higher order Euler ode

Table 2.505: higher order Euler ode


#	ODE	CAS classiﬁcation	Solved?

255	$x^{3} y^{'''} - 3 x^{2} y^{''} + 6 x y^{'} - 6 y = 0$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓

256	$x^{3} y^{'''} + 6 x^{2} y^{''} + 4 x y^{'} - 4 y = 0$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓

314	$a x^{3} y^{'''} + b x^{2} y^{''} + c x y^{'} + d y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

317	$x^{3} y^{'''} + 6 x^{2} y^{''} + 4 x y^{'} = 0$	[[_3rd_order, _missing_y]]	✓

318	$x^{3} y^{'''} - x^{2} y^{''} + x y^{'} = 0$	[[_3rd_order, _missing_y]]	✓

319	$x^{3} y^{'''} + 3 x^{2} y^{''} + x y^{'} = 0$	[[_3rd_order, _missing_y]]	✓

320	$x^{3} y^{'''} - 3 x^{2} y^{''} + x y^{'} = 0$	[[_3rd_order, _missing_y]]	✓

321	$x^{3} y^{'''} + 6 x^{2} y^{''} + 7 x y^{'} + y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓

958	$x^{3} y^{'''} + 6 x^{2} y^{''} + 4 x y^{'} = 0$	[[_3rd_order, _missing_y]]	✓

959	$x^{3} y^{'''} - x^{2} y^{''} + x y^{'} = 0$	[[_3rd_order, _missing_y]]	✓

960	$x^{3} y^{'''} + 3 x^{2} y^{''} + x y^{'} = 0$	[[_3rd_order, _missing_y]]	✓

961	$x^{3} y^{'''} - 3 x^{2} y^{''} + x y^{'} = 0$	[[_3rd_order, _missing_y]]	✓

962	$x^{3} y^{'''} + 6 x^{2} y^{''} + 7 x y^{'} + y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓

1467	$x^{3} y^{'''} + x^{2} y^{''} - 2 x y^{'} + 2 y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓

2107	$x^{3} y^{'''} - x^{2} y^{''} - 2 x y^{'} + 6 y = 0$ i.c.	[[_3rd_order, _exact, _linear, _homogeneous]]	✓

2109	$x^{3} y^{'''} - x^{2} y^{''} - 2 x y^{'} + 6 y = 0$ i.c.	[[_3rd_order, _exact, _linear, _homogeneous]]	✓

2110	$x^{3} y^{'''} - x^{2} y^{''} - 2 x y^{'} + 6 y = 0$ i.c.	[[_3rd_order, _exact, _linear, _homogeneous]]	✓

2111	$x^{3} y^{'''} - x^{2} y^{''} - 2 x y^{'} + 6 y = 0$ i.c.	[[_3rd_order, _exact, _linear, _homogeneous]]	✓

2112	$x^{3} y^{'''} - x^{2} y^{''} - 2 x y^{'} + 6 y = 0$ i.c.	[[_3rd_order, _exact, _linear, _homogeneous]]	✓

2222	$x^{3} y^{'''} - 3 x^{2} y^{''} + 6 x y^{'} - 6 y = 2 x$	[[_3rd_order, _with_linear_symmetries]]	✓

2223	$4 x^{3} y^{'''} + 4 x^{2} y^{''} - 5 x y^{'} + 2 y = 30 x^{2}$	[[_3rd_order, _with_linear_symmetries]]	✓

2224	$x^{3} y^{'''} + x^{2} y^{''} - 2 x y^{'} + 2 y = x^{2}$	[[_3rd_order, _exact, _linear, _nonhomogeneous]]	✓

2225	$16 x^{4} y^{''''} + 96 x^{3} y^{'''} + 72 x^{2} y^{''} - 24 x y^{'} + 9 y = 96 x^{5 / 2}$	[[_high_order, _with_linear_symmetries]]	✓

2226	$x^{4} y^{''''} - 4 x^{3} y^{'''} + 12 x^{2} y^{''} - 24 x y^{'} + 24 y = x^{4}$	[[_high_order, _with_linear_symmetries]]	✓

2227	$x^{4} y^{''''} + 6 x^{3} y^{'''} + 2 x^{2} y^{''} - 4 x y^{'} + 4 y = 12 x^{2}$	[[_high_order, _exact, _linear, _nonhomogeneous]]	✓

