Problems 16301 to 16400

Table 2.329: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

16301	$3 y^{'''} - 4 y^{''} - 5 y^{'} + 2 y = 0$	[[_3rd_order, _missing_x]]	✓	0.081

16302	$6 y^{'''} - 5 y^{''} - 2 y^{'} + y = 0$	[[_3rd_order, _missing_x]]	✓	0.076

16303	$y^{'''} - 5 y^{'} + 2 y = 0$	[[_3rd_order, _missing_x]]	✓	0.075

16304	$5 y^{'''} - 15 y^{'} + 11 y = 0$	[[_3rd_order, _missing_x]]	✓	0.138

16305	$y^{''''} + y^{'''} = 0$	[[_high_order, _missing_x]]	✓	0.078

16306	$y^{''''} - 9 y^{''} = 0$	[[_high_order, _missing_x]]	✓	0.078

16307	$y^{''''} - 16 y = 0$	[[_high_order, _missing_x]]	✓	0.095

16308	$y^{''''} - 6 y^{'''} - y^{''} + 54 y^{'} - 72 y = 0$	[[_high_order, _missing_x]]	✓	0.080

16309	$y^{''''} + 7 y^{'''} + 6 y^{''} - 32 y^{'} - 32 y = 0$	[[_high_order, _missing_x]]	✓	0.089

16310	$y^{''''} + 2 y^{'''} - 2 y^{''} + 8 y = 0$	[[_high_order, _missing_x]]	✓	0.092

16311	$y^{(5)} + 4 y^{''''} = 0$	[[_high_order, _missing_x]]	✓	0.081

16312	$y^{(5)} + 4 y^{'''} = 0$	[[_high_order, _missing_x]]	✓	0.076

16313	$y^{(5)} + 3 y^{''''} + 3 y^{'''} + y^{''} = 0$	[[_high_order, _missing_x]]	✓	0.083

16314	$y^{''''} + 2 y^{''} + y = 0$	[[_high_order, _missing_x]]	✓	0.094

16315	$y^{''''} + 8 y^{''} + 16 y = 0$	[[_high_order, _missing_x]]	✓	0.100

16316	$y^{(6)} + 3 y^{''''} + 3 y^{''} + y = 0$	[[_high_order, _missing_x]]	✓	0.094

16317	$y^{(6)} + 12 y^{''''} + 48 y^{''} + 64 y = 0$	[[_high_order, _missing_x]]	✓	0.093

16318	$y^{'''} - 2 y^{''} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.129

16319	$y^{'''} - y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.156

16320	$y^{''''} + 16 y^{'''} = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.132

16321	$y^{''''} - 8 y^{''} + 16 y = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.133

16322	$24 y^{'''} - 26 y^{''} + 9 y^{'} - y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.135

16323	$y^{''''} - 5 y^{''} + 4 y = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.144

16324	$y^{''''} - 16 y = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.100

16325	$8 y^{(5)} + 4 y^{''''} + 66 y^{'''} - 41 y^{''} - 37 y^{'} = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.121

16326	$2 y^{(5)} + 7 y^{''''} + 17 y^{'''} + 17 y^{''} + 5 y^{'} = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.121

16327	$y^{(5)} + 8 y^{''''} = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.162

16328	$y^{(6)} - 3 y^{''''} + 3 y^{''} - y = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.145

16329	$y^{'''} + 9 y^{''} + 16 y^{'} - 26 y = 0$	[[_3rd_order, _missing_x]]	✓	0.081

16330	$y^{''''} + 12 y^{'''} + 60 y^{''} + 124 y^{'} + 75 y = 0$	[[_high_order, _missing_x]]	✓	0.092

16331	$y^{'''} + 3 y^{''} + 2 y^{'} + 6 y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.150

16332	$y^{''''} - 8 y^{'''} + 30 y^{''} - 56 y^{'} + 49 y = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.156

16333	$\frac{31 y^{'''}}{100} + \frac{56 y^{''}}{5} - \frac{49 y^{'}}{5} + \frac{53 y}{10} = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	0.547

16334	$2 y y^{''} + y^{2} = {y^{'}}^{2}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]	✓	3.296

