Problems 13401 to 13500

Table 2.271: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

13401	$y^{''} + 4 y = 12 x^{2} - 16 x \cos (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.036

13402	$y^{''''} + 2 y^{'''} - 3 y^{''} = 18 x^{2} + 16 x e^{x} + 4 e^{3 x} - 9$	[[_high_order, _missing_y]]	✓	0.235

13403	$y^{''''} - 5 y^{'''} + 7 y^{''} - 5 y^{'} + 6 y = 5 \sin (x) - 12 \sin (2 x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	1.136

13404	$y^{''} - 4 y^{'} + 3 y = 9 x^{2} + 4$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.663

13405	$y^{''} + 5 y^{'} + 4 y = 16 x + 20 e^{x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.721

13406	$y^{''} - 8 y^{'} + 15 y = 9 x e^{2 x}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.658

13407	$y^{''} + 7 y^{'} + 10 y = 4 x e^{- 3 x}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.760

13408	$y^{''} + 8 y^{'} + 16 y = 8 e^{- 2 x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.848

13409	$y^{''} + 6 y^{'} + 9 y = 27 e^{- 6 x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.913

13410	$y^{''} + 4 y^{'} + 13 y = 18 e^{- 2 x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.941

13411	$y^{''} - 10 y^{'} + 29 y = 8 e^{5 x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.966

13412	$y^{''} - 4 y^{'} + 13 y = 8 \sin (3 x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.978

13413	$y^{''} - y^{'} - 6 y = 8 e^{2 x} - 5 e^{3 x}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.932

13414	$y^{''} - 2 y^{'} + y = 2 x e^{2 x} + 6 e^{x}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.931

13415	$y^{''} - y = 3 x^{2} e^{x}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.904

13416	$y^{''} + y = 3 x^{2} - 4 \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.010

13417	$y^{''} + 4 y = 8 \sin (2 x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.059

13418	$y^{'''} - 4 y^{''} + y^{'} + 6 y = 3 x e^{x} + 2 e^{x} - \sin (x)$ i.c.	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.349

13419	$y^{'''} - 6 y^{''} + 9 y^{'} - 4 y = 8 x^{2} + 3 - 6 e^{2 x}$ i.c.	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.244

13420	$y^{''} - 6 y^{'} + 8 y = x^{3} + x + e^{- 2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.570

13421	$y^{''} + 9 y = e^{3 x} + e^{- 3 x} + e^{3 x} \sin (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.779

13422	$y^{''} + 4 y^{'} + 5 y = e^{- 2 x} (\cos (x) + 1)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.719

13423	$y^{''} - 6 y^{'} + 9 y = x^{4} e^{x} + x^{3} e^{2 x} + x^{2} e^{3 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	67.351

13424	$y^{''} + 6 y^{'} + 13 y = x e^{- 3 x} \sin (2 x) + x^{2} e^{- 2 x} \sin (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	74.953

13425	$y^{'''} - 3 y^{''} + 2 y^{'} = x^{2} e^{x} + 3 x e^{2 x} + 5 x^{2}$	[[_3rd_order, _missing_y]]	✓	0.279

13426	$y^{'''} - 6 y^{''} + 12 y^{'} - 8 y = x e^{2 x} + x^{2} e^{3 x}$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.349

13427	$y^{''''} + 3 y^{'''} + 4 y^{''} + 3 y^{'} + y = x^{2} e^{- x} + 3 e^{- \frac{x}{2}} \cos (\frac{\sqrt{3} x}{2})$	[[_high_order, _linear, _nonhomogeneous]]	✓	1.620

13428	$y^{''''} - 16 y = x^{2} \sin (2 x) + x^{4} e^{2 x}$	[[_high_order, _linear, _nonhomogeneous]]	✓	36.065

13429	$y^{(6)} + 2 y^{(5)} + 5 y^{''''} = x^{3} + x^{2} e^{- x} + e^{- x} \sin (2 x)$	[[_high_order, _missing_y]]	✓	37.035

13430	$y^{''''} + 2 y^{''} + y = x^{2} \cos (x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	1.011

13431	$y^{''''} + 16 y = x e^{\sqrt{2} x} \sin (\sqrt{2} x) + e^{- \sqrt{2} x} \cos (\sqrt{2} x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	2.457

13432	$y^{''''} + 3 y^{''} - 4 y = \cos {(x)}^{2} - \cosh (x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	1.150

13433	$y^{''''} + 10 y^{''} + 9 y = \sin (2 x) \sin (x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	1.171

13434	$y^{''} + y = \cot (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.774

13435	$y^{''} + y = \tan {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.874

13436	$y^{''} + y = \sec (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.679

13437	$y^{''} + y = \sec {(x)}^{3}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.745

13438	$y^{''} + 4 y = \sec {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.877

13439	$y^{''} + y = \sec (x) \tan (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.871

13440	$y^{''} + 4 y^{'} + 5 y = e^{- 2 x} \sec (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.757

13441	$y^{''} - 2 y^{'} + 5 y = e^{x} \tan (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.870

13442	$y^{''} + 6 y^{'} + 9 y = \frac{e^{- 3 x}}{x^{3}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.650

13443	$y^{''} - 2 y^{'} + y = x e^{x} \ln (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.675

13444	$y^{''} + y = \sec (x) \csc (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.989

13445	$y^{''} + y = \tan {(x)}^{3}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.918

13446	$y^{''} + 3 y^{'} + 2 y = \frac{1}{e^{x} + 1}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.559

13447	$y^{''} + 3 y^{'} + 2 y = \frac{1}{e^{2 x} + 1}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.650

13448	$y^{''} + y = \frac{1}{1 + \sin (x)}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.897