2228	$x^{3} y^{'''} - 2 x^{2} y^{''} + 3 x y^{'} - 3 y = 4 x$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓

2229	$x^{3} y^{'''} - 5 x^{2} y^{''} + 14 x y^{'} - 18 y = x^{3}$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓

2230	$x^{3} y^{'''} - 6 x^{2} y^{''} + 16 x y^{'} - 16 y = 9 x^{4}$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓

2231	$x^{3} y^{'''} + x^{2} y^{''} - 2 x y^{'} + 2 y = x (x + 1)$ i.c.	[[_3rd_order, _exact, _linear, _nonhomogeneous]]	✓

2232	$x^{4} y^{''''} + 3 x^{3} y^{'''} - x^{2} y^{''} + 2 x y^{'} - 2 y = 9 x^{2}$ i.c.	[[_high_order, _exact, _linear, _nonhomogeneous]]	✓

2233	$4 x^{4} y^{''''} + 24 x^{3} y^{'''} + 23 x^{2} y^{''} - x y^{'} + y = 6 x$ i.c.	[[_high_order, _exact, _linear, _nonhomogeneous]]	✓

2234	$x^{4} y^{''''} + 5 x^{3} y^{'''} - 3 x^{2} y^{''} - 6 x y^{'} + 6 y = 40 x^{3}$ i.c.	[[_high_order, _exact, _linear, _nonhomogeneous]]	✓

2236	$x^{3} y^{'''} + x^{2} y^{''} - 2 x y^{'} + 2 y = F (x)$	[[_3rd_order, _exact, _linear, _nonhomogeneous]]	✓

2238	$x^{4} y^{''''} + 6 x^{3} y^{'''} + 2 x^{2} y^{''} - 4 x y^{'} + 4 y = F (x)$	[[_high_order, _exact, _linear, _nonhomogeneous]]	✓

3229	$x^{3} y^{'''} + 2 x^{2} y^{''} - x y^{'} + y = \frac{1}{x}$	[[_3rd_order, _exact, _linear, _nonhomogeneous]]	✓

3233	$4 x^{3} y^{'''} + 8 x^{2} y^{''} - x y^{'} + y = x + \ln (x)$	[[_3rd_order, _with_linear_symmetries]]	✓

3234	$3 x^{3} y^{'''} + 4 x^{2} y^{''} - 10 x y^{'} + 10 y = \frac{4}{x^{2}}$	[[_3rd_order, _with_linear_symmetries]]	✓

3235	$x^{4} y^{''''} + 7 x^{3} y^{'''} + 9 x^{2} y^{''} - 6 x y^{'} - 6 y = \cos (\ln (x))$	[[_high_order, _exact, _linear, _nonhomogeneous]]	✓

3236	$x^{3} y^{'''} - 2 x^{2} y^{''} - x y^{'} + 4 y = \sin (\ln (x))$	[[_3rd_order, _linear, _nonhomogeneous]]	✓

3709	$x^{3} y^{'''} + x^{2} y^{''} - 2 x y^{'} + 2 y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓

3710	$x^{3} y^{'''} + 3 x^{2} y^{''} - 6 x y^{'} = 0$	[[_3rd_order, _missing_y]]	✓

4165	$x^{3} y^{'''} + x^{2} y^{''} - 2 x y^{'} + 2 y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓

4511	$x^{3} y^{'''} + 2 x^{2} y^{''} - x y^{'} + y = 9 x^{2} \ln (x)$	[[_3rd_order, _exact, _linear, _nonhomogeneous]]	✓

4513	$x^{3} y^{'''} + 3 x^{2} y^{''} + x y^{'} - y = x^{2}$	[[_3rd_order, _with_linear_symmetries]]	✓

6696	$x^{3} y^{'''} + x y^{'} - y = 3 x^{4}$	[[_3rd_order, _with_linear_symmetries]]	✓

6751	$x^{3} y^{'''} + 2 x^{2} y^{''} = x + \sin (\ln (x))$	[[_3rd_order, _missing_y]]	✓

6752	$x^{3} y^{'''} + x y^{'} - y = 3 x^{4}$	[[_3rd_order, _with_linear_symmetries]]	✓

6899	$x^{3} y^{'''} + 2 x^{2} y^{''} - x y^{'} + y = 12 x^{2}$	[[_3rd_order, _exact, _linear, _nonhomogeneous]]	✓

