second order ode solved by an integrating factor

Table 2.471: second order ode solved by an integrating factor


#	ODE	CAS classiﬁcation	Solved?

223	$y^{''} + 2 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

224	$y^{''} - 10 y^{'} + 25 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

227	$x^{2} y^{''} - 2 x y^{'} + 2 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

240	$4 y^{''} + 4 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

241	$9 y^{''} - 12 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓

262	$x^{2} y^{''} - 2 x y^{'} + 2 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

275	$y^{''} + 6 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

277	$4 y^{''} - 12 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

325	$4 y^{''} + 4 y^{'} + y = 3 x e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

368	$y^{''} - 4 y^{'} + 4 y = 2 e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

377	$x^{2} y^{''} - 4 x y^{'} + 6 y = x^{3}$	[[_2nd_order, _with_linear_symmetries]]	✓

379	$4 x^{2} y^{''} - 4 x y^{'} + 3 y = 8 x^{4 / 3}$	[[_2nd_order, _with_linear_symmetries]]	✓

388	$x^{''} + 4 x^{'} + 4 x = 10 \cos (3 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

815	$y^{''} + 2 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

816	$y^{''} - 10 y^{'} + 25 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

819	$x^{2} y^{''} - 2 x y^{'} + 2 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

829	$4 y^{''} + 4 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

830	$9 y^{''} - 12 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓

849	$y^{''} + 6 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

851	$4 y^{''} - 12 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

864	$x^{''} + 8 x^{'} + 16 x = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

872	$4 y^{''} + 4 y^{'} + y = 3 x e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

894	$y^{''} - 4 y^{'} + 4 y = 2 e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

903	$x^{2} y^{''} - 4 x y^{'} + 6 y = x^{3}$	[[_2nd_order, _with_linear_symmetries]]	✓

905	$4 x^{2} y^{''} - 4 x y^{'} + 3 y = 8 x^{4 / 3}$	[[_2nd_order, _with_linear_symmetries]]	✓

913	$x^{''} + 4 x^{'} + 4 x = 10 \cos (3 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

1294	$t^{2} y^{''} + 4 t y^{'} + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓

1297	$t^{2} y^{''} - 4 t y^{'} + 6 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

1303	$y^{''} - 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

1304	$9 y^{''} + 6 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

1306	$4 y^{''} + 12 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

1308	$y^{''} - 6 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

1310	$16 y^{''} + 24 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

1311	$25 y^{''} - 20 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓

1313	$9 y^{''} - 12 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

1314	$y^{''} - 6 y^{'} + 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

1316	$y^{''} + 4 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

1317	$4 y^{''} + 12 y^{'} + 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

1318	$y^{''} - y^{'} + \frac{y}{4} = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

1335	$y^{''} + 2 y^{'} + y = 3 e^{- t}$	[[_2nd_order, _with_linear_symmetries]]	✓

1336	$4 y^{''} - 4 y^{'} + y = 16 e^{\frac{t}{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓

1339	$y^{''} + 4 y^{'} + 4 y = \frac{e^{- 2 t}}{t^{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

1342	$y^{''} - 2 y^{'} + y = \frac{e^{t}}{t^{2} + 1}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

1351	$t^{2} y^{''} - 2 t y^{'} + 2 y = 4 t^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓

1740	$y^{''} - 2 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

1741	$y^{''} - 2 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

1742	$(x^{2} - 1) y^{''} + 4 x y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓

1744	$y^{''} - 6 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

1745	$y^{''} - 2 a y^{'} + a^{2} y = 0$	[[_2nd_order, _missing_x]]	✓

1754	$(x^{2} - 4) y^{''} + 4 x y^{'} + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓

1809	$y^{''} - 2 y^{'} + y = 14 x^{3 / 2} e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

1813	$4 x^{2} y^{''} + (- 8 x^{2} + 4 x) y^{'} + (4 x^{2} - 4 x - 1) y = 4 \sqrt{x} e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

1814	$y^{''} + 4 x y^{'} + (4 x^{2} + 2) y = 4 e^{- x (2 + x)}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

1815	$x^{2} y^{''} - 4 x y^{'} + 6 y = x^{5 / 2}$	[[_2nd_order, _with_linear_symmetries]]	✓

1835	${(- 1 + x)}^{2} y^{''} - 2 (- 1 + x) y^{'} + 2 y = {(- 1 + x)}^{2}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓

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

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

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

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

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

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

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

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

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

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

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)]‘]]	✓

2567	$y^{''} - 6 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

2568	$4 y^{''} - 12 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

2569	$9 y^{''} + 6 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

2570	$4 y^{''} - 4 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

2572	$9 y^{''} - 12 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

2584	$y^{''} - 4 y^{'} + 4 y = t e^{2 t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

2588	$y^{''} + 4 y^{'} + 4 y = t^{5 / 2} e^{- 2 t}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓

