y^{'} = - 5 x - 3 y \end{matrix}]$	system_of_ODEs	✓	0.461

13756	$[\begin{matrix} x^{'} = 11 x - 2 y \\ y^{'} = 3 x + 4 y \end{matrix}]$	system_of_ODEs	✓	0.467

13757	$[\begin{matrix} x^{'} = x + 20 y \\ y^{'} = 40 x - 19 y \end{matrix}]$	system_of_ODEs	✓	0.475

13758	$[\begin{matrix} x^{'} = - 2 x + 2 y \\ y^{'} = x - y \end{matrix}]$	system_of_ODEs	✓	0.459

13759	$[\begin{matrix} x^{'} = - y \\ y^{'} = x - y \end{matrix}]$	system_of_ODEs	✓	0.768

13760	$[\begin{matrix} x^{'} = - 2 x + 3 y \\ y^{'} = - 6 x + 4 y \end{matrix}]$	system_of_ODEs	✓	0.552

13761	$[\begin{matrix} x^{'} = - 11 x - 2 y \\ y^{'} = 13 x - 9 y \end{matrix}]$	system_of_ODEs	✓	0.622

13762	$[\begin{matrix} x^{'} = 7 x - 5 y \\ y^{'} = 10 x - 3 y \end{matrix}]$	system_of_ODEs	✓	0.566

13763	$[\begin{matrix} x^{'} = 5 x - 4 y \\ y^{'} = x + y \end{matrix}]$	system_of_ODEs	✓	0.454

13764	$[\begin{matrix} x^{'} = - 6 x + 2 y \\ y^{'} = - 2 x - 2 y \end{matrix}]$	system_of_ODEs	✓	0.439

13765	$[\begin{matrix} x^{'} = - 3 x - y \\ y^{'} = x - 5 y \end{matrix}]$	system_of_ODEs	✓	0.446

13766	$[\begin{matrix} x^{'} = 13 x \\ y^{'} = 13 y \end{matrix}]$	system_of_ODEs	✓	0.293

13767	$[\begin{matrix} x^{'} = 7 x - 4 y \\ y^{'} = x + 3 y \end{matrix}]$	system_of_ODEs	✓	0.435

13768	$[\begin{matrix} x^{'} = y - x \\ y^{'} = y - x \end{matrix}]$	system_of_ODEs	✓	0.318

13769	$\tan (y) - \cot (x) y^{'} = 0$	[_separable]	✓	2.064

13770	$12 x + 6 y - 9 + (5 x + 2 y - 3) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.758

13771	$x y^{'} = y + \sqrt{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	8.567

13772	$x y^{'} + y = x^{3}$	[_linear]	✓	1.503

13773	$y - x y^{'} = x^{2} y y^{'}$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	4.178

13774	$x^{'} + 3 x = e^{2 t}$	[[_linear, ‘class A‘]]	✓	1.392

13775	$\sin (x) y + \cos (x) y^{'} = 1$	[_linear]	✓	2.015

13776	$y^{'} = e^{x - y}$	[_separable]	✓	2.396

13777	$x^{'} = x + \sin (t)$	[[_linear, ‘class A‘]]	✓	1.466

13778	$x (\ln (x) - \ln (y)) y^{'} - y = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	10.733

13779	$x y {y^{'}}^{2} - (x^{2} + y^{2}) y^{'} + x y = 0$	[_separable]	✓	1.210

13780	${y^{'}}^{2} = 9 y^{4}$	[_quadrature]	✓	1.503

13781	$x^{'} = e^{\frac{x}{t}} + \frac{x}{t}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	18.094

13782	$x^{2} + {y^{'}}^{2} = 1$	[_quadrature]	✓	0.348

13783	$y = x y^{'} + \frac{1}{y}$	[_separable]	✓	4.615

13784	$x = {y^{'}}^{3} - y^{'} + 2$	[_quadrature]	✓	1.017

13785	$y^{'} = \frac{y}{x + y^{3}}$	[[_homogeneous, ‘class G‘], _rational]	✓	1.663

13786	$y = {y^{'}}^{4} - {y^{'}}^{3} - 2$	[_quadrature]	✓	2.437

13787	${y^{'}}^{2} + y^{2} = 4$	[_quadrature]	✓	0.729

13788	$y^{'} = \frac{2 y - x - 4}{2 x - y + 5}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.830

13789	$y^{'} - \frac{y}{x + 1} + y^{2} = 0$	[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]	✓	2.040

13790	$y^{'} = x + y^{2}$ i.c.	[[_Riccati, _special]]	✓	15.077

13791	$y^{'} = x y^{3} + x^{2}$ i.c.	[_Abel]	✗	0.775

13792	$y^{'} = x^{2} - y^{2}$	[_Riccati]	✓	1.184

13793	$2 x + 2 y - 1 + (x + y - 2) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.884

13794	${y^{'}}^{3} - y^{'} e^{2 x} = 0$	[_quadrature]	✓	0.654

13795	$y = 5 x y^{'} - {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	0.477

13796	$y^{'} = x - y^{2}$ i.c.	[[_Riccati, _special]]	✓	17.322

13797	$y^{'} = {(x - 5 y)}^{1 / 3} + 2$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	1.954

13798	$(x - y) y - x^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	2.467

13799	$x^{'} + 5 x = 10 t + 2$ i.c.	[[_linear, ‘class A‘]]	✓	2.727

13800	$x^{'} = \frac{x}{t} + \frac{x^{2}}{t^{3}}$ i.c.	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	2.588

2.2.138 Problems 13701 to 13800