second order ode solved by an integrating factor

Table 2.473: second order ode solved by an integrating factor


#	ODE	ODE 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	$x^{2} y^{''} - 2 y^{'} x + 2 y = 0$ 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	$x^{2} y^{''} - 2 y^{'} x + 2 y = 0$	[[_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	$x^{2} y^{''} - 4 y^{'} x + 6 y = x^{3}$	[[_2nd_order, _with_linear_symmetries]]	✓

379	$4 x^{2} y^{''} - 4 y^{'} x + 3 y = 8 x^{4 / 3}$	[[_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	$x^{2} y^{''} - 2 y^{'} x + 2 y = 0$ 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	$x^{2} y^{''} - 4 y^{'} x + 6 y = x^{3}$	[[_2nd_order, _with_linear_symmetries]]	✓

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

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

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

1297	$t^{2} y^{''} - 4 y^{'} t + 6 y = 0$	[[_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	$t^{2} y^{''} - 2 y^{'} t + 2 y = 4 t^{2}$	[[_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	$(x^{2} - 1) y^{''} + 4 y^{'} x + 2 y = 0$ 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	$(x^{2} - 4) y^{''} + 4 y^{'} x + 2 y = 0$	[[_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	$y^{''} + 4 y^{'} x + (4 x^{2} + 2) y = 4 e^{- x (x + 2)}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

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

1835	${(x - 1)}^{2} y^{''} - 2 (x - 1) y^{'} + 2 y = {(x - 1)}^{2}$ 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	$y^{''} - 4 y^{'} t + (4 t^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓

2403	$y^{''} - 4 y^{'} + 4 y = e^{2 t} t$	[[_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	$y^{''} - 4 y^{'} + 4 y = e^{2 t} t$	[[_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	$x^{2} y^{''} - 2 y^{'} x + 2 y = 4 x + \sin (\ln (x))$	[[_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	$x^{2} y^{''} - 4 y^{'} x + 6 y = x^{4} \sin (x)$	[[_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	$x^{2} y^{''} + 4 y^{'} x + 2 y = 4 \ln (x)$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓

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

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

3778	$x^{2} y^{''} + 6 y^{'} x + 6 y = 4 e^{2 x}$	[[_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	$x^{2} y^{''} - 2 y^{'} x + 2 y = x^{2} + 2$	[[_2nd_order, _with_linear_symmetries]]	✓

4141	$y^{''} + 2 n y^{'} + n^{2} y = A \cos (p x)$ 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	$y^{''} - 4 y^{'} + 4 y = e^{x} (x + 1) + 2 e^{2 x} + 3 e^{3 x}$	[[_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	$y^{''} - \frac{2 y^{'}}{x} + \frac{2 y}{x^{2}} = x \ln (x)$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓

6026	$x^{2} y^{''} - 2 y^{'} x + 2 y = 0$	[[_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	$y^{''} + 2 y^{'} + y = 4 e^{x} + (1 - x) (- 1 + e^{2 x})$	[[_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	$y^{''} - 4 y^{'} x + (4 x^{2} - 2) y = 0$	[[_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	$x^{2} y^{''} - 2 y^{'} x + 2 y = \ln {(x)}^{2} - \ln (x^{2})$	[[_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	$x^{2} y^{''} - 2 y^{'} x + 2 y = x e^{- x}$	[[_2nd_order, _with_linear_symmetries]]	✓

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

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

8067	$x^{2} y^{''} - 2 y^{'} x + 2 y = 0$ 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	$y^{''} + 2 y^{'} x + (x^{2} + 1) y = 0$	[[_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	$x^{2} y^{''} - 4 y^{'} x + 6 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

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

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


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

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

11210	$(x^{2} + 1) y^{''} + 4 y^{'} x + 2 y - 2 \cos (x) + 2 x = 0$	[[_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]]	✓

12861	$y^{''} - 2 y^{'} + y = \frac{e^{x}}{{(1 - x)}^{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

