2.3.192 Problems 19101 to 19200

Table 2.967: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
19101	1542	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	6.198
19102	9888	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (y^{2} x^{2}-1\right ) y^{\prime }+2 x y^{3}&=0 \end {array} \]	✓	✓	✓	✓	6.200
19103	5159	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a x y^{\prime }+b y+x^{m} y^{n} \left (\alpha x y^{\prime }+\beta y\right )&=0 \end {array} \]	✓	✓	✓	✓	6.201
19104	24218	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime }&=0 \end {array} \]	✓	✓	✓	✗	6.203
19105	4686	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=2 y x -x^{3}+x \end {array} \]	✓	✓	✓	✓	6.204
19106	8618	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-x y^{2} \ln \left (x \right )+y^{\prime } x&=0 \end {array} \]	✓	✓	✓	✓	6.204
19107	8441	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-x^{3}+3 x y^{2}+2 y^{3}\right ) y^{\prime }+2 x^{3}+3 x^{2} y+y^{2}-y^{3}&=0 \end {array} \]	✓	✓	✓	✓	6.205
19108	22073	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \end {array} \]	✓	✓	✓	✓	6.207
19109	24274	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}-2 y y^{\prime } x +y^{2}&=y^{2} x^{2}+x^{4} \end {array} \]	✓	✓	✓	✓	6.207
19110	5022	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+y^{2} x^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \end {array} \]	✓	✓	✓	✓	6.208
19111	25218	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \end {array} \]	✓	✓	✓	✗	6.209
19112	9127	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3} x&=1+y^{\prime } \end {array} \]	✓	✓	✓	✗	6.212
19113	1228	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}-x^{3} \left (1-y^{\prime }\right )&=0 \end {array} \]	✓	✓	✓	✗	6.214
19114	2808	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}+y^{3}-3 y y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	6.214
19115	6107	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&={y^{\prime }}^{2} {\mathrm e}^{y^{\prime }} \end {array} \]	✓	✓	✓	✗	6.214
19116	19119	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} \left (y^{\prime }-1\right )&=\left (2-y^{\prime }\right )^{2} \end {array} \]	✓	✓	✓	✓	6.215
19117	18861	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (1+{y^{\prime }}^{2}\right )&=2 \alpha \end {array} \]	✓	✓	✓	✓	6.216
19118	21051	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{4}&=4 y \left (y^{\prime } x -2 y\right )^{2} \end {array} \]	✓	✓	✓	✓	6.217
19119	7224	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=2 y^{\prime } x +\frac {x^{2}}{2}+{y^{\prime }}^{2} \end {array} \]	✓	✓	✓	✓	6.219
19120	7681	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=\frac {k \left (x +y y^{\prime }\right )}{\sqrt {1+{y^{\prime }}^{2}}} \end {array} \]	✓	✓	✓	✓	6.220
19121	24824	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x&=y y^{\prime }+a {y^{\prime }}^{2} \end {array} \]	✓	✓	✓	✗	6.222
19122	689	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=x {y^{\prime }}^{2}+{y^{\prime }}^{3} \end {array} \]	✓	✓	✓	✗	6.225
19123	3317	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=y^{\prime } x +y^{\prime }-{y^{\prime }}^{2} \end {array} \]	✓	✓	✓	✓	6.225
19124	24810	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=2 y^{\prime } x +y^{2} {y^{\prime }}^{3} \end {array} \]	✓	✓	✓	✓	6.225
19125	4638	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2} \left (x^{2}-1\right )-2 y y^{\prime } x +y^{2}-1&=0 \end {array} \]	✓	✓	✓	✓	6.226
19126	11404	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+2 y^{\prime } x +2 y&=0 \end {array} \]	✓	✓	✓	✗	6.227
19127	21864	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sqrt {y-x} \end {array} \]	✓	✓	✓	✓	6.228
19128	20510	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sqrt {y-x}+1 \end {array} \]	✓	✓	✓	✓	6.230
19129	4703	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sqrt {y} \end {array} \]	✓	✓	✓	✗	6.231
19130	11813	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\ln \left (y\right ) y \end {array} \]	✓	✓	✓	✗	6.231
19131	18742	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y \ln \left (y\right )^{2} \end {array} \]	✓	✓	✓	✗	6.231
19132	14255	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-x +\sqrt {x^{2}+2 y} \end {array} \]	✓	✓	✓	✓	6.233
19133	26267	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-x -\sqrt {x^{2}+2 y} \end {array} \]	✓	✓	✓	✓	6.233
19134	27991	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x -2 y y^{\prime }+x {y^{\prime }}^{2}&=0 \end {array} \]	✓	✓	✓	✓	6.234