6932	$x^{3} y^{'''} + 2 x^{2} y^{''} + 20 x y^{'} - 78 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

7488	$x^{4} y^{''''} - x^{2} y^{''} + y = 0$	[[_high_order, _with_linear_symmetries]]	✓

7683	$x^{3} y^{'''} - 3 x^{2} y^{''} + 6 x y^{'} - 6 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

7703	$x^{3} y^{'''} + 2 x^{2} y^{''} - x y^{'} + y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓

8035	$x^{3} y^{'''} + 3 x^{2} y^{''} = 0$	[[_3rd_order, _missing_y]]	✓

8036	$x^{3} y^{'''} + x^{2} y^{''} - 2 x y^{'} + 2 y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓

8037	$x^{3} y^{'''} + 2 x^{2} y^{''} + x y^{'} - y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

8615	$x^{3} y^{'''} + 4 x^{2} y^{''} - 8 x y^{'} + 8 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

8876	$x^{4} y^{'''} + x^{3} y^{''} + x^{2} y^{'} + x y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

8877	$x^{4} y^{'''} + x^{3} y^{''} + x^{2} y^{'} + x y = x$	[[_3rd_order, _with_linear_symmetries]]	✓

8878	$5 x^{5} y^{''''} + 4 x^{4} y^{'''} + x^{2} y^{'} + x y = 0$	[[_high_order, _with_linear_symmetries]]	✓

11458	$x^{2} y^{'''} + 3 x y^{''} + (4 a^{2} x^{2 a} + 1 - 4 ν^{2} a^{2}) y^{'} = 4 a^{3} x^{2 a - 1} y$	[[_3rd_order, _with_linear_symmetries]]	✓

11476	$x^{3} y^{'''} + 3 x^{2} y^{''} - 2 x y^{'} + 2 y - 6 x^{3} (- 1 + x) \ln (x) + x^{3} (x + 8) = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

11479	$x^{3} y^{'''} + 6 x^{2} y^{''} + (a x^{3} - 12) y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

11482	$x^{3} y^{'''} + x^{2} y^{''} + \ln (x) + 2 x y^{'} - y - 2 x^{3} = 0$	[[_3rd_order, _linear, _nonhomogeneous]]	✓

11527	$x^{4} y^{''''} + 8 x^{3} y^{'''} + 12 x^{2} y^{''} = 0$	[[_high_order, _missing_y]]	✓

11528	$x^{4} y^{''''} + 8 x^{3} y^{'''} + 12 x^{2} y^{''} + a y = 0$	[[_high_order, _with_linear_symmetries]]	✓

12869	$x^{3} y^{'''} + x y^{'} - y = \ln (x) x$	[[_3rd_order, _with_linear_symmetries]]	✓

12870	$x^{3} y^{'''} + 2 x^{2} y^{''} + 2 y = 10 x + \frac{10}{x}$	[[_3rd_order, _exact, _linear, _nonhomogeneous]]	✓

12878	$x^{4} y^{''''} + 6 x^{3} y^{'''} + 9 x^{2} y^{''} + 3 x y^{'} + y = {(1 + \ln (x))}^{2}$	[[_high_order, _linear, _nonhomogeneous]]	✓

12884	$x^{3} y^{'''} + 2 x^{2} y^{''} - x y^{'} + y = \frac{1}{x}$	[[_3rd_order, _exact, _linear, _nonhomogeneous]]	✓

13178	$x^{3} y^{'''} + 2 x^{2} y^{''} - 10 x y^{'} - 8 y = 0$	[[_3rd_order, _fully, _exact, _linear]]	✓

13189	$x^{3} y^{'''} - 3 x^{2} y^{''} + 6 x y^{'} - 6 y = 0$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓

13319	$x^{3} y^{'''} - 4 x^{2} y^{''} + 8 x y^{'} - 8 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

13462	$x^{3} y^{'''} - 3 x^{2} y^{''} + 6 x y^{'} - 6 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

13463	$x^{3} y^{'''} + 2 x^{2} y^{''} - 10 x y^{'} - 8 y = 0$	[[_3rd_order, _fully, _exact, _linear]]	✓

13464	$x^{3} y^{'''} - x^{2} y^{''} - 6 x y^{'} + 18 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