12869	$y^{''} - 2 y^{'} + y = 2 x e^{2 x} - \sin {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

12871	$y^{''} + 2 y^{'} + y = 3 e^{2 x} - \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

12883	$y^{''} + 2 y^{'} + y = 2 x^{3} - x e^{3 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

12930	${(x - 1)}^{2} y^{''} + 4 (x - 1) y^{'} + 2 y = \cos (x)$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓

13041	$x^{''} - 4 x^{'} + 4 x = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

13043	$\frac{x^{''}}{2} + x^{'} + \frac{x}{2} = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

13045	$x^{''} - 4 x^{'} + 4 x = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

13047	$\frac{x^{''}}{2} + x^{'} + \frac{x}{2} = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

13086	$t x^{''} + 4 x^{'} + \frac{2 x}{t} = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

13097	$x^{''} - 2 x^{'} + x = \frac{e^{t}}{2 t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

13178	$(x^{2} + 1) y^{''} + 4 y^{'} x + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓

13188	$y^{''} - 4 y^{'} + 4 y = - 8 \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

13322	$y^{''} - 2 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

13323	$x^{2} y^{''} - 2 y^{'} x + 2 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

13342	$y^{''} - 8 y^{'} + 16 y = 0$	[[_2nd_order, _missing_x]]	✓

13343	$4 y^{''} + 4 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

13364	$y^{''} + 6 y^{'} + 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

13365	$4 y^{''} - 12 y^{'} + 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

13366	$y^{''} + 4 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

13367	$9 y^{''} - 6 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

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

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

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

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

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

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

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

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

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

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

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

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

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

13680	$y^{''} - 4 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

13687	$y^{''} + 2 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

13692	$y^{''} + 4 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

13698	$x^{''} + 2 x^{'} + x = e^{- t}$	[[_2nd_order, _with_linear_symmetries]]	✓

13704	$x^{''} + 4 x^{'} + 4 x = e^{2 t}$	[[_2nd_order, _with_linear_symmetries]]	✓

13725	$x^{2} y^{''} - 4 y^{'} x + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

13833	$x^{2} y^{''} - 4 y^{'} x + 6 y = 2$	[[_2nd_order, _with_linear_symmetries]]	✓

13836	$x^{''} - 4 x^{'} + 4 x = e^{t} + e^{2 t} + 1$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

13852	$y^{''} + 2 y^{'} + y = \sinh (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

13864	$x^{''} + 10 x^{'} + 25 x = 2^{t} + t e^{- 5 t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

13926	$y^{''} + 4 y^{'} x + (4 x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓

13933	$x \ln (x) y^{''} + 2 y^{'} - \frac{y}{x} = 1$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓

14021	$y^{''} + 2 y^{'} + y = 1$	[[_2nd_order, _missing_x]]	✓

14061	$y^{''} - 2 y^{'} + y = x^{3 / 2} e^{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

14088	$y^{''} - 2 k y^{'} + k^{2} y = e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓

14170	$y^{''} - 4 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓

14173	$4 y^{''} - 12 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

14187	$y^{''} - 2 a y^{'} + a^{2} y = e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓

14253	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

14274	$x^{2} y^{''} - 4 y^{'} x + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

14275	$x^{2} y^{''} - 4 y^{'} x + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

14276	$x^{2} y^{''} - 4 y^{'} x + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

14277	$x^{2} y^{''} - 4 y^{'} x + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

14278	$x^{2} y^{''} - 4 y^{'} x + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

14824	$y^{''} + 2 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

14844	$y^{''} + 2 y^{'} + y = e^{- t}$	[[_2nd_order, _with_linear_symmetries]]	✓

14875	$y^{''} + 2 y^{'} + y = \cos (3 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

14879	$y^{''} + 2 y^{'} + y = 2 \cos (2 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15228	$y^{''} - 4 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

