2.3.133 Problems 13201 to 13300

Table 2.815: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
13201	18386	\begin{align*} 4 y^{\prime \prime } x +2 y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.276
13202	20125	\begin{align*} y^{\prime \prime }&=x^{2} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.276
13203	24814	\begin{align*} y&=x^{6} {y^{\prime }}^{3}-y^{\prime } x \\ \end{align*}	✓	✓	✗	✗	1.276
13204	79	\begin{align*} 2 y^{\prime } x +y&=10 \sqrt {x} \\ \end{align*}	✓	✓	✓	✓	1.277
13205	6865	\begin{align*} x^{2}+y^{2}-2 y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.277
13206	9903	\begin{align*} x^{2} y^{\prime \prime }+x \left (3+2 x \right ) y^{\prime }+\left (1+3 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.277
13207	13816	\begin{align*} n \left (n +2\right ) y-3 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.277
13208	15088	\begin{align*} y y^{\prime } y^{\prime \prime }&={y^{\prime }}^{3}+{y^{\prime \prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.277
13209	18826	\begin{align*} y^{\prime \prime }+y&=3 \sin \left (2 t \right )+t \cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.277
13210	20910	\begin{align*} y^{\prime \prime } x -\left (x +4\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.277
13211	23923	\begin{align*} \left (2+x \right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	1.277
13212	25201	\begin{align*} \left (t -1\right ) y^{\prime \prime }-y^{\prime } t +y&=2 t \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.277
13213	25532	\begin{align*} y^{\prime }&=a y \\ \end{align*}	✓	✓	✓	✓	1.277
13214	9141	\begin{align*} 1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.278
13215	2193	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+26 y^{\prime \prime }-40 y^{\prime }+25 y&={\mathrm e}^{2 x} \left (3 \cos \left (x \right )-\left (1+3 x \right ) \sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	1.279
13216	13889	\begin{align*} \left (a \,x^{2}+b \right )^{2} y^{\prime \prime }+\left (2 a x +c \right ) \left (a \,x^{2}+b \right ) y^{\prime }+k y&=0 \\ \end{align*}	✓	✓	✓	✗	1.279
13217	21993	\begin{align*} y^{\prime }&=5 y \\ \end{align*}	✓	✓	✓	✓	1.279
13218	6282	\begin{align*} A y+\left (c \,x^{2}+b x +a \right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.280
13219	14188	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-\frac {y^{\prime }}{x}+x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.280
13220	23783	\begin{align*} x^{\prime }&=a x+b y \\ y^{\prime }&=c x+d y \\ \end{align*}	✓	✓	✓	✓	1.280
13221	5719	\begin{align*} y^{\prime \prime }+y&=8 \cos \left (x \right ) \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.281
13222	25582	\begin{align*} y^{\prime \prime }+2 p y^{\prime }+\omega _{n}^{2} y&=\omega _{n}^{2} t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.281
13223	7301	\begin{align*} y^{\prime \prime }+y&=x^{3}-1+2 \cos \left (x \right )+\left (2-4 x \right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.282
13224	8312	\begin{align*} y^{\prime }&=\frac {1}{y} \\ y \left (-2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.282
13225	20876	\begin{align*} x^{\prime \prime }+x&=2 \tan \left (t \right ) \\ x \left (0\right ) &= 4 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.282
13226	25202	\begin{align*} \left (t -1\right ) y^{\prime \prime }-y^{\prime } t +y&=2 t \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.282
13227	25480	\begin{align*} y^{\prime }&=y \left (1-\ln \left (y\right )\right ) \\ \end{align*}	✓	✓	✓	✓	1.282
13228	231	\begin{align*} y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.283
13229	1596	\begin{align*} y^{\prime }&=2 y-y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.283
13230	8991	\begin{align*} 4 x^{2} y^{\prime \prime }+\left (4 x^{4}-5 x \right ) y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.283
13231	15888	\begin{align*} y^{\prime }&=y^{2}-4 y+2 \\ y \left (0\right ) &= -4 \\ \end{align*}	✓	✓	✗	✓	1.283
13232	18037	\begin{align*} {y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x}&=0 \\ \end{align*}	✓	✓	✓	✗	1.283
