Problems 601 to 700

Table 2.15: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

601	$[\begin{matrix} x^{'} = - 3 y \\ y^{'} = 3 x \end{matrix}]$	system_of_ODEs	✓	0.354

602	$[\begin{matrix} x^{'} = 3 x - 2 y \\ y^{'} = 2 x + y \end{matrix}]$	system_of_ODEs	✓	0.660

603	$[\begin{matrix} x^{'} = 2 x + 4 y + 3 e^{t} \\ y^{'} = 5 x - y - t^{2} \end{matrix}]$	system_of_ODEs	✓	3.027

604	$[\begin{matrix} x^{'} = t x - e^{t} y + \cos (t) \\ y^{'} = e^{- t} x + t^{2} y - \sin (t) \end{matrix}]$	system_of_ODEs	✓	0.066

605	$[\begin{matrix} x^{'} = y + z \\ y^{'} = x + z \\ z^{'} = x + y \end{matrix}]$	system_of_ODEs	✓	0.424

606	$[\begin{matrix} x^{'} = 2 x - 3 y \\ y^{'} = x + y + 2 z \\ z^{'} = 5 y - 7 z \end{matrix}]$	system_of_ODEs	✓	10.146

607	$[\begin{matrix} x^{'} = 3 x - 4 y + z + t \\ y^{'} = x - 3 z + t^{2} \\ z^{'} = 6 y - 7 z + t^{3} \end{matrix}]$	system_of_ODEs	✓	67.175

608	$[\begin{matrix} x^{'} = t x - y + e^{t} z \\ y^{'} = 2 x + t^{2} y - z \\ z^{'} = e^{- t} x + 3 t y + t^{3} z \end{matrix}]$	system_of_ODEs	✓	0.067

609	$[\begin{matrix} x_{1}^{'} = x_{2} \\ x_{2}^{'} = 2 x_{3} \\ x_{3}^{'} = 3 x_{4} \\ x_{4}^{'} = 4 x_{1} \end{matrix}]$	system_of_ODEs	✓	1.716

610	$[\begin{matrix} x_{1}^{'} = x_{2} + x_{3} + 1 \\ x_{2}^{'} = x_{3} + x_{4} + t \\ x_{3}^{'} = x_{1} + x_{4} + t^{2} \\ x_{4}^{'} = x_{1} + x_{2} + t^{3} \end{matrix}]$	system_of_ODEs	✓	2.162

611	$[\begin{matrix} x_{1}^{'} = 4 x_{1} + 2 x_{2} \\ x_{2}^{'} = - 3 x_{1} - x_{2} \end{matrix}]$	system_of_ODEs	✓	0.379

612	$[\begin{matrix} x_{1}^{'} = - 3 x_{1} + 2 x_{2} \\ x_{2}^{'} = - 3 x_{1} + 4 x_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.489

613	$[\begin{matrix} x_{1}^{'} = 3 x_{1} - x_{2} \\ x_{2}^{'} = 5 x_{1} - 3 x_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.510

614	$[\begin{matrix} x_{1}^{'} = 4 x_{1} + x_{2} \\ x_{2}^{'} = - 2 x_{1} + x_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.501

615	$[\begin{matrix} x_{1}^{'} = 4 x_{1} - 3 x_{2} \\ x_{2}^{'} = 6 x_{1} - 7 x_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.517

616	$[\begin{matrix} x_{1}^{'} = 3 x_{1} - 2 x_{2} \\ x_{2}^{'} = - x_{1} + 3 x_{2} - 2 x_{3} \\ x_{3}^{'} = - x_{2} + 3 x_{3} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.591

617	$[\begin{matrix} x_{1}^{'} = x_{2} + x_{3} \\ x_{2}^{'} = x_{1} + x_{3} \\ x_{3}^{'} = x_{1} + x_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.455

618	$[\begin{matrix} x_{1}^{'} = x_{1} + 2 x_{2} + x_{3} \\ x_{2}^{'} = 6 x_{1} - x_{2} \\ x_{3}^{'} = - x_{1} - 2 x_{2} - x_{3} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.592

619	$[\begin{matrix} x_{1}^{'} = - 8 x_{1} - 11 x_{2} - 2 x_{3} \\ x_{2}^{'} = 6 x_{1} + 9 x_{2} + 2 x_{3} \\ x_{3}^{'} = - 6 x_{1} - 6 x_{2} + x_{3} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.569

