Problems 2301 to 2400

Table 2.49: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

2301	$\frac{2 t y}{t^{2} + 1} + y^{'} = \frac{1}{t^{2} + 1}$	[_linear]	✓	1.061

2302	$y + y^{'} = e^{t} t$	[[_linear, ‘class A‘]]	✓	1.227

2303	$t^{2} y + y^{'} = 1$	[_linear]	✓	1.229

2304	$t^{2} y + y^{'} = t^{2}$	[_separable]	✓	1.268

2305	$\frac{t y}{t^{2} + 1} + y^{'} = 1 - \frac{t^{3} y}{t^{4} + 1}$	[_linear]	✓	1.957

2306	$\sqrt{t^{2} + 1} y + y^{'} = 0$ i.c.	[_separable]	✓	3.528

2307	$\sqrt{t^{2} + 1} y e^{- t} + y^{'} = 0$	[_separable]	✓	1.574

2308	$y^{'} - 2 t y = t$ i.c.	[_separable]	✓	1.415

2309	$t y + y^{'} = 1 + t$ i.c.	[_linear]	✓	1.596

2310	$y + y^{'} = \frac{1}{t^{2} + 1}$ i.c.	[_linear]	✓	1.913

2311	$y^{'} - 2 t y = 1$ i.c.	[_linear]	✓	1.361

2312	$t y + (t^{2} + 1) y^{'} = {(t^{2} + 1)}^{5 / 2}$	[_linear]	✓	1.970

2313	$4 t y + (t^{2} + 1) y^{'} = t$ i.c.	[_separable]	✓	1.684

2314	$\frac{y}{t} + y^{'} = \frac{1}{t^{2}}$	[_linear]	✓	0.160

2315	$y^{'} + \frac{y}{\sqrt{t}} = e^{\frac{\sqrt{t}}{2}}$	[_linear]	✓	0.290

2316	$\frac{y}{t} + y^{'} = \cos (t) + \frac{\sin (t)}{t}$	[_linear]	✓	0.247

2317	$\tan (t) y + y^{'} = \cos (t) \sin (t)$	[_linear]	✓	0.271

2318	$(t^{2} + 1) y^{'} = 1 + y^{2}$	[_separable]	✓	1.800

2319	$y^{'} = (1 + t) (1 + y)$	[_separable]	✓	1.177

2320	$y^{'} = 1 - t + y^{2} - t y^{2}$	[_separable]	✓	2.377

2321	$y^{'} = e^{3 + t + y}$	[_separable]	✓	2.265

2322	$\cos (y) \sin (t) y^{'} = \cos (t) \sin (y)$	[_separable]	✓	2.808

2323	$t^{2} (1 + y^{2}) + 2 y y^{'} = 0$ i.c.	[_separable]	✓	2.631

2324	$y^{'} = \frac{2 t}{y + t^{2} y}$ i.c.	[_separable]	✓	2.132

2325	$\sqrt{t^{2} + 1} y^{'} = \frac{t y^{3}}{\sqrt{t^{2} + 1}}$ i.c.	[_separable]	✓	3.330

2326	$y^{'} = \frac{3 t^{2} + 4 t + 2}{- 2 + 2 y}$ i.c.	[_separable]	✓	2.059

2327	$\cos (y) y^{'} = - \frac{t \sin (y)}{t^{2} + 1}$ i.c.	[_separable]	✓	2.868

2328	$y^{'} = k (a - y) (b - y)$ i.c.	[_quadrature]	✓	6.723

2329	$3 y^{'} t = \cos (t) y$ i.c.	[_separable]	✓	2.969

2330	$y^{'} t = y + \sqrt{t^{2} + y^{2}}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	4.123

2331	$2 t y y^{'} = 3 y^{2} - t^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	46.920

2332	$(t - \sqrt{t y}) y^{'} = y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	47.203

2333	$y^{'} = \frac{t + y}{t - y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.607

2334	$e^{\frac{t}{y}} (y - t) y^{'} + y (1 + e^{\frac{t}{y}}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	4.776

2335	$y^{'} = \frac{t + y + 1}{t - y + 3}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.413

2336	$1 + t - 2 y + (4 t - 3 y - 6) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.343

2337	$t + 2 y + 3 + (2 t + 4 y - 1) y^{'} = 0$	[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.996

2338	$2 t \sin (y) + e^{t} y^{3} + (t^{2} \cos (y) + 3 e^{t} y^{2}) y^{'} = 0$	[_exact]	✓	3.490

2339	$1 + e^{t y} (1 + t y) + (1 + e^{t y} t^{2}) y^{'} = 0$	[_exact]	✓	2.021

2340	$\sec (t) \tan (t) + \sec {(t)}^{2} y + (\tan (t) + 2 y) y^{'} = 0$	[_exact, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	13.389

2341	$\frac{y^{2}}{2} - 2 e^{t} y + (- e^{t} + y) y^{'} = 0$	[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.659

2342	$2 t y^{3} + 3 t^{2} y^{2} y^{'} = 0$ i.c.	[_separable]	✓	2.269

2343	$2 t \cos (y) + 3 t^{2} y + (t^{3} - t^{2} \sin (y) - y) y^{'} = 0$ i.c.	[_exact]	✓	2.919

2344	$3 t^{2} + 4 t y + (2 t^{2} + 2 y) y^{'} = 0$ i.c.	[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.786