13233	21234	\begin{align*} x^{\prime }&=\left (a -2\right ) x+y \\ y^{\prime }&=-x+\left (a -2\right ) y \\ z^{\prime }&=-a z \\ \end{align*}	✓	✓	✓	✓	1.283
13234	22322	\begin{align*} y^{\prime }&=y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.283
13235	5044	\begin{align*} y y^{\prime }&=a_{0} +a_{1} y+a_{2} y^{2} \\ \end{align*}	✓	✓	✓	✓	1.284
13236	9937	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (x^{3}+x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.284
13237	18437	\begin{align*} x^{\prime }&=x+y-\cos \left (t \right ) \\ y^{\prime }&=-y-2 x+\cos \left (t \right )+\sin \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	1.284
13238	810	\begin{align*} y^{\prime \prime }+25 y&=0 \\ y \left (0\right ) &= 10 \\ y^{\prime }\left (0\right ) &= -10 \\ \end{align*}	✓	✓	✓	✓	1.285
13239	5579	\begin{align*} y^{2} {y^{\prime }}^{2}-2 y y^{\prime } x +a -x^{2}+2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.286
13240	7649	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	1.286
13241	15526	\begin{align*} y^{\prime }&=1-y \\ \end{align*}	✓	✓	✓	✓	1.286
13242	20650	\begin{align*} 2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=x^{3} \\ \end{align*}	✓	✓	✓	✗	1.286
13243	21522	\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (x \right )+\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.286
13244	24589	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{x}-x +\sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.286
13245	24926	\begin{align*} y^{\prime \prime }&=2 t +1 \\ \end{align*}	✓	✓	✓	✓	1.286
13246	26241	\begin{align*} \cos \left (y^{\prime }\right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.286
13247	18965	\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2}+4 x_{3} \\ x_{2}^{\prime }&=3 x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\ \end{align*}	✓	✓	✓	✓	1.287
13248	25223	\begin{align*} 2 t^{2} y^{\prime \prime }-5 y^{\prime } t +3 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.288
13249	16563	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.289
13250	18877	\begin{align*} t^{2} y^{\prime \prime }-2 y&=3 t^{2}-1 \\ \end{align*}	✓	✓	✓	✓	1.289
13251	26093	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x&=x^{3} \\ \end{align*}	✓	✓	✓	✓	1.289
13252	4019	\begin{align*} x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-\left (x +5\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.290
13253	9255	\begin{align*} y^{\prime \prime }+y^{\prime }&=10 x^{4}+2 \\ \end{align*}	✓	✓	✓	✓	1.290
13254	18388	\begin{align*} 9 \left (1-x \right ) x y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.291
13255	10441	\begin{align*} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-1\right ) y&=-3 \,{\mathrm e}^{x^{2}} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	1.292
13256	21940	\begin{align*} y^{\prime }-3 z&=5 \\ y-z^{\prime }-x&=3-2 t \\ z+x^{\prime }&=-1 \\ \end{align*}	✓	✓	✓	✓	1.292
13257	12293	\begin{align*} y^{\prime \prime }-\left (a^{2} x^{2}+a \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.293
13258	1095	\begin{align*} y^{\prime \prime } x +\sin \left (x \right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.294
13259	9898	\begin{align*} x \left (x -2\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	1.294
13260	17352	\begin{align*} 2 t^{2} y^{\prime \prime }-3 y^{\prime } t -3 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.294
13261	17749	\begin{align*} y^{\prime \prime }+5 y^{\prime }&=5 t^{2} \\ \end{align*}	✓	✓	✓	✓	1.294
13262	2434	\begin{align*} t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.295
13263	4482	\begin{align*} y^{\prime \prime }+y&=2 \sin \left (x \right )-3 \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.295
13264	8273	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.295
13265	12332	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-\left (x +1\right )^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	1.295
13266	15396	\begin{align*} y&=y^{\prime } x -\frac {1}{{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	1.295