13449	$y^{''} - 2 y^{'} + y = e^{x} \arcsin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.708

13450	$y^{''} + 3 y^{'} + 2 y = \frac{e^{- x}}{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.591

13451	$y^{''} - 2 y^{'} + y = x \ln (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.716

13452	$x^{2} y^{''} - 6 y^{'} x + 10 y = 3 x^{4} + 6 x^{3}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.261

13453	${(x + 1)}^{2} y^{''} - 2 (x + 1) y^{'} + 2 y = 1$	[[_2nd_order, _with_linear_symmetries]]	✓	1.371

13454	$(x^{2} + 2 x) y^{''} - 2 (x + 1) y^{'} + 2 y = {(x + 2)}^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.225

13455	$x^{2} y^{''} - x (x + 2) y^{'} + (x + 2) y = x^{3}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.893

13456	$x (x - 2) y^{''} - (x^{2} - 2) y^{'} + 2 (x - 1) y = 3 x^{2} {(x - 2)}^{2} e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.920

13457	$(2 x + 1) (x + 1) y^{''} + 2 y^{'} x - 2 y = {(2 x + 1)}^{2}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.404

13458	$\sin {(x)}^{2} y^{''} - 2 \cos (x) \sin (x) y^{'} + (\cos {(x)}^{2} + 1) y = \sin {(x)}^{3}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.321

13459	$y^{'''} - 3 y^{''} - y^{'} + 3 y = x^{2} e^{x}$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.168

13460	$x^{2} y^{''} - 3 y^{'} x + 3 y = 0$	[[_Emden, _Fowler]]	✓	0.995

13461	$x^{2} y^{''} + y^{'} x - 4 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.735

13462	$4 x^{2} y^{''} - 4 y^{'} x + 3 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.914

13463	$x^{2} y^{''} - 3 y^{'} x + 4 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.898

13464	$x^{2} y^{''} + y^{'} x + 4 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.868

13465	$x^{2} y^{''} - 3 y^{'} x + 13 y = 0$	[[_Emden, _Fowler]]	✓	1.007

13466	$3 x^{2} y^{''} - 4 y^{'} x + 2 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.945

13467	$x^{2} y^{''} + y^{'} x + 9 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.931

13468	$9 x^{2} y^{''} + 3 y^{'} x + y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.874

13469	$x^{2} y^{''} - 5 y^{'} x + 10 y = 0$	[[_Emden, _Fowler]]	✓	1.024

13470	$x^{3} y^{'''} - 3 x^{2} y^{''} + 6 y^{'} x - 6 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓	0.146

13471	$x^{3} y^{'''} + 2 x^{2} y^{''} - 10 y^{'} x - 8 y = 0$	[[_3rd_order, _fully, _exact, _linear]]	✓	0.143

13472	$x^{3} y^{'''} - x^{2} y^{''} - 6 y^{'} x + 18 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓	0.143

13473	$x^{2} y^{''} - 4 y^{'} x + 6 y = 4 x - 6$	[[_2nd_order, _with_linear_symmetries]]	✓	1.400

13474	$x^{2} y^{''} - 5 y^{'} x + 8 y = 2 x^{3}$	[[_2nd_order, _with_linear_symmetries]]	✓	1.232

13475	$x^{2} y^{''} + 4 y^{'} x + 2 y = 4 \ln (x)$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.945

13476	$x^{2} y^{''} + y^{'} x + 4 y = 2 x \ln (x)$	[[_2nd_order, _with_linear_symmetries]]	✓	1.832

13477	$x^{2} y^{''} + y^{'} x + 4 y = 4 \sin (\ln (x))$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.875

13478	$x^{3} y^{'''} - x^{2} y^{''} + 2 y^{'} x - 2 y = x^{3}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.256

13479	$x^{2} y^{''} - 2 y^{'} x - 10 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.407

13480	$x^{2} y^{''} - 4 y^{'} x + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.828

13481	$x^{2} y^{''} + 5 y^{'} x + 3 y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.568

13482	$x^{2} y^{''} - 2 y = 4 x - 8$ i.c.	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.168

13483	$x^{2} y^{''} - 4 y^{'} x + 4 y = - 6 x^{3} + 4 x^{2}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	2.005

13484	$x^{2} y^{''} + 2 y^{'} x - 6 y = 10 x^{2}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	1.323

13485	$x^{2} y^{''} - 5 y^{'} x + 8 y = 2 x^{3}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	1.554

13486	$x^{2} y^{''} - 6 y = \ln (x)$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.842

13487	${(x + 2)}^{2} y^{''} - (x + 2) y^{'} - 3 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.875

13488	${(2 x - 3)}^{2} y^{''} - 6 (2 x - 3) y^{'} + 12 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.959

13489	$y^{''} + y^{'} x + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.336

13490	$y^{''} + 8 y^{'} x - 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.397

13491	$y^{''} + y^{'} x + (2 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.413

13492	$y^{''} + y^{'} x + (x^{2} - 4) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.375

13493	$y^{''} + y^{'} x + (3 x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.451

13494	$y^{''} - y^{'} x + (3 x - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.474

13495	$(x^{2} + 1) y^{''} + y^{'} x + x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.447

13496	$(x - 1) y^{''} - (3 x - 2) y^{'} + 2 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.499

13497	$(x^{3} - 1) y^{''} + x^{2} y^{'} + x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.515

13498	$(3 + x) y^{''} + (x + 2) y^{'} + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.461

13499	$y^{''} - y^{'} x - y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.394

13500	$y^{''} + y^{'} x - 2 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.341

2.2.135 Problems 13401 to 13500