620	$[\begin{matrix} x_{1}^{'} = x_{1} - 4 x_{2} - 2 x_{4} \\ x_{2}^{'} = x_{2} \\ x_{3}^{'} = 6 x_{1} - 12 x_{2} - x_{3} - 6 x_{4} \\ x_{4}^{'} = - 4 x_{2} - x_{4} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.661

621	$[\begin{matrix} x_{1}^{'} = x_{1} + 2 x_{2} \\ x_{2}^{'} = 2 x_{1} + x_{2} \end{matrix}]$	system_of_ODEs	✓	0.326

622	$[\begin{matrix} x_{1}^{'} = 2 x_{1} + 3 x_{2} \\ x_{2}^{'} = 2 x_{1} + x_{2} \end{matrix}]$	system_of_ODEs	✓	0.350

623	$[\begin{matrix} x_{1}^{'} = 3 x_{1} + 4 x_{2} \\ x_{2}^{'} = 3 x_{1} + 2 x_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.496

624	$[\begin{matrix} x_{1}^{'} = 4 x_{1} + x_{2} \\ x_{2}^{'} = 6 x_{1} - x_{2} \end{matrix}]$	system_of_ODEs	✓	0.357

625	$[\begin{matrix} x_{1}^{'} = 6 x_{1} - 7 x_{2} \\ x_{2}^{'} = x_{1} - 2 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.411

626	$[\begin{matrix} x_{1}^{'} = 9 x_{1} + 5 x_{2} \\ x_{2}^{'} = - 6 x_{1} - 2 x_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.516

627	$[\begin{matrix} x_{1}^{'} = - 3 x_{1} + 4 x_{2} \\ x_{2}^{'} = 6 x_{1} - 5 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.409

628	$[\begin{matrix} x_{1}^{'} = x_{1} - 5 x_{2} \\ x_{2}^{'} = x_{1} - x_{2} \end{matrix}]$	system_of_ODEs	✓	0.430

629	$[\begin{matrix} x_{1}^{'} = 2 x_{1} - 5 x_{2} \\ x_{2}^{'} = 4 x_{1} - 2 x_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.506

630	$[\begin{matrix} x_{1}^{'} = - 3 x_{1} - 2 x_{2} \\ x_{2}^{'} = 9 x_{1} + 3 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.463

631	$[\begin{matrix} x_{1}^{'} = x_{1} - 2 x_{2} \\ x_{2}^{'} = 2 x_{1} + x_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.469

632	$[\begin{matrix} x_{1}^{'} = x_{1} - 5 x_{2} \\ x_{2}^{'} = x_{1} + 3 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.554

633	$[\begin{matrix} x_{1}^{'} = 5 x_{1} - 9 x_{2} \\ x_{2}^{'} = 2 x_{1} - x_{2} \end{matrix}]$	system_of_ODEs	✓	0.584

634	$[\begin{matrix} x_{1}^{'} = 3 x_{1} - 4 x_{2} \\ x_{2}^{'} = 4 x_{1} + 3 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.434

635	$[\begin{matrix} x_{1}^{'} = 7 x_{1} - 5 x_{2} \\ x_{2}^{'} = 4 x_{1} + 3 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.588

636	$[\begin{matrix} x_{1}^{'} = - 50 x_{1} + 20 x_{2} \\ x_{2}^{'} = 100 x_{1} - 60 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.412

637	$[\begin{matrix} x_{1}^{'} = 4 x_{1} + x_{2} + 4 x_{3} \\ x_{2}^{'} = x_{1} + 7 x_{2} + x_{3} \\ x_{3}^{'} = 4 x_{1} + x_{2} + 4 x_{3} \end{matrix}]$	system_of_ODEs	✓	0.474

638	$[\begin{matrix} x_{1}^{'} = x_{1} + 2 x_{2} + 2 x_{3} \\ x_{2}^{'} = 2 x_{1} + 7 x_{2} + x_{3} \\ x_{3}^{'} = 2 x_{1} + x_{2} + 7 x_{3} \end{matrix}]$	system_of_ODEs	✓	0.530

639	$[\begin{matrix} x_{1}^{'} = 4 x_{1} + x_{2} + x_{3} \\ x_{2}^{'} = x_{1} + 4 x_{2} + x_{3} \\ x_{3}^{'} = x_{1} + x_{2} + 4 x_{3} \end{matrix}]$	system_of_ODEs	✓	0.440

640	$[\begin{matrix} x_{1}^{'} = 5 x_{1} + x_{2} + 3 x_{3} \\ x_{2}^{'} = x_{1} + 7 x_{2} + x_{3} \\ x_{3}^{'} = 3 x_{1} + x_{2} + 5 x_{3} \end{matrix}]$	system_of_ODEs	✓	0.553