2595	$y^{''} + 4 y^{'} + 4 y = t e^{α t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

2598	$y^{''} + 2 y^{'} + y = e^{- t}$	[[_2nd_order, _with_linear_symmetries]]	✓

2601	$y^{''} - 6 y^{'} + 9 y = (3 t^{7} - 5 t^{4}) e^{3 t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

2610	$y^{''} - 6 y^{'} + 9 y = t^{3 / 2} e^{3 t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

2630	${(t - 1)}^{2} y^{''} - 2 (t - 1) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

3088	$y^{''} - 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

3128	$y^{''} + 4 y^{'} + 4 y = x^{3} e^{2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

3131	$y^{''} + 2 n y^{'} + n^{2} y = 5 \cos (6 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

3146	$y^{''} + 4 y^{'} + 4 y = e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓

3148	$y^{''} - 2 y^{'} + y = e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

3160	$y^{''} - 2 y^{'} + y = \frac{e^{x}}{{(1 - x)}^{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

3168	$4 y^{''} - 4 y^{'} + y = e^{\frac{x}{2}} \ln (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

3170	$y^{''} - 6 y^{'} + 9 y = e^{3 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

3175	$y^{''} + 4 y^{'} + 4 y = \frac{e^{x}}{2} + \frac{e^{- x}}{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

3178	$y^{''} + 4 y^{'} + 4 y = \frac{e^{3 x}}{2} - \frac{e^{- 3 x}}{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

3185	$y^{''} + 2 n^{2} y^{'} + n^{4} y = \sin (k x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

3230	$x^{2} y^{''} - 2 x y^{'} + 2 y = 4 x + \sin (\ln (x))$	[[_2nd_order, _with_linear_symmetries]]	✓

3487	$f^{''} + 6 f^{'} + 9 f = e^{- t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓

3490	$y^{''} + 2 y^{'} + y = 4 e^{- x}$	[[_2nd_order, _with_linear_symmetries]]	✓

3497	$y^{''} - 2 y^{'} + y = 2 x e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

3569	$x^{2} y^{''} - 4 x y^{'} + 6 y = x^{4} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

3571	$y^{''} - 2 a y^{'} + a^{2} y = 0$	[[_2nd_order, _missing_x]]	✓

3574	$y^{''} + 6 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

3717	$y^{''} + 4 y^{'} + 4 y = 5 x e^{- 2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

3735	$y^{''} + 2 y^{'} + y = 50 \sin (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

3737	$y^{''} + 4 y^{'} + 4 y = 169 \sin (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

3745	$y^{''} - 6 y^{'} + 9 y = 4 e^{3 x} \ln (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

3746	$y^{''} + 4 y^{'} + 4 y = \frac{e^{- 2 x}}{x^{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

3748	$y^{''} + 6 y^{'} + 9 y = \frac{2 e^{- 3 x}}{x^{2} + 1}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

3752	$y^{''} - 10 y^{'} + 25 y = \frac{2 e^{5 x}}{x^{2} + 4}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

3757	$y^{''} - 2 m y^{'} + m^{2} y = \frac{e^{m x}}{x^{2} + 1}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

3758	$y^{''} - 2 y^{'} + y = \frac{4 e^{x} \ln (x)}{x^{3}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

3759	$y^{''} + 2 y^{'} + y = \frac{e^{- x}}{\sqrt{- x^{2} + 4}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

3761	$y^{''} + 4 y^{'} + 4 y = \frac{4 e^{- 2 x}}{x^{2} + 1} + 2 x^{2} - 1$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

3762	$y^{''} + 4 y^{'} + 4 y = 15 e^{- 2 x} \ln (x) + 25 \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

3771	$y^{''} - 4 y^{'} + 4 y = 5 x e^{2 x}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓

3773	$x^{2} y^{''} + 4 x y^{'} + 2 y = 4 \ln (x)$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓

3774	$x^{2} y^{''} + 4 x y^{'} + 2 y = \cos (x)$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓

3777	$x^{2} y^{''} - 4 x y^{'} + 6 y = x^{4} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

3778	$x^{2} y^{''} + 6 x y^{'} + 6 y = 4 e^{2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

3797	$y^{''} + 6 y^{'} + 9 y = 4 e^{- 3 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

3798	$y^{''} + 6 y^{'} + 9 y = 4 e^{- 2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

3803	$y^{''} + 2 y^{'} + y = 2 x e^{- x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

4120	$y^{''} + 6 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

4121	$y^{''} + 6 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

4132	$y^{''} - 6 y^{'} + 9 y = e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

4140	$x^{2} y^{''} - 2 x y^{'} + 2 y = x^{2} + 2$	[[_2nd_order, _with_linear_symmetries]]	✓

4141	$y^{''} + 2 n y^{'} + n^{2} y = A \cos (x p)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓

4156	$y^{''} - 4 y^{'} + 4 y = x^{3} e^{2 x} + x e^{2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

4158	$y^{''} - 6 y^{'} + 9 y = e^{x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

4163	$25 y^{''} - 30 y^{'} + 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

4164	$9 y^{''} - 6 y^{'} + y = (4 x^{2} + 24 x + 18) e^{x}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓

4479	$y^{''} - 4 y^{'} + 4 y = (x + 1) e^{x} + 2 e^{2 x} + 3 e^{3 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

4488	$y^{''} - 4 y^{'} + 4 y = 4 x e^{2 x} \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

4499	$y^{''} - 2 y^{'} + y = \frac{e^{x}}{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

4505	$y^{''} + 2 y^{'} + y = 15 e^{- x} \sqrt{x + 1}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

4507	$y^{''} - 2 y^{'} + y = \frac{e^{2 x}}{{(e^{x} + 1)}^{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

5928	$y^{''} + 4 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓

5931	$y^{''} - 2 a y^{'} + a^{2} y = 0$	[[_2nd_order, _missing_x]]	✓

5946	$y^{''} + 4 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

5963	$y^{''} + 2 y^{'} + y = x^{2} e^{- x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

5981	$y^{''} + 2 y^{'} + y = x^{2} e^{- x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

5983	$y^{''} + 2 y^{'} + y = e^{- x} \ln (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

5986	$y^{''} + 2 y^{'} + y = \frac{e^{- x}}{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

5988	$y^{''} - 2 y^{'} + y = e^{x} \ln (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

5991	$y^{''} - \frac{2 y^{'}}{x} + \frac{2 y}{x^{2}} = \ln (x) x$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓

6026	$x^{2} y^{''} - 2 x y^{'} + 2 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

6136	$y^{''} - 4 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓

6152	$y^{''} - 4 y^{'} + 4 y = 16$	[[_2nd_order, _missing_x]]	✓

6156	$y^{''} + 6 y^{'} + 9 y = 12 e^{- x}$	[[_2nd_order, _with_linear_symmetries]]	✓

6159	$y^{''} + 2 y^{'} + y = 2 e^{- x}$	[[_2nd_order, _with_linear_symmetries]]	✓

6160	$y^{''} - 6 y^{'} + 9 y = 6 e^{3 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

6163	$y^{''} - 2 y^{'} + y = 2 \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

6174	$y^{''} - 6 y^{'} + 9 y = 12 x e^{3 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

6181	$y^{''} + 2 y^{'} + y = 4 e^{x} + (1 - x) (e^{2 x} - 1)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

6211	$r^{''} - 6 r^{'} + 9 r = 0$	[[_2nd_order, _missing_x]]	✓

6222	$y^{''} - 4 y^{'} + 4 y = 6 e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

6247	$y^{''} - 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

6255	$y^{''} - 4 x y^{'} + (4 x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓

6395	$y^{''} - 2 y^{'} + y = 2 \cos (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓

6481	$y^{''} + 2 y^{'} + y = e^{- 2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

6483	$y^{''} - 2 y^{'} + y = 4 \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

6488	$y^{''} - 6 y^{'} + 9 y = 54 x + 18$	[[_2nd_order, _with_linear_symmetries]]	✓

6490	$y^{''} + 2 y^{'} + y = 4 \sinh (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

6493	$y^{''} + 4 y^{'} + 4 y = 2 \cos {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

6518	$y^{''} - 2 y^{'} + y = x^{2} - 1$	[[_2nd_order, _with_linear_symmetries]]	✓

6519	$y^{''} - 2 y^{'} + y = 4 e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

6520	$y^{''} - 2 y^{'} + y = 4 \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

6521	$y^{''} - 2 y^{'} + y = 3 e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓

6522	$y^{''} - 2 y^{'} + y = x e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

6529	$y^{''} - 2 y^{'} + y = \frac{e^{x}}{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

6532	$t^{2} N^{''} - 2 t N^{'} + 2 N = t \ln (t)$	[[_2nd_order, _with_linear_symmetries]]	✓

6535	$y^{''} - 2 y^{'} + y = \frac{e^{x}}{x^{5}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

6573	$y^{''} - 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

6703	$y^{''} + 6 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

6716	$y^{''} - 6 y^{'} + 9 y = e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

6737	$y^{''} - 4 y^{'} + 4 y = e^{x} + x e^{2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

6746	$y^{''} - 4 y^{'} + 4 y = \frac{e^{2 x}}{x^{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

6750	$x^{2} y^{''} - 2 x y^{'} + 2 y = \ln {(x)}^{2} - \ln (x^{2})$	[[_2nd_order, _with_linear_symmetries]]	✓

6898	$y^{''} - 4 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓

7518	$s^{''} + 2 s^{'} + s = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