2345	$2 t - 2 e^{t y} \sin (2 t) + e^{t y} \cos (2 t) y + (- 3 + e^{t y} t \cos (2 t)) y^{'} = 0$ i.c.	[_exact]	✓	40.250

2346	$3 t y + y^{2} + (t^{2} + t y) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	4.362

2347	$y^{'} = y^{2} + \cos (t^{2})$ i.c.	[_Riccati]	✗	3.051

2348	$y^{'} = 1 + y + y^{2} \cos (t)$ i.c.	[_Riccati]	✗	12.490

2349	$y^{'} = t + y^{2}$ i.c.	[[_Riccati, _special]]	✓	16.256

2350	$y^{'} = e^{- t^{2}} + y^{2}$ i.c.	[_Riccati]	✗	1.921

2351	$y^{'} = e^{- t^{2}} + y^{2}$ i.c.	[_Riccati]	✗	2.036

2352	$y^{'} = e^{- t^{2}} + y^{2}$ i.c.	[_Riccati]	✗	1.921

2353	$y^{'} = y + e^{- y} + e^{- t}$ i.c.	[‘y=_G(x,y’)‘]	✗	1.676

2354	$y^{'} = y^{3} + e^{- 5 t}$ i.c.	[_Abel]	✗	1.211

2355	$y^{'} = e^{{(y - t)}^{2}}$ i.c.	[[_homogeneous, ‘class C‘], _dAlembert]	✓	2.170

2356	$y^{'} = (4 y + e^{- t^{2}}) e^{2 y}$ i.c.	[‘y=_G(x,y’)‘]	✗	1.794

2357	$y^{'} = e^{- t} + \ln (1 + y^{2})$ i.c.	[‘y=_G(x,y’)‘]	✗	2.006

2358	$y^{'} = \frac{(1 + \cos (4 t)) y}{4} - \frac{(1 - \cos (4 t)) y^{2}}{800}$ i.c.	[_Bernoulli]	✓	5.398

2359	$y^{'} = t^{2} + y^{2}$ i.c.	[[_Riccati, _special]]	✓	2.401

2360	$y^{'} = t (1 + y)$ i.c.	[_separable]	✓	1.288

2361	$y^{'} = t \sqrt{1 - y^{2}}$ i.c.	[_separable]	✓	5.384

2362	$2 t^{2} y^{''} + 3 y^{'} t - y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.357

2363	$y^{''} + y^{'} t + y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.838

2364	$y^{''} - y = 0$	[[_2nd_order, _missing_x]]	✓	1.550

2365	$6 y^{''} - 7 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.341

2366	$y^{''} - 3 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.423

2367	$3 y^{''} + 6 y^{'} + 3 y = 0$	[[_2nd_order, _missing_x]]	✓	0.359

2368	$y^{''} - 3 y^{'} - 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.556

2369	$2 y^{''} + y^{'} - 10 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.568

2370	$5 y^{''} + 5 y^{'} - y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.712

2371	$y^{''} - 6 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.736

2372	$y^{''} + 5 y^{'} + 6 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.399

2373	$t^{2} y^{''} + α t y^{'} + β y = 0$	[[_Emden, _Fowler]]	✓	1.501

2374	$t^{2} y^{''} + 5 y^{'} t - 5 y = 0$	[[_Emden, _Fowler]]	✓	0.844

2375	$t^{2} y^{''} - y^{'} t - 2 y = 0$ i.c.	[[_Emden, _Fowler]]	✓	1.701

2376	$y^{''} + 2 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.870

2377	$y^{''} + y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.594

2378	$2 y^{''} + 3 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓	0.572

2379	$y^{''} + 2 y^{'} + 3 y = 0$	[[_2nd_order, _missing_x]]	✓	0.569

2380	$4 y^{''} - y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.566

2381	$y^{''} + y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.845

2382	$y^{''} + 2 y^{'} + 5 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.695

2383	$2 y^{''} - y^{'} + 3 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.051

2384	$3 y^{''} - 2 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.067

2385	$t^{2} y^{''} + y^{'} t + y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.922

2386	$t^{2} y^{''} + 2 y^{'} t + 2 y = 0$	[[_Emden, _Fowler]]	✓	1.101

2387	$y^{''} - 6 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	0.360

2388	$4 y^{''} - 12 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	0.395

2389	$9 y^{''} + 6 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.646

2390	$4 y^{''} - 4 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.606

2391	$y^{''} + 2 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.683

2392	$9 y^{''} - 12 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.669

2393	$y^{''} - \frac{2 (1 + t) y^{'}}{t^{2} + 2 t - 1} + \frac{2 y}{t^{2} + 2 t - 1} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.933

2394	$y^{''} - 4 y^{'} t + (4 t^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.477

2395	$(- t^{2} + 1) y^{''} - 2 y^{'} t + 2 y = 0$	[_Gegenbauer]	✓	0.995

2396	$(t^{2} + 1) y^{''} - 2 y^{'} t + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.912

2397	$(- t^{2} + 1) y^{''} - 2 y^{'} t + 6 y = 0$	[_Gegenbauer]	✓	0.572

2398	$(2 t + 1) y^{''} - 4 (1 + t) y^{'} + 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.683

2399	$t^{2} y^{''} + y^{'} t + (t^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.666

2400	$t^{2} y^{''} + 3 y^{'} t + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.055

2.2.24 Problems 2301 to 2400