19135	8877	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \end {array} \]	✓	✓	✓	✓	6.235
19136	14337	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} \left (y^{\prime }-1\right )&=\left (2-y^{\prime }\right )^{2} \end {array} \]	✓	✓	✓	✓	6.237
19137	12471	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{4}&=4 y \left (y^{\prime } x -2 y\right )^{2} \end {array} \]	✗	✗	✗	✗	6.238
19138	11885	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}-2 y y^{\prime } x +2 y x&=0 \end {array} \]	✗	✓	✓	✗	6.245
19139	26871	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&={y^{\prime }}^{2}-y^{\prime } x +\frac {x^{3}}{2} \end {array} \]	✓	✓	✓	✓	6.247
19140	13218	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=2 y^{\prime } x +\frac {x^{2}}{2}+{y^{\prime }}^{2} \end {array} \]	✓	✓	✓	✓	6.250
19141	3775	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x}&=0 \end {array} \]	✓	✓	✓	✓	6.252
19142	17973	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime \prime \prime }}^{2}+x^{2}&=1 \end {array} \]	✓	✓	✓	✗	6.253
19143	24146	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\frac {1}{\sqrt {y}} \end {array} \]	✓	✓	✓	✗	6.254
19144	1517	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a^{3} y^{\prime \prime \prime } y^{\prime \prime }&=\sqrt {1+c^{2} {y^{\prime \prime }}^{2}} \end {array} \]	✓	✓	✓	✓	6.255
19145	14690	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }&=\sqrt {1+{y^{\prime \prime }}^{2}} \end {array} \]	✓	✓	✓	✓	6.255
19146	6370	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 \left (2 a -y\right ) y^{\prime \prime }&=1+{y^{\prime }}^{2} \end {array} \]	✓	✓	✓	✗	6.257
19147	12127	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime \prime \prime }+{y^{\prime \prime \prime }}^{3}&=0 \end {array} \]	✗	✓	✓	✗	6.257
19148	3781	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime \prime }+{y^{\prime }}^{2}&=\ln \left (y\right ) y^{2} \end {array} \]	✓	✓	✓	✓	6.258
19149	22360	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \end {array} \]	✓	✓	✓	✓	6.258
19150	25750	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y y^{\prime \prime }+x {y^{\prime }}^{2}-y y^{\prime }&=0 \end {array} \]	✗	✓	✗	✗	6.258
19151	9775	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} n \,x^{3} y^{\prime \prime }&=\left (y-y^{\prime } x \right )^{2} \end {array} \]	✓	✓	✓	✗	6.259
19152	3315	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} \left (x^{2} y^{\prime \prime }-y^{\prime } x +y\right )&=x^{3} \end {array} \]	✓	✓	✓	✗	6.263
19153	11517	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{2} y^{\prime \prime }-3 y^{2} y^{\prime } x +4 y^{3}+x^{6}&=0 \end {array} \]	✓	✓	✓	✓	6.263
19154	21413	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }-x y^{2}&=0 \end {array} \]	✓	✓	✓	✓	6.264
19155	2819	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2} y^{\prime }+2 y x \right ) y^{\prime \prime }+4 x {y^{\prime }}^{2}+8 y y^{\prime } x +4 y^{2}-1&=0 \end {array} \]	✓	✓	✓	✓	6.266
19156	4426	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (y x +1\right ) y^{\prime \prime }+x^{2} {y^{\prime }}^{2}+\left (4 y x +2\right ) y^{\prime }+y^{2}+1&=0 \end {array} \]	✓	✓	✓	✓	6.266
19157	24309	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a^{2} y^{\prime \prime }&=2 x \sqrt {1+{y^{\prime }}^{2}} \end {array} \]	✓	✓	✓	✓	6.268
19158	17040	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y y^{\prime \prime }+x^{2} {y^{\prime }}^{2}-5 y y^{\prime } x&=4 y^{2} \end {array} \]	✓	✓	✓	✓	6.269
19159	25199	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime }&=0 \end {array} \]	✓	✓	✓	✗	6.269
19160	1182	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 {y^{\prime \prime \prime }}^{2}-3 y^{\prime \prime } y^{\prime \prime \prime \prime }&=0 \end {array} \]	✓	✓	✓	✓	6.273
19161	10053	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 40 {y^{\prime \prime \prime }}^{3}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+9 {y^{\prime \prime }}^{2} y^{\left (5\right )}&=0 \end {array} \]	✓	✓	✓	✓	6.276
19162	21538	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime \prime }}^{2}+2 y^{\prime \prime } x -y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	6.276
19163	13901	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime \prime }}^{2}-2 y^{\prime \prime } x -y^{\prime }&=0 \end {array} \]	✗	✗	✗	✗	6.278
19164	15219	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+12 y^{\prime } x -12 y&=0 \end {array} \]	✓	✓	✓	✓	6.278
19165	6567	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-\frac {3 y^{\prime \prime }}{x}+\frac {6 y^{\prime }}{x^{2}}-\frac {6 y}{x^{3}}&=0 \end {array} \]	✗	✗	✗	✗	6.279