7536	$y^{''} + 6 y^{'} + 9 y = 50 e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

7537	$y^{''} - 4 y^{'} + 4 y = 50 e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

7657	$y^{''} - 2 i y^{'} - y = 0$	[[_2nd_order, _missing_x]]	✓

7664	$y^{''} - 2 i y^{'} - y = e^{i x} - 2 e^{- i x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

7938	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

7941	$y^{''} - 4 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓

7944	$4 y^{''} - 12 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

7947	$4 y^{''} + 20 y^{'} + 25 y = 0$	[[_2nd_order, _missing_x]]	✓

7957	$y^{''} - 6 y^{'} + 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

7972	$y^{''} + 10 y^{'} + 25 y = 14 e^{- 5 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

7978	$y^{''} - 2 y^{'} + y = 6 e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓

7986	$y^{''} + 2 y^{'} + y = e^{- x} \ln (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

7998	$y^{''} - 2 y^{'} + y = 2 x$	[[_2nd_order, _with_linear_symmetries]]	✓

8004	$x^{2} y^{''} - 2 x y^{'} + 2 y = x e^{- x}$	[[_2nd_order, _with_linear_symmetries]]	✓

8041	$y^{''} + 6 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

8060	$y^{''} + 4 y^{'} + 4 y = \ln (x) x$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

8067	$x^{2} y^{''} - 2 x y^{'} + 2 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

8530	$y^{''} - 6 y^{'} + 9 y = e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓

8752	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

8963	$y^{''} + 2 x y^{'} + (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓

8964	$y^{''} + 2 \cot (x) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓

8966	$4 x^{2} y^{''} + (- 8 x^{2} + 4 x) y^{'} + (4 x^{2} - 4 x - 1) y = 4 \sqrt{x} e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

9169	$x^{2} y^{''} - 4 x y^{'} + 6 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

11038	$y^{''} + 4 x y^{'} + (4 x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓

11041	$y^{''} - 4 x y^{'} + (4 x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓


11156	$x^{2} y^{''} - 2 x y^{'} + 2 y - x^{5} \ln (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓

11166	$x^{2} y^{''} - 4 x y^{'} + 6 y - x^{4} + x^{2} = 0$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

11210	$(x^{2} + 1) y^{''} + 4 x y^{'} + 2 y - 2 \cos (x) + 2 x = 0$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓

11261	$4 x^{2} y^{''} - 4 x (2 x - 1) y^{'} + (4 x^{2} - 4 x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓

11319	$y^{''} = \frac{2 (a x + 2 b) y^{'}}{x (a x + b)} - \frac{(2 a x + 6 b) y}{(a x + b) x^{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓

11345	$y^{''} = - \frac{2 x y^{'}}{x^{2} + 1} - \frac{y}{{(x^{2} + 1)}^{2}}$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

11383	$y^{''} = - \frac{(2 x^{2} + 1) y^{'}}{x^{3}} - \frac{(- 2 x^{2} + 1) y}{4 x^{6}}$	[[_2nd_order, _with_linear_symmetries]]	✓

12467	$y^{''} + 2 a x^{n} y^{'} + a (a x^{2 n} + n x^{n - 1}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓

12698	$y^{''} + 2 a e^{λ x} y^{'} + a e^{λ x} (a e^{λ x} + λ) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓

12853	$y^{''} - 2 y^{'} + y = \frac{e^{x}}{{(1 - x)}^{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

12861	$y^{''} - 2 y^{'} + y = 2 x e^{2 x} - \sin {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

12863	$y^{''} + 2 y^{'} + y = 3 e^{2 x} - \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

12875	$y^{''} + 2 y^{'} + y = 2 x^{3} - x e^{3 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

12922	${(- 1 + x)}^{2} y^{''} + 4 (- 1 + x) y^{'} + 2 y = \cos (x)$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓

13033	$x^{''} - 4 x^{'} + 4 x = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

13035	$\frac{x^{''}}{2} + x^{'} + \frac{x}{2} = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

13037	$x^{''} - 4 x^{'} + 4 x = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

13039	$\frac{x^{''}}{2} + x^{'} + \frac{x}{2} = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

13078	$t x^{''} + 4 x^{'} + \frac{2 x}{t} = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

13089	$x^{''} - 2 x^{'} + x = \frac{e^{t}}{2 t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

13170	$(x^{2} + 1) y^{''} + 4 x y^{'} + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓

13180	$y^{''} - 4 y^{'} + 4 y = - 8 \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

13314	$y^{''} - 2 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

13315	$x^{2} y^{''} - 2 x y^{'} + 2 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

13334	$y^{''} - 8 y^{'} + 16 y = 0$	[[_2nd_order, _missing_x]]	✓

13335	$4 y^{''} + 4 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

13356	$y^{''} + 6 y^{'} + 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

13357	$4 y^{''} - 12 y^{'} + 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

