Problems 2401 to 2500

Table 2.51: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	Maple	Mma	Sympy

2401	$t^{2} y^{''} - y^{'} t + y = 0$	[[_Emden, _Fowler]]	✓	✓	✓	✓

2402	$y^{''} + y = \sec (t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

2403	$y^{''} - 4 y^{'} + 4 y = e^{2 t} t$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

2404	$2 y^{''} - 3 y^{'} + y = (t^{2} + 1) e^{t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

2405	$y^{''} - 3 y^{'} + 2 y = t e^{3 t} + 1$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

2406	$3 y^{''} + 4 y^{'} + y = \sin (t) e^{- t}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

2407	$y^{''} + 4 y^{'} + 4 y = t^{5 / 2} e^{- 2 t}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

2408	$y^{''} - 3 y^{'} + 2 y = \sqrt{1 + t}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

2409	$y^{''} - y = f (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

2410	$y^{''} + \frac{t^{2} y}{4} = f \cos (t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✗

2411	$y^{''} - \frac{2 t y^{'}}{t^{2} + 1} + \frac{2 y}{t^{2} + 1} = t^{2} + 1$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

2412	$m y^{''} + c y^{'} + k y = F_{0} \cos (ω t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

2413	$y^{''} + y^{'} t + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✓

2414	$y^{''} - t y = 0$	[[_Emden, _Fowler]]	✓	✓	✓	✓

2415	$(t^{2} + 2) y^{''} - y^{'} t - 3 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✓

2416	$y^{''} - t^{3} y = 0$	[[_Emden, _Fowler]]	✓	✓	✓	✓

2417	$t (2 - t) y^{''} - 6 (t - 1) y^{'} - 4 y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✓

2418	$y^{''} + t^{2} y = 0$ i.c.	[[_Emden, _Fowler]]	✓	✓	✓	✓

2419	$y^{''} - t^{3} y = 0$ i.c.	[[_Emden, _Fowler]]	✓	✓	✓	✓

2420	$y^{''} + (t^{2} + 2 t + 1) y^{'} - (4 + 4 t) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

2421	$y^{''} - 2 y^{'} t + λ y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

2422	$(- t^{2} + 1) y^{''} - 2 y^{'} t + α (α + 1) y = 0$	[_Gegenbauer]	✓	✓	✓	✓

2423	$(- t^{2} + 1) y^{''} - y^{'} t + α^{2} y = 0$	[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	✓	✓	✓

2424	$y^{''} + t^{3} y^{'} + 3 t^{2} y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✓

2425	$y^{''} + t^{3} y^{'} + 3 t^{2} y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✓

2426	$(1 - t) y^{''} + y^{'} t + y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✓

2427	$y^{''} + y^{'} + t y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

2428	$y^{''} + y^{'} t + e^{t} y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

2429	$y^{''} + y^{'} + e^{t} y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

2430	$y^{''} + y^{'} + e^{- t} y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

2431	$t^{2} y^{''} - 5 y^{'} t + 9 y = 0$	[[_Emden, _Fowler]]	✓	✓	✓	✓

2432	$t^{2} y^{''} + 5 y^{'} t - 5 y = 0$	[[_Emden, _Fowler]]	✓	✓	✓	✓

2433	$2 t^{2} y^{''} + 3 y^{'} t - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✓

2434	${(t - 1)}^{2} y^{''} - 2 (t - 1) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	✓	✓	✓

2435	$t^{2} y^{''} + 3 y^{'} t + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✓

2436	$t^{2} y^{''} - y^{'} t + y = 0$	[[_Emden, _Fowler]]	✓	✓	✓	✓

2437	${(t - 2)}^{2} y^{''} + 5 (t - 2) y^{'} + 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

2438	$t^{2} y^{''} + y^{'} t + y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	✓	✓	✓

2439	$t^{2} y^{''} - y^{'} t + 2 y = 0$ i.c.	[[_Emden, _Fowler]]	✓	✓	✓	✓

2440	$t^{2} y^{''} - 3 y^{'} t + 4 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	✓	✓	✓

2441	$t {(t - 2)}^{2} y^{''} + y^{'} t + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

2442	$t {(t - 2)}^{2} y^{''} + y^{'} t + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	✗	✓	✗

2443	$\sin (t) y^{''} + \cos (t) y^{'} + \frac{y}{t} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

2444	$(e^{t} - 1) y^{''} + e^{t} y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

2445	$(- t^{2} + 1) y^{''} + \frac{y^{'}}{\sin (1 + t)} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	✗	✓	✗

2446	$t^{3} y^{''} + \sin (t^{3}) y^{'} + t y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

2447	$2 t^{2} y^{''} + 3 y^{'} t - (1 + t) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

2448	$2 t y^{''} + (1 - 2 t) y^{'} - y = 0$	[_Laguerre]	✓	✓	✓	✓

2449	$2 t y^{''} + (1 + t) y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

2450	$2 t^{2} y^{''} - y^{'} t + (1 + t) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

2451	$4 t y^{''} + 3 y^{'} - 3 y = 0$	[[_Emden, _Fowler]]	✓	✓	✓	✓

2452	$2 t^{2} y^{''} + (t^{2} - t) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

2453	$t^{3} y^{''} - y^{'} t - (t^{2} + \frac{5}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	✗	✓	✗

2454	$t^{2} y^{''} + (- t^{2} + t) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

2455	$t y^{''} - (t^{2} + 2) y^{'} + t y = 0$	[_Lienard]	✓	✓	✓	✓

2456	$t^{2} y^{''} + (- t^{2} + 3 t) y^{'} - t y = 0$	[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	✓	✓	✓