19166	1172	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \end {array} \]	✓	✓	✓	✓	6.280
19167	21210	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y&=0 \end {array} \]	✓	✓	✓	✓	6.280
19168	5441	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (x \right )^{2} y^{\prime \prime }&=2 y \end {array} \]	✓	✓	✓	✓	6.284
19169	17934	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=0 \end {array} \]	✓	✓	✓	✓	6.285
19170	20589	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime } x -y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \end {array} \]	✓	✓	✓	✓	6.285
19171	11482	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime \prime }-y^{\prime \prime } x +y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	6.288
19172	10121	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=2 x^{3} \end {array} \]	✗	✗	✗	✗	6.289
19173	13783	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {x y^{\prime }}{1-x}-\frac {y}{1-x}&=-1+x \end {array} \]	✗	✗	✗	✗	6.291
19174	19928	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 y x +\left (x^{2}+2\right ) y^{\prime }-2 y^{\prime \prime } x +\left (x^{2}+2\right ) y^{\prime \prime \prime }&=x^{4}+12 \end {array} \]	✓	✓	✓	✓	6.295
19175	25002	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y^{\prime }&=0 \end {array} \]	✓	✓	✓	✓	6.296
19176	145	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=0 \end {array} \]	✓	✓	✗	✗	6.297
19177	12380	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y}{x^{2} \ln \left (x \right )}&={\mathrm e}^{x} \left (\frac {2}{x}+\ln \left (x \right )\right ) \end {array} \]	✗	✓	✓	✗	6.298
19178	12922	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+p_{1} y^{\prime }+p_{2} y&=0 \end {array} \]	✓	✓	✓	✗	6.298
19179	19797	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y&=0 \end {array} \]	✓	✓	✓	✓	6.299
19180	6236	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (x \right )^{2} y^{\prime \prime }+\cos \left (x \right ) \sin \left (x \right ) y^{\prime }&=y \end {array} \]	✓	✓	✓	✓	6.300
19181	11383	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }&=0 \end {array} \]	✗	✗	✗	✗	6.302
19182	18924	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \end {array} \]	✓	✓	✓	✓	6.304
19183	3680	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+4 y&=0 \end {array} \]	✓	✓	✓	✗	6.311
19184	27313	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-y&=0 \end {array} \]	✓	✓	✓	✓	6.311
19185	8739	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }+y^{\prime }-y&=0 \end {array} \]	✓	✓	✓	✓	6.315
19186	7706	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y&=0 \end {array} \]	✓	✓	✓	✓	6.316
19187	2958	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&=x^{2} \end {array} \]	✓	✓	✓	✓	6.317
19188	24374	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-6 y^{\prime }+8 y&={\mathrm e}^{x}+{\mathrm e}^{2 x} \end {array} \]	✓	✓	✓	✗	6.324
19189	25831	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&=x \,{\mathrm e}^{x} \end {array} \]	✓	✓	✓	✓	6.324
19190	8593	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-4 y^{\prime }+6 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&={\mathrm e}^{x} \left (x +1\right ) \end {array} \]	✓	✓	✓	✓	6.325
19191	20092	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y+y^{\prime \prime }&=\sin \left (2 x \right ) x \end {array} \]	✓	✓	✓	✓	6.326
19192	9810	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) \end {array} \]	✓	✓	✓	✗	6.328
19193	19252	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=\frac {{\mathrm e}^{x}-{\mathrm e}^{-x}}{{\mathrm e}^{x}+{\mathrm e}^{-x}} \end {array} \]	✓	✓	✓	✓	6.328
19194	19921	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y&=4 x^{2} {\mathrm e}^{x^{2}} \end {array} \]	✓	✓	✓	✓	6.329
19195	20194	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sin \left (2 x \right ) \sin \left (x \right ) \end {array} \]	✓	✓	✓	✗	6.329
19196	17041	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=\ln \left (2 \sin \left (\frac {x}{2}\right )\right ) \end {array} \]	✓	✓	✓	✓	6.330
19197	17812	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {n \left (n +1\right ) y}{x^{2}}&=0 \end {array} \]	✓	✓	✓	✓	6.332
19198	19316	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x \end {array} \]	✓	✓	✓	✗	6.334
19199	11353	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=x \ln \left (x \right ) \end {array} \]	✓	✓	✓	✗	6.335
19200	8748	\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y&=x^{2}+\frac {1}{x} \end {array} \]	✓	✓	✓	✓	6.336