15229	$x^{2} y^{''} - 4 y^{'} x + 6 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

15230	$4 x^{2} y^{''} + 4 y^{'} x - y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

15233	${(x + 1)}^{2} y^{''} - 2 (x + 1) y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

15234	$x^{2} y^{''} - 4 y^{'} x + 6 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

15256	$y^{''} - 10 y^{'} + 25 y = 0$	[[_2nd_order, _missing_x]]	✓

15257	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

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

15259	$25 y^{''} - 10 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

15260	$16 y^{''} - 24 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

15261	$9 y^{''} + 12 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓

15262	$y^{''} - 8 y^{'} + 16 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

15263	$y^{''} - 8 y^{'} + 16 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

15264	$y^{''} - 8 y^{'} + 16 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

15265	$4 y^{''} + 4 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

15266	$4 y^{''} + 4 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

15267	$4 y^{''} + 4 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

15327	$4 x^{2} y^{''} + 4 y^{'} x - y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

15347	$y^{''} + 6 y^{'} + 9 y = 169 \sin (2 x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15348	$x^{2} y^{''} - 4 y^{'} x + 6 y = 10 x + 12$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓

15354	$x^{2} y^{''} - 4 y^{'} x + 6 y = 1$	[[_2nd_order, _with_linear_symmetries]]	✓

15355	$x^{2} y^{''} - 4 y^{'} x + 6 y = x$	[[_2nd_order, _with_linear_symmetries]]	✓

15356	$x^{2} y^{''} - 4 y^{'} x + 6 y = 22 x + 24$	[[_2nd_order, _with_linear_symmetries]]	✓

15362	$y^{''} - 6 y^{'} + 9 y = 27 e^{6 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

15367	$y^{''} - 6 y^{'} + 9 y = 25 \sin (6 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15373	$y^{''} - 6 y^{'} + 9 y = 18 x^{2} + 3 x + 4$	[[_2nd_order, _with_linear_symmetries]]	✓

15377	$y^{''} - 6 y^{'} + 9 y = e^{2 x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15380	$y^{''} - 2 y^{'} + y = (- 6 x - 8) \cos (2 x) + (8 x - 11) \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15381	$y^{''} - 2 y^{'} + y = (12 x - 4) e^{- 5 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15387	$y^{''} - 6 y^{'} + 9 y = 10 e^{3 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

15390	$y^{''} - 10 y^{'} + 25 y = 6 e^{5 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

15391	$y^{''} - 10 y^{'} + 25 y = 6 e^{- 5 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

15414	$y^{''} - 10 y^{'} + 25 y = 3 x^{2} e^{5 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15415	$y^{''} - 10 y^{'} + 25 y = 3 x^{4}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15430	$y^{''} - 6 y^{'} + 9 y = 27 e^{6 x} + 25 \sin (6 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15442	$x^{2} y^{''} - 2 y^{'} x + 2 y = 3 \sqrt{x}$	[[_2nd_order, _with_linear_symmetries]]	✓

15446	$y^{''} - 4 y^{'} + 4 y = (24 x^{2} + 2) e^{2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15447	$y^{''} + 4 y^{'} + 4 y = \frac{e^{- 2 x}}{x^{2} + 1}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15465	$y^{''} - 12 y^{'} + 36 y = 0$	[[_2nd_order, _missing_x]]	✓

15472	$y^{''} + 6 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

15484	$16 y^{''} - 8 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

15491	$y^{''} + 20 y^{'} + 100 y = 0$	[[_2nd_order, _missing_x]]	✓

15495	$y^{''} - 12 y^{'} + 36 y = 25 \sin (3 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15497	$y^{''} - 12 y^{'} + 36 y = 81 e^{3 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

15499	$y^{''} - 12 y^{'} + 36 y = 3 x e^{6 x} - 2 e^{6 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15502	$y^{''} + 6 y^{'} + 9 y = 10 e^{- 3 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