16335	$y^{'''} + y^{''} = e^{t}$	[[_3rd_order, _missing_y]]	✓	0.124

16336	$y^{''''} - 16 y = 1$	[[_high_order, _missing_x]]	✓	0.129

16337	$y^{(5)} - y^{''''} = 1$	[[_high_order, _missing_x]]	✓	0.129

16338	$y^{''''} + 9 y^{''} = 1$	[[_high_order, _missing_x]]	✓	0.124

16339	$y^{''''} + 9 y^{''} = 9 e^{3 t}$	[[_high_order, _missing_y]]	✓	0.148

16340	$y^{'''} + 10 y^{''} + 34 y^{'} + 40 y = t e^{- 4 t} + 2 e^{- 3 t} \cos (t)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.862

16341	$y^{'''} + 6 y^{''} + 11 y^{'} + 6 y = 2 e^{- 3 t} - t e^{- t}$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.220

16342	$y^{''''} - 6 y^{'''} + 13 y^{''} - 24 y^{'} + 36 y = 108 t$	[[_high_order, _with_linear_symmetries]]	✓	0.160

16343	$y^{'''} + 6 y^{''} - 14 y^{'} - 104 y = - 111 e^{t}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.161

16344	$y^{''''} - 10 y^{'''} + 38 y^{''} - 64 y^{'} + 40 y = 153 e^{- t}$	[[_high_order, _with_linear_symmetries]]	✓	0.186

16345	$y^{'''} + 4 y^{'} = \tan (2 t)$	[[_3rd_order, _missing_y]]	✓	0.766

16346	$y^{'''} + 4 y^{'} = \sec (2 t) \tan (2 t)$	[[_3rd_order, _missing_y]]	✓	0.696

16347	$y^{''''} + 4 y^{''} = \sec {(2 t)}^{2}$	[[_high_order, _missing_y]]	✓	0.946

16348	$y^{''''} + 4 y^{''} = \tan {(2 t)}^{2}$	[[_high_order, _missing_y]]	✓	0.950

16349	$y^{'''} + 9 y^{'} = \sec (3 t)$	[[_3rd_order, _missing_y]]	✓	1.131

16350	$y^{'''} + y^{'} = - \sec (t) \tan (t)$	[[_3rd_order, _missing_y]]	✓	0.706

16351	$y^{'''} + 4 y^{'} = \sec (2 t)$	[[_3rd_order, _missing_y]]	✓	0.685

16352	$y^{'''} - 2 y^{''} = - \frac{1}{t^{2}} - \frac{2}{t}$	[[_3rd_order, _missing_y]]	✓	0.279

16353	$y^{'''} - 3 y^{''} + 3 y^{'} - y = \frac{e^{t}}{t}$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.257

16354	$y^{'''} - 4 y^{''} - 11 y^{'} + 30 y = e^{4 t}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.155

16355	$y^{'''} + 3 y^{''} - 10 y^{'} - 24 y = e^{- 3 t}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.127

16356	$y^{'''} - 13 y^{'} + 12 y = \cos (t)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.167

16357	$y^{'''} + 3 y^{''} + 2 y^{'} = \cos (t)$	[[_3rd_order, _missing_y]]	✓	0.156

16358	$y^{(6)} + y^{''''} = - 24$	[[_high_order, _missing_x]]	✓	0.136

16359	$y^{''''} + y^{''} = \tan {(t)}^{2}$	[[_high_order, _missing_y]]	✓	0.798

16360	$y^{'''} - y^{''} = 3 t^{2}$ i.c.	[[_3rd_order, _missing_y]]	✓	0.182

16361	$y^{''''} + y^{''} = \sec {(t)}^{2}$ i.c.	[[_high_order, _missing_y]]	✓	0.853

16362	$y^{'''} + y^{'} = \sec (t)$ i.c.	[[_3rd_order, _missing_y]]	✓	0.642

16363	$y^{''''} + y^{''} = \cos (t)$ i.c.	[[_high_order, _missing_y]]	✓	0.636

16364	$y^{''''} + y^{''} = t$ i.c.	[[_high_order, _missing_y]]	✓	0.146

16365	$t^{2} \ln (t) y^{'''} - t y^{''} + y^{'} = 1$	[[_3rd_order, _missing_y]]	✓	0.959

16366	$(t^{2} + t) y^{'''} + (- t^{2} + 2) y^{''} - (t + 2) y^{'} = - 2 - t$	[[_3rd_order, _missing_y]]	✓	1.045

16367	$2 t^{3} y^{'''} + t^{2} y^{''} + y^{'} t - y = - 3 t^{2}$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓	0.385