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

13584	$t^{3} x^{'''} - 3 t^{2} x^{''} + 6 t x^{'} - 6 x = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

14265	$x^{3} y^{'''} - 3 x^{2} y^{''} + 6 x y^{'} - 6 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

15324	$x^{3} y^{'''} + 2 x^{2} y^{''} - 4 x y^{'} + 4 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

15325	$x^{3} y^{'''} + 2 x^{2} y^{''} + x y^{'} - y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

15326	$x^{3} y^{'''} - 5 x^{2} y^{''} + 14 x y^{'} - 18 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

15327	$x^{3} y^{'''} - 3 x^{2} y^{''} + 7 x y^{'} - 8 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

15328	$x^{4} y^{''''} + 6 x^{3} y^{'''} + 15 x^{2} y^{''} + 9 x y^{'} + 16 y = 0$	[[_high_order, _with_linear_symmetries]]	✓

15329	$x^{4} y^{''''} + 6 x^{3} y^{'''} - 3 x^{2} y^{''} - 9 x y^{'} + 9 y = 0$	[[_high_order, _exact, _linear, _homogeneous]]	✓

15330	$x^{4} y^{''''} + 2 x^{3} y^{'''} + x^{2} y^{''} - x y^{'} + y = 0$	[[_high_order, _with_linear_symmetries]]	✓

15331	$x^{4} y^{''''} + 6 x^{3} y^{'''} + 7 x^{2} y^{''} + x y^{'} - y = 0$	[[_high_order, _exact, _linear, _homogeneous]]	✓

15451	$x^{3} y^{'''} - 3 x^{2} y^{''} + 6 x y^{'} - 6 y = x^{3}$	[[_3rd_order, _with_linear_symmetries]]	✓

15452	$x^{3} y^{'''} - 3 x^{2} y^{''} + 6 x y^{'} - 6 y = e^{- x^{2}}$	[[_3rd_order, _with_linear_symmetries]]	✓

15455	$x^{4} y^{''''} + 6 x^{3} y^{'''} - 3 x^{2} y^{''} - 9 x y^{'} + 9 y = 12 x \sin (x^{2})$	[[_high_order, _exact, _linear, _nonhomogeneous]]	✓

16359	$2 t^{3} y^{'''} + t^{2} y^{''} + t y^{'} - y = - 3 t^{2}$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓

16373	$x^{3} y^{'''} + 22 x^{2} y^{''} + 124 x y^{'} + 140 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

16374	$x^{3} y^{'''} - 4 x^{2} y^{''} - 46 x y^{'} + 100 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

16375	$x^{3} y^{'''} + 2 x^{2} y^{''} - 4 x y^{'} + 4 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

16376	$x^{3} y^{'''} + 4 x^{2} y^{''} + 6 x y^{'} + 4 y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓

16377	$x^{3} y^{'''} + 2 x y^{'} - 2 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

16378	$x^{3} y^{'''} + 3 x^{2} y^{''} - 2 x y^{'} - 2 y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓

16379	$x^{3} y^{'''} + 6 x^{2} y^{''} + 7 x y^{'} + y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓

16389	$x^{3} y^{'''} + 3 x^{2} y^{''} - 11 x y^{'} + 16 y = \frac{1}{x^{3}}$	[[_3rd_order, _with_linear_symmetries]]	✓

16390	$x^{3} y^{'''} + 16 x^{2} y^{''} + 70 x y^{'} + 80 y = \frac{1}{x^{13}}$	[[_3rd_order, _with_linear_symmetries]]	✓

16395	$x^{3} y^{'''} + 10 x^{2} y^{''} - 20 x y^{'} + 20 y = 0$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓

16396	$x^{3} y^{'''} + 15 x^{2} y^{''} + 54 x y^{'} + 42 y = 0$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓

16397	$x^{3} y^{'''} - 2 x^{2} y^{''} + 5 x y^{'} - 5 y = 0$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓

16398	$x^{3} y^{'''} - 6 x^{2} y^{''} + 17 x y^{'} - 17 y = 0$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓

16406	$x^{3} y^{'''} + 3 x^{2} y^{''} + 37 x y^{'} = 0$	[[_3rd_order, _missing_y]]	✓

16407	$x^{3} y^{'''} + 3 x^{2} y^{''} - 3 x y^{'} = 0$	[[_3rd_order, _missing_y]]	✓