15504	$y^{''} + 6 y^{'} + 9 y = 2 \cos (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15508	$4 y^{''} - 12 y^{'} + 9 y = x e^{\frac{3 x}{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

15729	$x^{2} y^{''} - 12 y^{'} x + 42 y = 0$	[[_Emden, _Fowler]]	✓

15755	$t^{2} y^{''} - 12 y^{'} t + 42 y = 0$ i.c.	[[_Emden, _Fowler]]	✓

16107	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

16148	$4 y^{''} + 4 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

16149	$y^{''} - 6 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

16158	$y^{''} - 2 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

16159	$y^{''} + 4 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

16167	$9 y^{''} + 6 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

16184	$y^{''} - 2 y^{'} + y = t^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓

16204	$y^{''} + 4 y^{'} + 4 y = - 32 t^{2} \cos (2 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16218	$y^{''} + 8 y^{'} + 16 y = 4$ i.c.	[[_2nd_order, _missing_x]]	✓

16256	$y^{''} - 2 y^{'} + y = \frac{e^{t}}{t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

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

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

16259	$y^{''} + 6 y^{'} + 9 y = \frac{e^{- 3 t}}{t}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16260	$y^{''} + 6 y^{'} + 9 y = e^{- 3 t} \ln (t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16262	$y^{''} + 4 y^{'} + 4 y = e^{- 2 t} \sqrt{- t^{2} + 1}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16263	$y^{''} - 2 y^{'} + y = e^{t} \sqrt{- t^{2} + 1}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16264	$y^{''} - 10 y^{'} + 25 y = e^{5 t} \ln (2 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16265	$y^{''} - 4 y^{'} + 4 y = e^{2 t} \arctan (t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16266	$y^{''} + 8 y^{'} + 16 y = \frac{e^{- 4 t}}{t^{2} + 1}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16286	$4 y^{''} + 4 y^{'} + y = e^{- \frac{t}{2}}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓

16408	$x^{2} y^{''} + 4 y^{'} x + 2 y = \ln (x)$ i.c.	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓

16412	$x^{2} y^{''} + 4 y^{'} x + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓

16425	$x^{2} y^{''} + 4 y^{'} x + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓

16494	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

16528	$y^{''} - 8 y^{'} + 16 y = \frac{e^{4 t}}{t^{3}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16529	$y^{''} - 8 y^{'} + 16 y = \frac{e^{4 t}}{t^{3}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16530	$y^{''} - 2 y^{'} + y = e^{t} \ln (t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16531	$y^{''} - 2 y^{'} + y = e^{t} \ln (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16534	$y^{''} + 4 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓

16537	$x^{2} y^{''} - 4 y^{'} x + 6 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

16590	$x^{''} + 6 x^{'} + 9 x = 0$	[[_2nd_order, _missing_x]]	✓

16884	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

16907	$y^{''} - 8 y^{'} + 16 y = (1 - x) e^{4 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16908	$y^{''} - 10 y^{'} + 25 y = e^{5 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

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

16947	$y^{''} - 4 y^{'} + 4 y = x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓

16949	$y^{''} - 2 k y^{'} + k^{2} y = e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓

16950	$y^{''} + 4 y^{'} + 4 y = 8 e^{- 2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

16959	$y^{''} - 2 m y^{'} + m^{2} y = \sin (n x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16971	$y^{''} - 2 y^{'} + y = x^{3}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16974	$y^{''} + 2 y^{'} + y = x^{2} e^{- x} \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

16989	$y^{''} - 2 y^{'} + y = 2 + e^{x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

17007	$y^{''} - 4 y^{'} + 4 y = 4 x + \sin (x) + \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

17008	$y^{''} + 2 y^{'} + y = 1 + 2 \cos (x) + \cos (2 x) - \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

17010	$y^{''} + 6 y^{'} + 9 y = 18 e^{- 3 x} + 8 \sin (x) + 6 \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