641	$[\begin{matrix} x_{1}^{'} = 5 x_{1} - 6 x_{3} \\ x_{2}^{'} = 2 x_{1} - x_{2} - 2 x_{3} \\ x_{3}^{'} = 4 x_{1} - 2 x_{2} - 4 x_{3} \end{matrix}]$	system_of_ODEs	✓	0.620

642	$[\begin{matrix} x_{1}^{'} = 3 x_{1} + 2 x_{2} + 2 x_{3} \\ x_{2}^{'} = - 5 x_{1} - 4 x_{2} - 2 x_{3} \\ x_{3}^{'} = 5 x_{1} + 5 x_{2} + 3 x_{3} \end{matrix}]$	system_of_ODEs	✓	0.607

643	$[\begin{matrix} x_{1}^{'} = 3 x_{1} + x_{2} + x_{3} \\ x_{2}^{'} = - 5 x_{1} - 3 x_{2} - x_{3} \\ x_{3}^{'} = 5 x_{1} + 5 x_{2} + 3 x_{3} \end{matrix}]$	system_of_ODEs	✓	0.557

644	$[\begin{matrix} x_{1}^{'} = 2 x_{1} + x_{2} - x_{3} \\ x_{2}^{'} = - 4 x_{1} - 3 x_{2} - x_{3} \\ x_{3}^{'} = 4 x_{1} + 4 x_{2} + 2 x_{3} \end{matrix}]$	system_of_ODEs	✓	0.771

645	$[\begin{matrix} x_{1}^{'} = 5 x_{1} + 5 x_{2} + 2 x_{3} \\ x_{2}^{'} = - 6 x_{1} - 6 x_{2} - 5 x_{3} \\ x_{3}^{'} = 6 x_{1} + 6 x_{2} + 5 x_{3} \end{matrix}]$	system_of_ODEs	✓	0.828

646	$[\begin{matrix} x_{1}^{'} = 3 x_{1} + x_{3} \\ x_{2}^{'} = 9 x_{1} - x_{2} + 2 x_{3} \\ x_{3}^{'} = - 9 x_{1} + 4 x_{2} - x_{3} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.923

647	$[\begin{matrix} x_{1}^{'} = x_{1} \\ x_{2}^{'} = 2 x_{1} + 2 x_{2} \\ x_{3}^{'} = 3 x_{2} + 3 x_{3} \\ x_{4}^{'} = 4 x_{3} + 4 x_{4} \end{matrix}]$	system_of_ODEs	✓	0.823

648	$[\begin{matrix} x_{1}^{'} = - 2 x_{1} + 9 x_{4} \\ x_{2}^{'} = 4 x_{1} + 2 x_{2} - 10 x_{4} \\ x_{3}^{'} = - x_{3} + 8 x_{4} \\ x_{4}^{'} = x_{4} \end{matrix}]$	system_of_ODEs	✓	0.803

649	$[\begin{matrix} x_{1}^{'} = 2 x_{1} \\ x_{2}^{'} = - 21 x_{1} - 5 x_{2} - 27 x_{3} - 9 x_{4} \\ x_{3}^{'} = 5 x_{3} \\ x_{4}^{'} = - 21 x_{3} - 2 x_{4} \end{matrix}]$	system_of_ODEs	✓	0.957

650	$[\begin{matrix} x_{1}^{'} = 4 x_{1} + x_{2} + x_{3} + 7 x_{4} \\ x_{2}^{'} = x_{1} + 4 x_{2} + 10 x_{3} + x_{4} \\ x_{3}^{'} = x_{1} + 10 x_{2} + 4 x_{3} + x_{4} \\ x_{4}^{'} = 7 x_{1} + x_{2} + x_{3} + 4 x_{4} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.976