13358	$y^{''} + 4 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

13359	$9 y^{''} - 6 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

13400	$y^{''} + 8 y^{'} + 16 y = 8 e^{- 2 x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓

13401	$y^{''} + 6 y^{'} + 9 y = 27 e^{- 6 x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓

13406	$y^{''} - 2 y^{'} + y = 2 x e^{2 x} + 6 e^{x}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓

13415	$y^{''} - 6 y^{'} + 9 y = x^{4} e^{x} + x^{3} e^{2 x} + x^{2} e^{3 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

13434	$y^{''} + 6 y^{'} + 9 y = \frac{e^{- 3 x}}{x^{3}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

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

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

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

13445	${(x + 1)}^{2} y^{''} - 2 (x + 1) y^{'} + 2 y = 1$	[[_2nd_order, _with_linear_symmetries]]	✓

13454	$4 x^{2} y^{''} - 4 x y^{'} + 3 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

13465	$x^{2} y^{''} - 4 x y^{'} + 6 y = 4 x - 6$	[[_2nd_order, _with_linear_symmetries]]	✓

13467	$x^{2} y^{''} + 4 x y^{'} + 2 y = 4 \ln (x)$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓

13472	$x^{2} y^{''} - 4 x y^{'} + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

13672	$y^{''} - 4 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

13679	$y^{''} + 2 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

13684	$y^{''} + 4 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

13690	$x^{''} + 2 x^{'} + x = e^{- t}$	[[_2nd_order, _with_linear_symmetries]]	✓

13696	$x^{''} + 4 x^{'} + 4 x = e^{2 t}$	[[_2nd_order, _with_linear_symmetries]]	✓

13717	$x^{2} y^{''} - 4 x y^{'} + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

13825	$x^{2} y^{''} - 4 x y^{'} + 6 y = 2$	[[_2nd_order, _with_linear_symmetries]]	✓

13828	$x^{''} - 4 x^{'} + 4 x = e^{t} + e^{2 t} + 1$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

13844	$y^{''} + 2 y^{'} + y = \sinh (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

13856	$x^{''} + 10 x^{'} + 25 x = 2^{t} + t e^{- 5 t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

13918	$y^{''} + 4 x y^{'} + (4 x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓

13925	$x \ln (x) y^{''} + 2 y^{'} - \frac{y}{x} = 1$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓

14013	$y^{''} + 2 y^{'} + y = 1$	[[_2nd_order, _missing_x]]	✓

14053	$y^{''} - 2 y^{'} + y = x^{3 / 2} e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

14080	$y^{''} - 2 k y^{'} + k^{2} y = e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓

14162	$y^{''} - 4 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓

14165	$4 y^{''} - 12 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

14179	$y^{''} - 2 a y^{'} + a^{2} y = e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓

14245	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

14266	$x^{2} y^{''} - 4 x y^{'} + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

14267	$x^{2} y^{''} - 4 x y^{'} + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

14268	$x^{2} y^{''} - 4 x y^{'} + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

14269	$x^{2} y^{''} - 4 x y^{'} + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

14270	$x^{2} y^{''} - 4 x y^{'} + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

14816	$y^{''} + 2 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

14836	$y^{''} + 2 y^{'} + y = e^{- t}$	[[_2nd_order, _with_linear_symmetries]]	✓

14867	$y^{''} + 2 y^{'} + y = \cos (3 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

14871	$y^{''} + 2 y^{'} + y = 2 \cos (2 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15220	$y^{''} - 4 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

15221	$x^{2} y^{''} - 4 x y^{'} + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

15222	$4 x^{2} y^{''} + 4 x y^{'} - y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

15225	${(x + 1)}^{2} y^{''} - 2 (x + 1) y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

15226	$x^{2} y^{''} - 4 x y^{'} + 6 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

15248	$y^{''} - 10 y^{'} + 25 y = 0$	[[_2nd_order, _missing_x]]	✓

15249	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

15250	$4 y^{''} - 4 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

15251	$25 y^{''} - 10 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

15252	$16 y^{''} - 24 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

15253	$9 y^{''} + 12 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓

15254	$y^{''} - 8 y^{'} + 16 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

15255	$y^{''} - 8 y^{'} + 16 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

15256	$y^{''} - 8 y^{'} + 16 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

15257	$4 y^{''} + 4 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

15258	$4 y^{''} + 4 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

15259	$4 y^{''} + 4 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

15319	$4 x^{2} y^{''} + 4 x y^{'} - y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

15339	$y^{''} + 6 y^{'} + 9 y = 169 \sin (2 x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15340	$x^{2} y^{''} - 4 x y^{'} + 6 y = 10 x + 12$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓

15346	$x^{2} y^{''} - 4 x y^{'} + 6 y = 1$	[[_2nd_order, _with_linear_symmetries]]	✓