17019	$y^{''} - 6 y^{'} + 9 y = 9 x^{2} - 12 x + 2$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓

17021	$y^{''} - 4 y^{'} + 4 y = 2 e^{2 x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓

17024	$y^{''} + 6 y^{'} + 9 y = 10 \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓

17029	$y^{''} - 6 y^{'} + 9 y = 16 e^{- x} + 9 x - 6$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓

17061	$x^{2} y^{''} + 4 y^{'} x + 2 y = 2 \ln {(x)}^{2} + 12 x$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓

17081	$y^{''} - 2 y^{'} + y = \frac{e^{x}}{x^{2} + 1}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

17101	$x^{''} + 2 x^{'} + x = 0$	[[_2nd_order, _missing_x]]	✓

17154	$y^{''} - 4 y^{'} + 4 y = π^{2} - x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓

17156	$y^{''} - 4 y^{'} + 4 y = \arcsin (\sin (x))$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

17497	$y^{''} - 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

17514	$y^{''} - 4 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓

17515	$9 y^{''} + 6 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

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

17521	$9 y^{''} + 12 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓

17526	$25 y^{''} - 20 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓

17532	$y^{''} + 4 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓

17533	$9 y^{''} - 24 y^{'} + 16 y = 0$	[[_2nd_order, _missing_x]]	✓

17540	$9 y^{''} - 12 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

17544	$y^{''} + 6 y^{'} + 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

17548	$y^{''} + 4 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

17557	$x^{2} y^{''} + 4 y^{'} x + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓

17576	$y^{''} + 2 y^{'} + y = 2 e^{- t}$	[[_2nd_order, _with_linear_symmetries]]	✓

17579	$y^{''} + 2 y^{'} + y = 3 e^{- t}$	[[_2nd_order, _with_linear_symmetries]]	✓

17580	$4 y^{''} - 4 y^{'} + y = 16 e^{\frac{t}{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓

17588	$y^{''} - 2 y^{'} + y = e^{t} t + 4$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓

17596	$y^{''} - 4 y^{'} + 4 y = 2 t^{2} + 4 e^{2 t} t + t \sin (2 t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

17603	$x^{2} y^{''} - 2 y^{'} x + 2 y = 3 x^{2} + 2 \ln (x)$	[[_2nd_order, _with_linear_symmetries]]	✓

17618	$y^{''} + 2 y^{'} + y = 3 e^{- t}$	[[_2nd_order, _with_linear_symmetries]]	✓

17619	$4 y^{''} - 4 y^{'} + y = 16 e^{\frac{t}{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓

17622	$y^{''} + 4 y^{'} + 4 y = \frac{e^{2 t}}{t^{2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

17625	$y^{''} - 2 y^{'} + y = \frac{e^{t}}{t^{2} + 1}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

17636	$t^{2} y^{''} - 2 y^{'} t + 2 y = 4 t^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓

17930	$x^{2} y^{''} - 2 y^{'} x + 2 y = 2 x^{3}$	[[_2nd_order, _with_linear_symmetries]]	✓

17945	$y^{''} - 4 y^{'} + 4 y = x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓

17956	$x^{2} y^{''} - 4 y^{'} x + 6 y = x$	[[_2nd_order, _with_linear_symmetries]]	✓

18192	$x^{2} y^{''} - 2 y^{'} x + 2 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

18194	$y^{''} - 4 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓

18200	$y^{''} + 2 y^{'} x + (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓

18218	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

18221	$y^{''} - 4 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓

18224	$4 y^{''} - 12 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓

18227	$4 y^{''} + 20 y^{'} + 25 y = 0$	[[_2nd_order, _missing_x]]	✓

18232	$16 y^{''} - 8 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

18237	$y^{''} - 6 y^{'} + 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

18254	$y^{''} + 10 y^{'} + 25 y = 14 e^{- 5 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

18260	$y^{''} - 2 y^{'} + y = 6 e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓

18266	$y^{''} - 2 y^{'} + y = 2 x$	[[_2nd_order, _with_linear_symmetries]]	✓

18269	$y^{''} + 2 y^{'} + y = e^{- x} \ln (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

18285	$x^{2} y^{''} - 2 y^{'} x + 2 y = x e^{- x}$	[[_2nd_order, _with_linear_symmetries]]	✓

18311	$y^{''} + 4 y^{'} + 4 y = 10 x^{3} e^{- 2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

18312	$y^{''} - 2 y^{'} + y = e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓

18326	$y^{''} + 2 y^{'} + y = 2 x^{2} e^{- 2 x} + 3 e^{2 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

18335	$y^{''} - 4 y^{'} + 4 y = e^{2 x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

18442	$t^{2} x^{''} - 6 x^{'} t + 12 x = 0$	[[_Emden, _Fowler]]	✓

18445	$t^{2} x^{''} - 2 x^{'} t + 2 x = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

18447	$x^{''} - 4 x^{'} + 4 x = 0$	[[_2nd_order, _missing_x]]	✓

18452	$x^{''} + 2 x^{'} + x = 0$ i.c.	[[_2nd_order, _missing_x]]	✓

18547	$v^{''} + \frac{2 x v^{'}}{x^{2} + 1} + \frac{v}{{(x^{2} + 1)}^{2}} = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

18599	$y^{''} - 2 y^{'} + y = e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓

18600	$y^{''} - 2 y^{'} + y = x$	[[_2nd_order, _with_linear_symmetries]]	✓

18620	$(x^{2} - 1) y^{''} + 4 y^{'} x + 2 y = 2 x$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓

18621	$(x^{2} + 1) y^{''} + 4 y^{'} x + 2 y = x$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓

18624	$(3 x^{2} + x) y^{''} + 2 (1 + 6 x) y^{'} + 6 y = \sin (x)$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓

18653	$y^{''} - \frac{2 y^{'}}{x} + \frac{2 y}{x^{2}} = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓

18807	$y^{''} + 2 y^{'} + y = 2 e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓

18811	$y^{''} - 2 y^{'} + y = 3 e^{\frac{5 x}{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓

18835	$y^{''} - 2 y^{'} + y = x^{2} e^{3 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

18863	$x^{2} y^{''} + 4 y^{'} x + 2 y = e^{x}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓

18865	${(x + a)}^{2} y^{''} - 4 (x + a) y^{'} + 6 y = x$	[[_2nd_order, _with_linear_symmetries]]	✓

19094	$y^{''} + 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓

19106	$y^{''} - 2 y^{'} + y = 2 e^{\frac{5 x}{2}}$	[[_2nd_order, _with_linear_symmetries]]	✓

19126	$y^{''} + 2 y^{'} + y = x \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

19129	$y^{''} - 2 y^{'} + y = x e^{x} \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

19130	$y^{''} - 4 y^{'} + 4 y = 8 x^{2} e^{2 x} \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

19257	$x^{2} y^{''} - 4 y^{'} x + 6 y = x^{4}$	[[_2nd_order, _with_linear_symmetries]]	✓

19262	$x^{2} y^{''} + 4 y^{'} x + 2 y = e^{x}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓

19414	$y^{''} + 2 y^{'} x + (x^{2} + 1) y = x^{3} + 3 x$	[[_2nd_order, _with_linear_symmetries]]	✓

19467	$y^{''} - 2 y^{'} + y = x \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

19469	$y^{''} - 2 y^{'} + y = x^{2} e^{3 x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

19470	$y^{''} + 4 y^{'} + 4 y = 2 \sinh (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

19472	$y^{''} - 2 y^{'} + y = x \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓

19516	${(x + a)}^{2} y^{''} - 4 (x + a) y^{'} + 6 y = x$	[[_2nd_order, _with_linear_symmetries]]	✓

2.4.11 second order ode solved by an integrating factor