Problems 7301 to 7400

Table 2.149: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

7301	$y^{''} + 3 x y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.349

7302	$(- x^{2} + 1) y^{''} - 2 x y^{'} + 30 y = 0$ i.c.	[_Gegenbauer]	✓	0.385

7303	$(- 2 + x) y^{'} = x y$ i.c.	[_separable]	✓	0.487

7304	${(- 2 + x)}^{2} y^{''} + (x + 2) y^{'} - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.421

7305	$x y^{''} + 2 y^{'} + x y = 0$	[_Lienard]	✓	0.597

7306	$x y^{''} + y = 0$	[[_Emden, _Fowler]]	✓	1.071

7307	$x y^{''} + (2 x + 1) y^{'} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.655

7308	$x y^{''} + 2 x^{3} y^{'} + (x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.330

7309	$y^{''} + (- 1 + x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.360

7310	$x y^{''} + y^{'} + x y = 0$	[_Lienard]	✓	0.422

7311	$2 x (- 1 + x) y^{''} - (x + 1) y^{'} + y = 0$	[_Jacobi]	✓	0.707

7312	$x y^{''} + 2 y^{'} + 4 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.601

7313	$x y^{''} + (2 - 2 x) y^{'} + (- 2 + x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.688

7314	$x^{2} y^{''} + 6 x y^{'} + (4 x^{2} + 6) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.691

7315	$x y^{''} + (1 - 2 x) y^{'} + (- 1 + x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.586

7316	$2 x (1 - x) y^{''} - (1 + 6 x) y^{'} - 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.730

7317	$x (1 - x) y^{''} + (\frac{1}{2} + 2 x) y^{'} - 2 y = 0$	[_Jacobi]	✓	0.770

7318	$4 x y^{''} + y^{'} + 8 y = 0$	[[_Emden, _Fowler]]	✓	0.691

7319	$4 (t^{2} - 3 t + 2) y^{''} - 2 y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.583

7320	$2 (t^{2} - 5 t + 6) y^{''} + (2 t - 3) y^{'} - 8 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.477

7321	$3 t (t + 1) y^{''} + t y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.326

7322	$x^{2} y^{''} + x y^{'} + (x^{2} - \frac{4}{49}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.634

7323	$x y^{''} + y^{'} + \frac{y}{4} = 0$	[[_Emden, _Fowler]]	✓	0.498

7324	$y^{''} + (e^{- 2 x} - \frac{1}{9}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.720

7325	$x^{2} y^{''} + \frac{(x + \frac{3}{4}) y}{4} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.700

7326	$x^{2} y^{''} + x y^{'} + \frac{(x^{2} - 1) y}{4} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.671

7327	${(2 x + 1)}^{2} y^{''} + 2 (2 x + 1) y^{'} + 16 x (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.483

7328	$x^{2} y^{''} + x y^{'} + (x^{2} - 6) y = 0$	[_Bessel]	✓	0.656

7329	$x y^{''} + 5 y^{'} + x y = 0$	[_Lienard]	✓	1.163

7330	$9 x^{2} y^{''} + 9 x y^{'} + (36 x^{4} - 16) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.562

7331	$y^{''} + x y = 0$	[[_Emden, _Fowler]]	✓	0.225

7332	$4 x y^{''} + 4 y^{'} + y = 0$	[[_Emden, _Fowler]]	✓	0.516

7333	$x y^{''} + y^{'} + 36 y = 0$	[[_Emden, _Fowler]]	✓	0.516

7334	$y^{''} + k^{2} x^{2} y = 0$	[[_Emden, _Fowler]]	✓	0.295

7335	$y^{''} + k^{2} x^{4} y = 0$	[[_Emden, _Fowler]]	✓	0.292

7336	$x y^{''} - 5 y^{'} + x y = 0$	[_Lienard]	✓	1.102

7337	$y^{''} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓	0.389

7338	$x y^{''} + (1 - 2 x) y^{'} + (- 1 + x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.628

7339	${(- 1 + x)}^{2} y^{''} - (- 1 + x) y^{'} - 35 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.415

7340	$16 {(x + 1)}^{2} y^{''} + 3 y = 0$	[[_Emden, _Fowler]]	✓	0.389

7341	$x^{2} y^{''} + x y^{'} + (x^{2} - 5) y = 0$	[_Bessel]	✓	0.682

7342	$x^{2} y^{''} + 2 x^{3} y^{'} + (x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.690

7343	$x y^{''} - (x + 1) y^{'} + y = 0$	[_Laguerre]	✓	0.646

7344	$x y^{''} + 3 y^{'} + 4 x^{3} y = 0$	[[_Emden, _Fowler]]	✓	0.491

7345	$y^{''} + \frac{y}{4 x} = 0$	[[_Emden, _Fowler]]	✓	1.048

7346	$x y^{''} + y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.404

7347	$y^{'} + \frac{26 y}{5} = \frac{97 \sin (2 t)}{5}$ i.c.	[[_linear, ‘class A‘]]	✓	0.535

7348	$y^{'} + 2 y = 0$ i.c.	[_quadrature]	✓	0.333

7349	$y^{''} - y^{'} - 6 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.293

7350	$y^{''} + 9 y = 10 e^{- t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.312

7351	$y^{''} - \frac{y}{4} = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.251

7352	$y^{''} - 6 y^{'} + 5 y = 29 \cos (2 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.394

7353	$y^{''} + 7 y^{'} + 12 y = 21 e^{3 t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.339