651	$y^{'} = 2 x + 1$ i.c.	[_quadrature]	✓	0.479

652	$y^{'} = {(x - 2)}^{2}$ i.c.	[_quadrature]	✓	0.998

653	$y^{'} = \sqrt{x}$ i.c.	[_quadrature]	✓	0.933

654	$y^{'} = \frac{1}{x^{2}}$ i.c.	[_quadrature]	✓	0.896

655	$y^{'} = \frac{1}{\sqrt{x + 2}}$ i.c.	[_quadrature]	✓	1.180

656	$y^{'} = x \sqrt{x^{2} + 9}$ i.c.	[_quadrature]	✓	1.565

657	$y^{'} = \frac{10}{x^{2} + 1}$ i.c.	[_quadrature]	✓	1.047

658	$y^{'} = \cos (2 x)$ i.c.	[_quadrature]	✓	0.987

659	$y^{'} = \frac{1}{\sqrt{- x^{2} + 1}}$ i.c.	[_quadrature]	✓	1.164

660	$y^{'} = x e^{- x}$ i.c.	[_quadrature]	✓	1.137

661	$y^{'} = - y - \sin (x)$	[[_linear, ‘class A‘]]	✓	1.820

662	$y^{'} = x + y$	[[_linear, ‘class A‘]]	✓	1.303

663	$y^{'} = y - \sin (x)$	[[_linear, ‘class A‘]]	✓	1.768

664	$y^{'} = x - y$	[[_linear, ‘class A‘]]	✓	1.204

665	$y^{'} = y - x + 1$	[[_linear, ‘class A‘]]	✓	1.526

666	$y^{'} = x - y + 1$	[[_linear, ‘class A‘]]	✓	1.599

667	$y^{'} = x^{2} - y$	[[_linear, ‘class A‘]]	✓	1.316

668	$y^{'} = x^{2} - y - 2$	[[_linear, ‘class A‘]]	✓	1.381

669	$y^{'} = 2 x^{2} y^{2}$ i.c.	[_separable]	✓	3.158

670	$y^{'} = \ln (y) x$	[_separable]	✓	1.439

671	$y^{'} = y^{1 / 3}$ i.c.	[_quadrature]	✓	2.137

672	$y^{'} = y^{1 / 3}$ i.c.	[_quadrature]	✓	1.856

673	$y y^{'} = x - 1$ i.c.	[_separable]	✓	5.478

674	$y y^{'} = x - 1$ i.c.	[_separable]	✓	6.940

675	$y^{'} = \ln (1 + y^{2})$ i.c.	[_quadrature]	✓	2.871

676	$y^{'} = x^{2} - y^{2}$	[_Riccati]	✓	2.025

677	$y^{'} + 2 x y = 0$	[_separable]	✓	1.561

678	$y^{'} + 2 x y^{2} = 0$	[_separable]	✓	2.366

679	$y^{'} = y \sin (x)$	[_separable]	✓	1.954

680	$(x + 1) y^{'} = 4 y$	[_separable]	✓	1.749

681	$2 \sqrt{x} y^{'} = \sqrt{1 - y^{2}}$	[_separable]	✓	2.035

682	$y^{'} = 3 \sqrt{x y}$	[[_homogeneous, ‘class G‘]]	✓	8.341

683	$y^{'} = 4 {(x y)}^{1 / 3}$	[[_homogeneous, ‘class G‘]]	✓	5.401

684	$y^{'} = 2 x \sec (y)$	[_separable]	✓	1.880

685	$(- x^{2} + 1) y^{'} = 2 y$	[_separable]	✓	1.892

686	$(x^{2} + 1) y^{'} = {(1 + y)}^{2}$	[_separable]	✓	3.344

687	$y^{'} = x y^{3}$	[_separable]	✓	3.980

688	$y y^{'} = x (1 + y^{2})$	[_separable]	✓	2.710

689	$y^{'} = \frac{1 + \sqrt{x}}{1 + \sqrt{y}}$	[_separable]	✓	2.201

690	$y^{'} = \frac{(x - 1) y^{5}}{x^{2} (2 y^{3} - y)}$	[_separable]	✓	2.235

691	$(x^{2} + 1) \tan (y) y^{'} = x$	[_separable]	✓	2.382

692	$y^{'} = 1 + x + y + x y$	[_separable]	✓	1.772

693	$x^{2} y^{'} = 1 - x^{2} + y^{2} - x^{2} y^{2}$	[_separable]	✓	3.797

694	$y^{'} = y e^{x}$ i.c.	[_separable]	✓	3.139

695	$y^{'} = 3 x^{2} (1 + y^{2})$ i.c.	[_separable]	✓	3.500

696	$2 y y^{'} = \frac{x}{\sqrt{x^{2} - 16}}$ i.c.	[_separable]	✓	3.435

697	$y^{'} = 4 x^{3} y - y$ i.c.	[_separable]	✓	2.179

698	$y^{'} + 1 = 2 y$ i.c.	[_quadrature]	✓	1.672

699	$y^{'} \tan (x) = y$ i.c.	[_separable]	✓	2.420

700	$y^{'} x - y = 2 x^{2} y$ i.c.	[_separable]	✓	2.031

2.2.7 Problems 601 to 700