16408	$x^{3} y^{'''} + x y^{'} - y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

16409	$x^{3} y^{'''} + 3 x^{2} y^{''} - 3 x y^{'} = - 8$	[[_3rd_order, _missing_y]]	✓

16421	$x^{3} y^{'''} + 16 x^{2} y^{''} + 79 x y^{'} + 125 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

16422	$x^{4} y^{''''} + 5 x^{3} y^{'''} - 12 x^{2} y^{''} - 12 x y^{'} + 48 y = 0$	[[_high_order, _with_linear_symmetries]]	✓

16423	$x^{4} y^{''''} + 14 x^{3} y^{'''} + 55 x^{2} y^{''} + 65 x y^{'} + 15 y = 0$	[[_high_order, _exact, _linear, _homogeneous]]	✓

16424	$x^{4} y^{''''} + 8 x^{3} y^{'''} + 27 x^{2} y^{''} + 35 x y^{'} + 45 y = 0$	[[_high_order, _with_linear_symmetries]]	✓

16425	$x^{4} y^{''''} + 10 x^{3} y^{'''} + 27 x^{2} y^{''} + 21 x y^{'} + 4 y = 0$	[[_high_order, _with_linear_symmetries]]	✓

16426	$x^{3} y^{'''} + 9 x^{2} y^{''} + 44 x y^{'} + 58 y = 0$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓

17734	$x^{3} y^{'''} + x^{2} y^{''} - 2 x y^{'} + 2 y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓

17914	$2 x^{3} y^{'''} - 6 x^{2} y^{''} + 12 x y^{'} - 12 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

17915	$y^{'''} - \frac{3 y^{''}}{x} + \frac{6 y^{'}}{x^{2}} - \frac{6 y}{x^{3}} = 0$	[[_3rd_order, _fully, _exact, _linear]]	✓

17919	$x^{3} y^{'''} - 3 x^{2} y^{''} + 6 x y^{'} - 6 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

17951	$x^{3} y^{'''} - x^{2} y^{''} + 2 x y^{'} - 2 y = x^{3} + 3 x$	[[_3rd_order, _with_linear_symmetries]]	✓

18297	$x^{3} y^{'''} + 3 x^{2} y^{''} = 0$	[[_3rd_order, _missing_y]]	✓

18298	$x^{3} y^{'''} + x^{2} y^{''} - 2 x y^{'} + 2 y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓

18299	$x^{3} y^{'''} + 2 x^{2} y^{''} + x y^{'} - y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

18511	$x^{4} y^{''''} + x^{3} y^{'''} - 20 x^{2} y^{''} + 20 x y^{'} = 17 x^{6}$	[[_high_order, _missing_y]]	✓

18512	$t^{4} x^{''''} - 2 t^{3} x^{'''} - 20 t^{2} x^{''} + 12 t x^{'} + 16 x = \cos (3 \ln (t))$	[[_high_order, _exact, _linear, _nonhomogeneous]]	✓

18519	$x^{3} y^{'''} + x^{2} y^{''} + x y^{'} + y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

18538	$x^{3} v^{'''} + 2 x^{2} v^{''} + v = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

18605	$x^{3} y^{'''} + 7 x^{2} y^{''} + 8 x y^{'} = \ln {(x)}^{2}$	[[_3rd_order, _missing_y]]	✓

18607	$x^{3} y^{'''} - 3 x^{2} y^{''} + 6 x y^{'} - 6 y = x^{3}$	[[_3rd_order, _with_linear_symmetries]]	✓

18608	$x^{3} y^{'''} + 2 x^{2} y^{''} - 4 x y^{'} + 4 y = \ln (x)$	[[_3rd_order, _with_linear_symmetries]]	✓

18609	$x^{3} y^{'''} + 4 x^{2} y^{''} + x y^{'} - y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓

18846	$x^{3} y^{'''} + 3 x^{2} y^{''} + x y^{'} + y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓

18847	$x^{4} y^{''''} + 6 x^{3} y^{'''} + 9 x^{2} y^{''} + 3 x y^{'} + y = 0$	[[_high_order, _with_linear_symmetries]]	✓

18854	$y^{'''} - \frac{4 y^{''}}{x} + \frac{5 y^{'}}{x^{2}} - \frac{2 y}{x^{3}} = 1$	[[_3rd_order, _exact, _linear, _nonhomogeneous]]	✓