13267	13664	\begin{align*} y^{\prime \prime }-\left (a^{2} x^{2}+a \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.296
13268	13885	\begin{align*} \left (a \,x^{2}+b \right )^{2} y^{\prime \prime }+2 a x \left (a \,x^{2}+b \right ) y^{\prime }+c y&=0 \\ \end{align*}	✓	✓	✓	✗	1.296
13269	16422	\begin{align*} y^{\prime \prime } x +2 y^{\prime }&=6 \\ y \left (1\right ) &= 4 \\ y^{\prime }\left (1\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	1.296
13270	25962	\begin{align*} y^{\prime \prime }+y^{\prime }&=8 \sin \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.296
13271	2071	\begin{align*} x^{2} y^{\prime \prime }+x \left (2+x \right ) y^{\prime }-\left (2-3 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.297
13272	12465	\begin{align*} x^{2} y^{\prime \prime }-x \left (x +4\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.297
13273	23474	\begin{align*} 3 x y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime }&=3 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	1.298
13274	7109	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.299
13275	8993	\begin{align*} 3 x^{2} y^{\prime \prime }+5 y^{\prime } x +3 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.299
13276	14201	\begin{align*} x^{\prime }&=x \left (1-\frac {x}{4}\right ) \\ \end{align*}	✓	✓	✓	✓	1.299
13277	22723	\begin{align*} 4 y+y^{\prime \prime }&=\cos \left (x \right ) \cos \left (2 x \right ) \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.299
13278	24141	\begin{align*} a^{2}-x y^{\prime } \sqrt {-a^{2}+x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	1.299
13279	809	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	1.300
13280	3351	\begin{align*} 3 x \left (3 x +2\right ) y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.300
13281	7173	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.300
13282	17711	\begin{align*} 9 y^{\prime \prime } x +14 y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.300
13283	24852	\begin{align*} 4 y^{2} {y^{\prime }}^{3}-2 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	1.300
13284	24575	\begin{align*} y^{\prime \prime }+y^{\prime }&=-2 x +2 \\ \end{align*}	✓	✓	✓	✓	1.302
13285	25200	\begin{align*} \left (t -1\right ) y^{\prime \prime }-y^{\prime } t +y&=2 t \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.302
13286	2608	\begin{align*} y^{\prime \prime }+y&=\cos \left (t \right ) \cos \left (2 t \right ) \cos \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.303
13287	18178	\begin{align*} y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y&=a \sin \left (x n +\alpha \right ) \\ \end{align*}	✓	✓	✓	✓	1.303
13288	2635	\begin{align*} t^{2} y^{\prime \prime }-y^{\prime } t -2 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.304
13289	18093	\begin{align*} y^{\prime \prime } x&=y^{\prime } \\ \end{align*}	✓	✓	✓	✓	1.304
13290	121	\begin{align*} y^{\prime }&=\left (4 x +y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.305
13291	861	\begin{align*} x^{2} y^{\prime \prime }+7 y^{\prime } x +25 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.305
13292	19168	\begin{align*} \sin \left (x \right )^{2} y^{\prime \prime }&=2 y \\ \end{align*}	✓	✓	✓	✗	1.305
13293	156	\begin{align*} y^{3} y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	1.306
13294	2073	\begin{align*} x^{2} y^{\prime \prime }+10 y^{\prime } x +\left (14+x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.306
13295	5048	\begin{align*} y y^{\prime }&=\sqrt {y^{2}-a^{2}} \\ \end{align*}	✓	✓	✓	✓	1.306
13296	5590	\begin{align*} 2 y^{2} {y^{\prime }}^{2}+2 y y^{\prime } x -1+x^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.306
13297	8264	\begin{align*} y^{\prime }&=y \left (y-3\right ) \\ \end{align*}	✓	✓	✓	✓	1.306
13298	15041	\begin{align*} y&=5 y^{\prime } x -{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.306
13299	16101	\begin{align*} y^{\prime \prime }+4 y^{\prime }&=3 t +2 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.306
13300	16717	\begin{align*} y^{\prime \prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.306