2457	$t^{2} y^{''} + t (1 + t) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

2458	$t y^{''} - (t + 4) y^{'} + 2 y = 0$	[_Laguerre]	✓	✓	✓	✗

2459	$t^{2} y^{''} + (t^{2} - 3 t) y^{'} + 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

2460	$t^{2} y^{''} + y^{'} t - (1 + t) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

2461	$t y^{''} + y^{'} t + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

2462	$t y^{''} + (- t^{2} + 1) y^{'} + 4 t y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

2463	$t^{2} y^{''} + y^{'} t + t^{2} y = 0$	[_Lienard]	✓	✓	✓	✓

2464	$t^{2} y^{''} + y^{'} t + (t^{2} - v^{2}) y = 0$	[_Bessel]	✓	✓	✓	✗

2465	$t y^{''} + (1 - t) y^{'} + λ y = 0$	[_Laguerre]	✓	✓	✓	✓

2466	$2 \sin (t) y^{''} + (1 - t) y^{'} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

2467	$t^{2} y^{''} + y^{'} t + (1 + t) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

2468	$t y^{''} + y^{'} - 4 y = 0$	[[_Emden, _Fowler]]	✓	✓	✓	✓

2469	$t^{2} y^{''} - t (1 + t) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

2470	$t^{2} y^{''} + y^{'} t + (t^{2} - 1) y = 0$	[_Bessel]	✓	✓	✓	✓

2471	$t y^{''} + 3 y^{'} - 3 y = 0$	[[_Emden, _Fowler]]	✓	✓	✓	✓

2472	$\cos (t) y + y^{'} = 0$	[_separable]	✓	✓	✓	✓

2473	$\sqrt{t} \sin (t) y + y^{'} = 0$	[_separable]	✓	✓	✓	✓

2474	$\frac{2 t y}{t^{2} + 1} + y^{'} = \frac{1}{t^{2} + 1}$	[_linear]	✓	✓	✓	✓

2475	$y + y^{'} = e^{t} t$	[[_linear, ‘class A‘]]	✓	✓	✓	✓

2476	$t^{2} y + y^{'} = 1$	[_linear]	✓	✓	✓	✓

2477	$t^{2} y + y^{'} = t^{2}$	[_separable]	✓	✓	✓	✓

2478	$\frac{t y}{t^{2} + 1} + y^{'} = 1 - \frac{t^{3} y}{t^{4} + 1}$	[_linear]	✓	✓	✓	✗

2479	$\sqrt{t^{2} + 1} y + y^{'} = 0$ i.c.	[_separable]	✓	✓	✓	✓

2480	$\sqrt{t^{2} + 1} y e^{- t} + y^{'} = 0$ i.c.	[_separable]	✓	✓	✓	✓

2481	$\sqrt{t^{2} + 1} y e^{- t} + y^{'} = 0$ i.c.	[_separable]	✓	✓	✓	✓

2482	$y^{'} - 2 t y = t$ i.c.	[_separable]	✓	✓	✓	✓

2483	$t y + y^{'} = 1 + t$ i.c.	[_linear]	✓	✓	✓	✓

2484	$y + y^{'} = \frac{1}{t^{2} + 1}$ i.c.	[_linear]	✓	✓	✓	✓

2485	$y^{'} - 2 t y = 1$ i.c.	[_linear]	✓	✓	✓	✓

2486	$t y + (t^{2} + 1) y^{'} = {(t^{2} + 1)}^{5 / 2}$	[_linear]	✓	✓	✓	✓

2487	$4 t y + (t^{2} + 1) y^{'} = t$ i.c.	[_separable]	✓	✓	✓	✓

2488	$y + y^{'} = {\begin{array}{cc} 2 & 0 \leq t \leq 1 \\ 0 & 1 < t \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

2489	$(t^{2} + 1) y^{'} = 1 + y^{2}$	[_separable]	✓	✓	✓	✓

2490	$y^{'} = (1 + t) (1 + y)$	[_separable]	✓	✓	✓	✓

2491	$y^{'} = 1 - t + y^{2} - t y^{2}$	[_separable]	✓	✓	✓	✓

2492	$y^{'} = e^{3 + t + y}$	[_separable]	✓	✓	✓	✓

2493	$\cos (y) \sin (t) y^{'} = \cos (t) \sin (y)$	[_separable]	✓	✓	✓	✓

2494	$t^{2} (1 + y^{2}) + 2 y y^{'} = 0$ i.c.	[_separable]	✓	✓	✓	✓

2495	$y^{'} = \frac{2 t}{y + t^{2} y}$ i.c.	[_separable]	✓	✓	✓	✓

2496	$\sqrt{1 + y^{2}} y^{'} = \frac{t y^{3}}{\sqrt{t^{2} + 1}}$ i.c.	[_separable]	✓	✓	✗	✓

2497	$y^{'} = \frac{3 t^{2} + 4 t + 2}{- 2 + 2 y}$ i.c.	[_separable]	✓	✓	✓	✓

2498	$\cos (y) y^{'} = - \frac{t \sin (y)}{t^{2} + 1}$ i.c.	[_separable]	✓	✓	✓	✓

2499	$y^{'} = k (a - y) (b - y)$ i.c.	[_quadrature]	✓	✓	✓	✓

2500	$3 y^{'} t = \cos (t) y$ i.c.	[_separable]	✓	✓	✓	✓

2.2.25 Problems 2401 to 2500