16368	$t y^{''''} + 2 y^{'''} = \frac{45}{8 t^{7 / 2}}$ i.c.	[[_high_order, _missing_y]]	✓	0.248

16369	$4 x^{2} y^{''} - 8 y^{'} x + 5 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.947

16370	$3 x^{2} y^{''} - 4 y^{'} x + 2 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.891

16371	$2 x^{2} y^{''} - 8 y^{'} x + 8 y = 0$	[[_Emden, _Fowler]]	✓	0.978

16372	$2 x^{2} y^{''} - 7 y^{'} x + 7 y = 0$	[[_Emden, _Fowler]]	✓	1.083

16373	$4 x^{2} y^{''} + 17 y = 0$	[[_Emden, _Fowler]]	✓	0.538

16374	$9 x^{2} y^{''} - 9 y^{'} x + 10 y = 0$	[[_Emden, _Fowler]]	✓	1.001

16375	$2 x^{2} y^{''} - 2 y^{'} x + 20 y = 0$	[[_Emden, _Fowler]]	✓	0.983

16376	$x^{2} y^{''} - 5 y^{'} x + 10 y = 0$	[[_Emden, _Fowler]]	✓	1.002

16377	$4 x^{2} y^{''} + 8 y^{'} x + y = 0$	[[_Emden, _Fowler]]	✓	0.874

16378	$4 x^{2} y^{''} + y = 0$	[[_Emden, _Fowler]]	✓	0.354

16379	$x^{2} y^{''} - 5 y^{'} x + 9 y = 0$	[[_Emden, _Fowler]]	✓	0.882

16380	$x^{2} y^{''} + 7 y^{'} x + 9 y = 0$	[[_Emden, _Fowler]]	✓	0.899

16381	$x^{3} y^{'''} + 22 x^{2} y^{''} + 124 y^{'} x + 140 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓	0.147

16382	$x^{3} y^{'''} - 4 x^{2} y^{''} - 46 y^{'} x + 100 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓	0.141

16383	$x^{3} y^{'''} + 2 x^{2} y^{''} - 4 y^{'} x + 4 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓	0.146

16384	$x^{3} y^{'''} + 4 x^{2} y^{''} + 6 y^{'} x + 4 y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓	0.157

16385	$x^{3} y^{'''} + 2 y^{'} x - 2 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓	0.139

16386	$x^{3} y^{'''} + 3 x^{2} y^{''} - 2 y^{'} x - 2 y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓	0.142

16387	$x^{3} y^{'''} + 6 x^{2} y^{''} + 7 y^{'} x + y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓	0.137

16388	$x^{3} y^{''''} + 6 x^{2} y^{'''} + 7 x y^{''} + y^{'} = 0$	[[_high_order, _missing_y]]	✓	0.281

16389	$x^{2} y^{''} + 5 y^{'} x + 4 y = \frac{1}{x^{5}}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.354

16390	$x^{2} y^{''} - 5 y^{'} x + 9 y = x^{3}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.580

16391	$x^{2} y^{''} + y^{'} x + y = \frac{1}{x^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.608

16392	$x^{2} y^{''} + y^{'} x + 4 y = \frac{1}{x^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.714

16393	$x^{2} y^{''} + 2 y^{'} x - 6 y = 2 x$	[[_2nd_order, _with_linear_symmetries]]	✓	0.911

16394	$x^{2} y^{''} + y^{'} x - 16 y = \ln (x)$	[[_2nd_order, _with_linear_symmetries]]	✓	1.652

16395	$x^{2} y^{''} + y^{'} x + 4 y = 8$	[[_2nd_order, _with_linear_symmetries]]	✓	1.345

16396	$x^{2} y^{''} + y^{'} x + 36 y = x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.512

16397	$x^{3} y^{'''} + 3 x^{2} y^{''} - 11 y^{'} x + 16 y = \frac{1}{x^{3}}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.371

16398	$x^{3} y^{'''} + 16 x^{2} y^{''} + 70 y^{'} x + 80 y = \frac{1}{x^{13}}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.289

16399	$3 x^{2} y^{''} - 4 y^{'} x + 2 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.628

16400	$2 x^{2} y^{''} - 7 y^{'} x + 7 y = 0$ i.c.	[[_Emden, _Fowler]]	✓	1.905

2.2.164 Problems 16301 to 16400