15347	$x^{2} y^{''} - 4 x y^{'} + 6 y = x$	[[_2nd_order, _with_linear_symmetries]]	✓

15348	$x^{2} y^{''} - 4 x y^{'} + 6 y = 22 x + 24$	[[_2nd_order, _with_linear_symmetries]]	✓

15354	$y^{''} - 6 y^{'} + 9 y = 27 e^{6 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

15359	$y^{''} - 6 y^{'} + 9 y = 25 \sin (6 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15365	$y^{''} - 6 y^{'} + 9 y = 18 x^{2} + 3 x + 4$	[[_2nd_order, _with_linear_symmetries]]	✓

15369	$y^{''} - 6 y^{'} + 9 y = e^{2 x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15372	$y^{''} - 2 y^{'} + y = (- 6 x - 8) \cos (2 x) + (8 x - 11) \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15373	$y^{''} - 2 y^{'} + y = (12 x - 4) e^{- 5 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15379	$y^{''} - 6 y^{'} + 9 y = 10 e^{3 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

15382	$y^{''} - 10 y^{'} + 25 y = 6 e^{5 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

15383	$y^{''} - 10 y^{'} + 25 y = 6 e^{- 5 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

15406	$y^{''} - 10 y^{'} + 25 y = 3 x^{2} e^{5 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15407	$y^{''} - 10 y^{'} + 25 y = 3 x^{4}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15422	$y^{''} - 6 y^{'} + 9 y = 27 e^{6 x} + 25 \sin (6 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15434	$x^{2} y^{''} - 2 x y^{'} + 2 y = 3 \sqrt{x}$	[[_2nd_order, _with_linear_symmetries]]	✓

15438	$y^{''} - 4 y^{'} + 4 y = (24 x^{2} + 2) e^{2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15439	$y^{''} + 4 y^{'} + 4 y = \frac{e^{- 2 x}}{x^{2} + 1}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15457	$y^{''} - 12 y^{'} + 36 y = 0$	[[_2nd_order, _missing_x]]	✓

15464	$y^{''} + 6 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

15476	$16 y^{''} - 8 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

15483	$y^{''} + 20 y^{'} + 100 y = 0$	[[_2nd_order, _missing_x]]	✓

15487	$y^{''} - 12 y^{'} + 36 y = 25 \sin (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15489	$y^{''} - 12 y^{'} + 36 y = 81 e^{3 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

15491	$y^{''} - 12 y^{'} + 36 y = 3 x e^{6 x} - 2 e^{6 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15494	$y^{''} + 6 y^{'} + 9 y = 10 e^{- 3 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

15496	$y^{''} + 6 y^{'} + 9 y = 2 \cos (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15500	$4 y^{''} - 12 y^{'} + 9 y = x e^{\frac{3 x}{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15721	$x^{2} y^{''} - 12 x y^{'} + 42 y = 0$	[[_Emden, _Fowler]]	✓

15747	$t^{2} y^{''} - 12 t y^{'} + 42 y = 0$ i.c.	[[_Emden, _Fowler]]	✓

16099	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

16140	$4 y^{''} + 4 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

16141	$y^{''} - 6 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

16150	$y^{''} - 2 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

16151	$y^{''} + 4 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

16159	$9 y^{''} + 6 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

16176	$y^{''} - 2 y^{'} + y = t^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓

16196	$y^{''} + 4 y^{'} + 4 y = - 32 t^{2} \cos (2 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16210	$y^{''} + 8 y^{'} + 16 y = 4$ i.c.	[[_2nd_order, _missing_x]]	✓

16248	$y^{''} - 2 y^{'} + y = \frac{e^{t}}{t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16249	$y^{''} - 4 y^{'} + 4 y = \frac{e^{2 t}}{t^{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16250	$y^{''} + 8 y^{'} + 16 y = \frac{e^{- 4 t}}{t^{4}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16251	$y^{''} + 6 y^{'} + 9 y = \frac{e^{- 3 t}}{t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16252	$y^{''} + 6 y^{'} + 9 y = e^{- 3 t} \ln (t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16254	$y^{''} + 4 y^{'} + 4 y = e^{- 2 t} \sqrt{- t^{2} + 1}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16255	$y^{''} - 2 y^{'} + y = e^{t} \sqrt{- t^{2} + 1}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16256	$y^{''} - 10 y^{'} + 25 y = e^{5 t} \ln (2 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16257	$y^{''} - 4 y^{'} + 4 y = e^{2 t} \arctan (t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16258	$y^{''} + 8 y^{'} + 16 y = \frac{e^{- 4 t}}{t^{2} + 1}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16278	$4 y^{''} + 4 y^{'} + y = e^{- \frac{t}{2}}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓

16400	$x^{2} y^{''} + 4 x y^{'} + 2 y = \ln (x)$ i.c.	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓

