Problems 2601 to 2700

Table 2.55: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

2601	$y^{''} - 6 y^{'} + 9 y = (3 t^{7} - 5 t^{4}) e^{3 t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.655

2602	$y^{''} - 2 y^{'} + 5 y = 2 \cos {(t)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.728

2603	$y^{''} - 2 y^{'} + 5 y = 2 \cos {(t)}^{2} e^{t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.683

2604	$y^{''} + y^{'} - 6 y = \sin (t) + e^{2 t} t$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.910

2605	$y^{''} + y^{'} + 4 y = t^{2} + (2 t + 3) (1 + \cos (t))$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.958

2606	$y^{''} - 3 y^{'} + 2 y = e^{t} + e^{2 t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.560

2607	$y^{''} + 2 y^{'} = 1 + t^{2} + e^{- 2 t}$	[[_2nd_order, _missing_y]]	✓	1.319

2608	$y^{''} + y = \cos (t) \cos (2 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.137

2609	$y^{''} + y = \cos (t) \cos (2 t) \cos (3 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.741

2610	$y^{''} - 6 y^{'} + 9 y = t^{3 / 2} e^{3 t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.663

2611	$y^{''} + y^{'} t + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.332

2612	$y^{''} - t y = 0$	[[_Emden, _Fowler]]	✓	0.341

2613	$(t^{2} + 2) y^{''} - y^{'} t - 3 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.450

2614	$y^{''} - t^{3} y = 0$	[[_Emden, _Fowler]]	✓	0.281

2615	$t (2 - t) y^{''} - 6 (t - 1) y^{'} - 4 y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.537

2616	$y^{''} + t^{2} y = 0$ i.c.	[[_Emden, _Fowler]]	✓	0.333

2617	$y^{''} - t^{3} y = 0$ i.c.	[[_Emden, _Fowler]]	✓	0.390

2618	$y^{''} + (t^{2} + 2 t + 1) y^{'} - (4 + 4 t) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.498

2619	$y^{''} - 2 y^{'} t + λ y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.442

2620	$(- t^{2} + 1) y^{''} - 2 y^{'} t + α (α + 1) y = 0$	[_Gegenbauer]	✓	0.563

2621	$(- t^{2} + 1) y^{''} - y^{'} t + α^{2} y = 0$	[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.523

2622	$y^{''} + t^{3} y^{'} + 3 t^{2} y = e^{t}$ i.c.	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	0.507

2623	$(1 - t) y^{''} + y^{'} t + y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.524

2624	$y^{''} + y^{'} + t y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.507

2625	$y^{''} + y^{'} t + e^{t} y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.593

2626	$y^{''} + y^{'} + e^{t} y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.619

2627	$y^{''} + y^{'} + e^{- t} y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.884

2628	$t^{2} y^{''} + 5 y^{'} t - 5 y = 0$	[[_Emden, _Fowler]]	✓	0.927

2629	$2 t^{2} y^{''} + 3 y^{'} t - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.000

2630	${(t - 1)}^{2} y^{''} - 2 (t - 1) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.857

2631	$t^{2} y^{''} + 3 y^{'} t + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.008

2632	$t^{2} y^{''} - y^{'} t + y = 0$	[[_Emden, _Fowler]]	✓	0.981

2633	${(t - 2)}^{2} y^{''} + 5 (t - 2) y^{'} + 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.704

2634	$t^{2} y^{''} + y^{'} t + y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.857

2635	$t^{2} y^{''} + 3 y^{'} t + 2 y = 0$	[[_Emden, _Fowler]]	✓	1.083

2636	$t^{2} y^{''} - y^{'} t - 2 y = 0$ i.c.	[[_Emden, _Fowler]]	✓	1.609

2637	$t^{2} y^{''} - 3 y^{'} t + 4 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.434

2638	$t {(t - 2)}^{2} y^{''} + y^{'} t + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.523

2639	$t {(t - 2)}^{2} y^{''} + y^{'} t + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.219

2640	$\sin (t) y^{''} + \cos (t) y^{'} + \frac{y}{t} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.773

2641	$(e^{t} - 1) y^{''} + e^{t} y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.802

2642	$(- t^{2} + 1) y^{''} + \frac{y^{'}}{\sin (1 + t)} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.351

2643	$t^{3} y^{''} + \sin (t^{2}) y^{'} + t y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.560

2644	$2 t^{2} y^{''} + 3 y^{'} t - (1 + t) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.785

2645	$2 t y^{''} + (1 - 2 t) y^{'} - y = 0$	[_Laguerre]	✓	0.663

2646	$2 t y^{''} + (1 + t) y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.665

2647	$2 t^{2} y^{''} - y^{'} t + (1 + t) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.722

2648	$4 t y^{''} + 3 y^{'} - 3 y = 0$	[[_Emden, _Fowler]]	✓	0.674

2649	$2 t^{2} y^{''} + (t^{2} - t) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.765

2650	$t^{2} y^{''} - y^{'} t - (t^{2} + \frac{5}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.654

2651	$t^{2} y^{''} + (- t^{2} + t) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.730

2652	$t y^{''} - (t^{2} + 2) y^{'} + t y = 0$	[_Lienard]	✓	0.633

2653	$t^{2} y^{''} + (- t^{2} + 3 t) y^{'} - t y = 0$	[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.715