7354	$y^{''} - 4 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.294

7355	$y^{''} - 4 y^{'} + 3 y = 6 t - 8$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.322

7356	$y^{''} + \frac{y}{25} = \frac{t^{2}}{50}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.189

7357	$y^{''} + 3 y^{'} + \frac{9 y}{4} = 9 t^{3} + 64$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.339

7358	$y^{''} - 2 y^{'} - 3 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.453

7359	$y^{'} - 6 y = 0$ i.c.	[_quadrature]	✓	0.429

7360	$y^{''} + 2 y^{'} + 5 y = 50 t - 100$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.492

7361	$y^{''} + 3 y^{'} - 4 y = 6 e^{2 t - 3}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.401

7362	$9 y^{''} - 6 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.196

7363	$y^{''} + 6 y^{'} + 8 y = e^{- 3 t} - e^{- 5 t}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.335

7364	$y^{''} + 10 y^{'} + 24 y = 144 t^{2}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.196

7365	$y^{''} + 9 y = {\begin{array}{cc} 8 \sin (t) & 0 < t < π \\ 0 & π < t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.960

7366	$y^{''} + 3 y^{'} + 2 y = {\begin{array}{cc} 4 t & 0 < t < 1 \\ 8 & 1 < t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	12.877

7367	$y^{''} + y^{'} - 2 y = {\begin{array}{cc} 3 \sin (t) - \cos (t) & 0 < t < 2 π \\ 3 \sin (2 t) - \cos (2 t) & 2 π < t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.559

7368	$y^{''} + 3 y^{'} + 2 y = {\begin{array}{cc} 1 & 0 < t < 1 \\ 0 & 1 < t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.072

7369	$y^{''} + y = {\begin{array}{cc} t & 0 < t < 1 \\ 0 & 1 < t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.966

7370	$y^{''} + 2 y^{'} + 5 y = {\begin{array}{cc} 10 \sin (t) & 0 < t < 2 π \\ 0 & 2 π < t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	4.152

7371	$y^{''} + 4 y = {\begin{array}{cc} 8 t^{2} & 0 < t < 5 \\ 0 & 5 < t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.901

7372	$y^{''} + 4 y = δ (t - π)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.739

7373	$y^{''} + 16 y = 4 δ (t - 3 π)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.780

7374	$y^{''} + y = δ (t - π) - δ (t - 2 π)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.743

7375	$y^{''} + 4 y^{'} + 5 y = δ (t - 1)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.203

7376	$4 y^{''} + 24 y^{'} + 37 y = 17 e^{- t} + δ (t - \frac{1}{2})$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.408

7377	$y^{''} + 3 y^{'} + 2 y = 10 \sin (t) + 10 δ (t - 1)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.963

7378	$y^{''} + 4 y^{'} + 5 y = (1 - Heaviside (t - 10)) e^{t} - e^{10} δ (t - 10)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.947

7379	$y^{''} + 5 y^{'} + 6 y = δ (t - \frac{π}{2}) + \cos (t) Heaviside (t - π)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.555

7380	$y^{''} + 5 y^{'} + 6 y = Heaviside (t - 1) + δ (t - 2)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.240

7381	$y^{''} + 2 y^{'} + 5 y = 25 t - 100 δ (t - π)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.928

7382	$y^{'} = \frac{x^{2}}{y}$	[_separable]	✓	2.125

7383	$y^{'} = \frac{x^{2}}{y (x^{3} + 1)}$	[_separable]	✓	1.873

7384	$y^{'} = y \sin (x)$	[_separable]	✓	1.938

7385	$x y^{'} = \sqrt{1 - y^{2}}$	[_separable]	✓	6.479

7386	$y^{'} = \frac{x^{2}}{1 + y^{2}}$	[_separable]	✓	1.295

7387	$x y y^{'} = \sqrt{1 + y^{2}}$	[_separable]	✓	6.459

7388	$(x^{2} - 1) y^{'} + 2 x y^{2} = 0$ i.c.	[_separable]	✓	2.224

7389	$y^{'} = 3 y^{2 / 3}$ i.c.	[_quadrature]	✓	2.096

7390	$x y^{'} + y = y^{2}$ i.c.	[_separable]	✓	2.645

7391	$2 x^{2} y y^{'} + y^{2} = 2$	[_separable]	✓	2.715

7392	$y^{'} - x y^{2} = 2 x y$	[_separable]	✓	2.451

7393	$(1 + z^{'}) e^{- z} = 1$	[_quadrature]	✓	1.851

7394	$y^{'} = \frac{3 x^{2} + 4 x + 2}{2 y - 2}$ i.c.	[_separable]	✓	2.398

7395	$e^{x} - (e^{x} + 1) y y^{'} = 0$ i.c.	[_separable]	✓	3.591

7396	$\frac{y}{- 1 + x} + \frac{x y^{'}}{y + 1} = 0$	[_separable]	✓	2.862

7397	$x + 2 x^{3} + (y + 2 y^{3}) y^{'} = 0$	[_separable]	✓	2.790

7398	$\frac{1}{\sqrt{x}} + \frac{y^{'}}{\sqrt{y}} = 0$	[_separable]	✓	12.070

7399	$\frac{1}{\sqrt{- x^{2} + 1}} + \frac{y^{'}}{\sqrt{1 - y^{2}}} = 0$	[_separable]	✓	41.108

7400	$2 x \sqrt{1 - y^{2}} + y y^{'} = 0$	[_separable]	✓	2.153

2.2.74 Problems 7301 to 7400