16404	$x^{2} y^{''} + 4 x y^{'} + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓

16417	$x^{2} y^{''} + 4 x y^{'} + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓

16486	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

16520	$y^{''} - 8 y^{'} + 16 y = \frac{e^{4 t}}{t^{3}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16521	$y^{''} - 8 y^{'} + 16 y = \frac{e^{4 t}}{t^{3}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16522	$y^{''} - 2 y^{'} + y = e^{t} \ln (t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16523	$y^{''} - 2 y^{'} + y = e^{t} \ln (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16526	$y^{''} + 4 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓

16529	$x^{2} y^{''} - 4 x y^{'} + 6 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

16582	$x^{''} + 6 x^{'} + 9 x = 0$	[[_2nd_order, _missing_x]]	✓

16876	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

16899	$y^{''} - 8 y^{'} + 16 y = (1 - x) e^{4 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16900	$y^{''} - 10 y^{'} + 25 y = e^{5 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

16931	$y^{''} + 2 y^{'} + y = - 2$	[[_2nd_order, _missing_x]]	✓

16939	$y^{''} - 4 y^{'} + 4 y = x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓

16941	$y^{''} - 2 k y^{'} + k^{2} y = e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓

16942	$y^{''} + 4 y^{'} + 4 y = 8 e^{- 2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

16951	$y^{''} - 2 m y^{'} + m^{2} y = \sin (n x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16963	$y^{''} - 2 y^{'} + y = x^{3}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16966	$y^{''} + 2 y^{'} + y = x^{2} e^{- x} \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16981	$y^{''} - 2 y^{'} + y = 2 + e^{x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16999	$y^{''} - 4 y^{'} + 4 y = 4 x + \sin (x) + \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

17000	$y^{''} + 2 y^{'} + y = 1 + 2 \cos (x) + \cos (2 x) - \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

17002	$y^{''} + 6 y^{'} + 9 y = 18 e^{- 3 x} + 8 \sin (x) + 6 \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

17011	$y^{''} - 6 y^{'} + 9 y = 9 x^{2} - 12 x + 2$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓

17013	$y^{''} - 4 y^{'} + 4 y = 2 e^{2 x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓

17016	$y^{''} + 6 y^{'} + 9 y = 10 \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓

17021	$y^{''} - 6 y^{'} + 9 y = 16 e^{- x} + 9 x - 6$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓

17053	$x^{2} y^{''} + 4 x y^{'} + 2 y = 2 \ln {(x)}^{2} + 12 x$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓

17073	$y^{''} - 2 y^{'} + y = \frac{e^{x}}{x^{2} + 1}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

17093	$x^{''} + 2 x^{'} + x = 0$	[[_2nd_order, _missing_x]]	✓

17146	$y^{''} - 4 y^{'} + 4 y = π^{2} - x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓

17148	$y^{''} - 4 y^{'} + 4 y = \arcsin (\sin (x))$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

17489	$y^{''} - 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

17506	$y^{''} - 4 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓

17507	$9 y^{''} + 6 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

17510	$4 y^{''} - 4 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

17513	$9 y^{''} + 12 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓

17518	$25 y^{''} - 20 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓

17524	$y^{''} + 4 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓

17525	$9 y^{''} - 24 y^{'} + 16 y = 0$	[[_2nd_order, _missing_x]]	✓

17532	$9 y^{''} - 12 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

17536	$y^{''} + 6 y^{'} + 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

17540	$y^{''} + 4 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

17549	$x^{2} y^{''} + 4 x y^{'} + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓

17568	$y^{''} + 2 y^{'} + y = 2 e^{- t}$	[[_2nd_order, _with_linear_symmetries]]	✓

17571	$y^{''} + 2 y^{'} + y = 3 e^{- t}$	[[_2nd_order, _with_linear_symmetries]]	✓

17572	$4 y^{''} - 4 y^{'} + y = 16 e^{\frac{t}{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓

17580	$y^{''} - 2 y^{'} + y = t e^{t} + 4$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓

17588	$y^{''} - 4 y^{'} + 4 y = 2 t^{2} + 4 t e^{2 t} + t \sin (2 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

17595	$x^{2} y^{''} - 2 x y^{'} + 2 y = 3 x^{2} + 2 \ln (x)$	[[_2nd_order, _with_linear_symmetries]]	✓

17610	$y^{''} + 2 y^{'} + y = 3 e^{- t}$	[[_2nd_order, _with_linear_symmetries]]	✓

17611	$4 y^{''} - 4 y^{'} + y = 16 e^{\frac{t}{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓

17614	$y^{''} + 4 y^{'} + 4 y = \frac{e^{2 t}}{t^{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

17617	$y^{''} - 2 y^{'} + y = \frac{e^{t}}{t^{2} + 1}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