18856	$x^{3} y^{'''} - 3 x^{2} y^{''} + 7 x y^{'} - 8 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

18858	$x^{3} y^{'''} + 6 x^{2} y^{''} + 4 x y^{'} - 4 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

18859	$x^{3} y^{'''} + 2 x^{2} y^{''} + 2 y = 10 c + \frac{10}{x}$	[[_3rd_order, _exact, _linear, _nonhomogeneous]]	✓

18863	$x^{4} y^{''''} + 6 x^{3} y^{'''} + 9 x^{2} y^{''} + 3 x y^{'} + y = {(1 + \ln (x))}^{2}$	[[_high_order, _linear, _nonhomogeneous]]	✓

18864	$x^{4} y^{'''} + 2 x^{3} y^{''} - x^{2} y^{'} + x y = 1$	[[_3rd_order, _with_linear_symmetries]]	✓

19238	$x^{3} y^{'''} + 4 x^{2} y^{''} - 2 y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓

19240	$x^{3} y^{'''} - 3 x^{2} y^{''} + 6 x y^{'} - 6 y = \ln {(x)}^{2}$	[[_3rd_order, _with_linear_symmetries]]	✓

19241	$y^{'''} - \frac{4 y^{''}}{x} + \frac{5 y^{'}}{x^{2}} - \frac{2 y}{x^{3}} = 1$	[[_3rd_order, _exact, _linear, _nonhomogeneous]]	✓

19243	$x^{3} y^{'''} - 3 x^{2} y^{''} + 7 x y^{'} - 8 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

19257	$x^{4} y^{''''} + 6 x^{3} y^{'''} + 9 x^{2} y^{''} + 3 x y^{'} + y = 4 x$	[[_high_order, _with_linear_symmetries]]	✓

19258	$x^{3} y^{'''} + 6 x^{2} y^{''} + 8 x y^{'} + 2 y = x^{2} + 3 x - 4$	[[_3rd_order, _exact, _linear, _nonhomogeneous]]	✓

19260	$x^{3} y^{'''} - 3 x^{2} y^{''} + 7 x y^{'} - 8 y = x^{2} + \frac{1}{x^{2}}$	[[_3rd_order, _reducible, _mu_y2]]	✓

19261	$x^{4} y^{''''} + 2 x^{3} y^{'''} + x^{2} y^{''} - x y^{'} + y = x + \ln (x)$	[[_high_order, _with_linear_symmetries]]	✓

19264	$x^{3} y^{'''} + 2 x^{2} y^{''} - x y^{'} + y = \ln (x) x$	[[_3rd_order, _exact, _linear, _nonhomogeneous]]	✓

19265	$x^{4} y^{''''} + 6 x^{3} y^{'''} + 9 x^{2} y^{''} + 3 x y^{'} + y = {(1 + \ln (x))}^{2}$	[[_high_order, _linear, _nonhomogeneous]]	✓

19271	$x^{3} y^{'''} + 6 x^{2} y^{''} + 8 x y^{'} + 2 y = x^{2} + 3 x - 4$	[[_3rd_order, _exact, _linear, _nonhomogeneous]]	✓

19290	$x^{3} y^{'''} = 1$	[[_3rd_order, _quadrature]]	✓

19335	$n x^{3} y^{'''} = y - x y^{'}$	[[_3rd_order, _with_linear_symmetries]]	✓

19363	$x^{3} y^{'''} + x^{2} y^{''} - 2 x y^{'} + 2 y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓

19499	$x^{4} y^{'''} + 2 x^{3} y^{''} - x^{2} y^{'} + x y = 1$	[[_3rd_order, _with_linear_symmetries]]	✓

19501	$x^{3} y^{'''} - x^{2} y^{''} + 2 x y^{'} - 2 y = x^{2} + 3 x$	[[_3rd_order, _with_linear_symmetries]]	✓

19502	$x^{3} y^{'''} + 6 x^{2} y^{''} + 4 x y^{'} - 4 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✓

19503	$x^{3} y^{'''} + 3 x^{2} y^{''} + x y^{'} + y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓

19505	$x^{3} y^{'''} + 2 x^{2} y^{''} + 2 y = 10 x + \frac{10}{x}$	[[_3rd_order, _exact, _linear, _nonhomogeneous]]	✓

2.5.2 higher order Euler ode