2654	$t^{2} y^{''} + t (1 + t) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.858

2655	$t y^{''} - (t + 4) y^{'} + 2 y = 0$	[_Laguerre]	✓	0.779

2656	$t^{2} y^{''} + (t^{2} - 3 t) y^{'} + 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.271

2657	$t^{2} y^{''} + y^{'} t - (1 + t) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.425

2658	$t y^{''} + y^{'} t + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.357

2659	$t^{2} y^{''} + (- t^{2} + 1) y^{'} + 4 t y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.216

2660	$t^{2} y^{''} + y^{'} t + t^{2} y = 0$	[_Lienard]	✓	0.536

2661	$t^{2} y^{''} + y^{'} t + (t^{2} - v^{2}) y = 0$	[_Bessel]	✓	0.674

2662	$t y^{''} + (1 - t) y^{'} + λ y = 0$	[_Laguerre]	✓	0.862

2663	$t (1 - t) y^{''} + (γ - (α + β + 1) t) y^{'} - α β y = 0$	[_Jacobi]	✓	1.047

2664	$2 \sin (t) y^{''} + (1 - t) y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.920

2665	$t^{2} y^{''} + y^{'} t + (1 + t) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.596

2666	$t y^{''} + y^{'} - 4 y = 0$	[[_Emden, _Fowler]]	✓	0.613

2667	$t^{2} y^{''} - t (1 + t) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.611

2668	$t^{2} y^{''} + y^{'} t + (t^{2} - 1) y = 0$	[_Bessel]	✓	1.349

2669	$t y^{''} + 3 y^{'} - 3 y = 0$	[[_Emden, _Fowler]]	✓	1.364

2670	$t^{2} y^{''} + t p (t) y^{'} + q (t) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	33.017

2671	$y^{''} - 5 y^{'} + 4 y = e^{2 t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.301

2672	$2 y^{''} + y^{'} - y = e^{3 t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.307

2673	$y^{''} + 2 y^{'} + y = e^{- t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.302

2674	$y^{''} + y = t^{2} \sin (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.495

2675	$y^{''} + 3 y^{'} + 7 y = \cos (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.526

2676	$y^{''} + y^{'} + y = t^{3}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.533

2677	$y^{'''} - 6 y^{''} + 11 y^{'} - 6 y = e^{4 t}$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓	0.418

2678	$y^{''} - 3 y^{'} + 2 y = e^{- t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.395

2679	$y^{''} + y = \sin (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.457

2680	$y^{''} + y = t \sin (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.495

2681	$y^{''} - 2 y^{'} + y = e^{t} t$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.290

2682	$y^{''} - 2 y^{'} + 7 y = \sin (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.501

2683	$y^{''} + y^{'} + y = 1 + e^{- t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.577

2684	$y^{''} + y = {\begin{array}{cc} 2 & 0 \leq t \leq 3 \\ 3 t - 7 & 3 < t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.086

2685	$y^{''} + 2 y^{'} + y = 2 (- 3 + t) Heaviside (- 3 + t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.911

2686	$y^{''} + y^{'} + y = Heaviside (t - π) - Heaviside (t - 2 π)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	8.013

2687	$y^{''} + 4 y = {\begin{array}{cc} 1 & 0 \leq t < 4 \\ 0 & 4 < t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.076

2688	$y^{''} + y = {\begin{array}{cc} \sin (t) & 0 \leq t < π \\ \cos (t) & π \leq t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.462

2689	$y^{''} + y = {\begin{array}{cc} \cos (t) & 0 \leq t < \frac{π}{2} \\ 0 & \frac{π}{2} \leq t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.144

2690	$y^{''} + 2 y^{'} + y = {\begin{array}{cc} \sin (2 t) & 0 \leq t < \frac{π}{2} \\ 0 & \frac{π}{2} \leq t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.521

2691	$y^{''} + y^{'} + 7 y = {\begin{array}{cc} t & 0 \leq t < 2 \\ 0 & 2 \leq t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	11.885

2692	$y^{''} + y = {\begin{array}{cc} t^{2} & 0 \leq t < 1 \\ 0 & 1 \leq t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.259

2693	$y^{''} - 2 y^{'} + y = {\begin{array}{cc} 0 & 0 \leq t < 1 \\ t & 1 \leq t < 2 \\ 0 & 2 \leq t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.754

2694	$y^{''} + 4 y^{'} + 5 y = δ (t - 1)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.160

2695	$y^{''} + 4 y = \sin (t) + δ (t - π)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.874

2696	$y^{''} + y^{'} + y = 2 δ (t - 1) - δ (t - 2)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	4.052

2697	$y^{''} + 2 y^{'} + y = e^{- t} + 3 δ (- 3 + t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.887

2698	$[\begin{matrix} x^{'} = 6 x - 3 y \\ y^{'} = 2 x + y \end{matrix}]$	system_of_ODEs	✓	0.341

2699	$[\begin{matrix} x^{'} = - 2 x + y + t \\ y^{'} = - 4 x + 3 y - 1 \end{matrix}]$	system_of_ODEs	✓	0.581

2700	$[\begin{matrix} x^{'} = 6 x - 3 y \\ y^{'} = 2 x + y \end{matrix}]$	system_of_ODEs	✓	0.422

2.2.27 Problems 2601 to 2700