17628	$t^{2} y^{''} - 2 t y^{'} + 2 y = 4 t^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓

17922	$x^{2} y^{''} - 2 x y^{'} + 2 y = 2 x^{3}$	[[_2nd_order, _with_linear_symmetries]]	✓

17937	$y^{''} - 4 y^{'} + 4 y = x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓

17948	$x^{2} y^{''} - 4 x y^{'} + 6 y = x$	[[_2nd_order, _with_linear_symmetries]]	✓

18184	$x^{2} y^{''} - 2 x y^{'} + 2 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

18186	$y^{''} - 4 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓

18192	$y^{''} + 2 x y^{'} + (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓

18210	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

18213	$y^{''} - 4 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓

18216	$4 y^{''} - 12 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

18219	$4 y^{''} + 20 y^{'} + 25 y = 0$	[[_2nd_order, _missing_x]]	✓

18224	$16 y^{''} - 8 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

18229	$y^{''} - 6 y^{'} + 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

18246	$y^{''} + 10 y^{'} + 25 y = 14 e^{- 5 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

18252	$y^{''} - 2 y^{'} + y = 6 e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓

18258	$y^{''} - 2 y^{'} + y = 2 x$	[[_2nd_order, _with_linear_symmetries]]	✓

18261	$y^{''} + 2 y^{'} + y = e^{- x} \ln (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

18277	$x^{2} y^{''} - 2 x y^{'} + 2 y = x e^{- x}$	[[_2nd_order, _with_linear_symmetries]]	✓

18303	$y^{''} + 4 y^{'} + 4 y = 10 x^{3} e^{- 2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

18304	$y^{''} - 2 y^{'} + y = e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓

18318	$y^{''} + 2 y^{'} + y = 2 x^{2} e^{- 2 x} + 3 e^{2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

18327	$y^{''} - 4 y^{'} + 4 y = e^{2 x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

18434	$t^{2} x^{''} - 6 t x^{'} + 12 x = 0$	[[_Emden, _Fowler]]	✓

18437	$t^{2} x^{''} - 2 t x^{'} + 2 x = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

18439	$x^{''} - 4 x^{'} + 4 x = 0$	[[_2nd_order, _missing_x]]	✓

18444	$x^{''} + 2 x^{'} + x = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

18539	$v^{''} + \frac{2 x v^{'}}{x^{2} + 1} + \frac{v}{{(x^{2} + 1)}^{2}} = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

18591	$y^{''} - 2 y^{'} + y = e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓

18592	$y^{''} - 2 y^{'} + y = x$	[[_2nd_order, _with_linear_symmetries]]	✓

18612	$(x^{2} - 1) y^{''} + 4 x y^{'} + 2 y = 2 x$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓

18613	$(x^{2} + 1) y^{''} + 4 x y^{'} + 2 y = x$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓

18616	$(3 x^{2} + x) y^{''} + 2 (1 + 6 x) y^{'} + 6 y = \sin (x)$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓

18645	$y^{''} - \frac{2 y^{'}}{x} + \frac{2 y}{x^{2}} = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓

18799	$y^{''} + 2 y^{'} + y = 2 e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

18803	$y^{''} - 2 y^{'} + y = 3 e^{\frac{5 x}{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓

18827	$y^{''} - 2 y^{'} + y = x^{2} e^{3 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

18855	$x^{2} y^{''} + 4 x y^{'} + 2 y = e^{x}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓

18857	${(x + a)}^{2} y^{''} - 4 (x + a) y^{'} + 6 y = x$	[[_2nd_order, _with_linear_symmetries]]	✓

19086	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

19098	$y^{''} - 2 y^{'} + y = 2 e^{\frac{5 x}{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓

19118	$y^{''} + 2 y^{'} + y = x \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

19121	$y^{''} - 2 y^{'} + y = x e^{x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

19122	$y^{''} - 4 y^{'} + 4 y = 8 x^{2} e^{2 x} \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

19249	$x^{2} y^{''} - 4 x y^{'} + 6 y = x^{4}$	[[_2nd_order, _with_linear_symmetries]]	✓

19254	$x^{2} y^{''} + 4 x y^{'} + 2 y = e^{x}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓

19406	$y^{''} + 2 x y^{'} + (x^{2} + 1) y = x^{3} + 3 x$	[[_2nd_order, _with_linear_symmetries]]	✓

19459	$y^{''} - 2 y^{'} + y = x \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

19461	$y^{''} - 2 y^{'} + y = x^{2} e^{3 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

19462	$y^{''} + 4 y^{'} + 4 y = 2 \sinh (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

19464	$y^{''} - 2 y^{'} + y = x \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

19508	${(x + a)}^{2} y^{''} - 4 (x + a) y^{'} + 6 y = x$	[[_2nd_order, _with_linear_symmetries]]	✓

2.4.11 second order ode solved by an integrating factor