2.3.136 Problems 13501 to 13600

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

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
13501	1596	\begin{align*} y^{\prime }&=2 y-y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.263
13502	4507	\begin{align*} y^{\prime \prime }+y^{\prime }&=\frac {1}{{\mathrm e}^{x}+1} \\ \end{align*}	✓	✓	✓	✓	1.263
13503	6450	\begin{align*} y y^{\prime \prime }&=b +a {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.263
13504	7211	\begin{align*} y^{\prime \prime }+q y^{\prime }&=\frac {2 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	1.263
13505	9910	\begin{align*} y^{\prime \prime } x -\left (x +3\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.263
13506	14317	\begin{align*} x^{\prime \prime }+2 x&=\cos \left (\sqrt {2}\, t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.263
13507	20737	\begin{align*} 4 x {y^{\prime }}^{2}&=\left (3 x -a \right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.263
13508	21112	\begin{align*} x^{\prime \prime }-3 x^{\prime }+2 x&=0 \\ x \left (1\right ) &= 0 \\ x^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.263
13509	22862	\begin{align*} U^{\prime \prime }+\frac {2 U^{\prime }}{r}+a U&=0 \\ \end{align*} Series expansion around \(r=0\).	✓	✓	✓	✗	1.263
13510	5719	\begin{align*} y^{\prime \prime }+y&=8 \cos \left (x \right ) \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.264
13511	9919	\begin{align*} x \left (x +3\right ) y^{\prime \prime }-9 y^{\prime }-6 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.264
13512	14978	\begin{align*} y^{\prime \prime }-2 y^{\prime } x -4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.265
13513	23285	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	1.265
13514	26052	\begin{align*} {y^{\prime }}^{3}&=a \,x^{4} \\ \end{align*}	✓	✓	✓	✓	1.265
13515	5840	\begin{align*} a k \,x^{-1+k} y+a \,x^{k} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.266
13516	9871	\begin{align*} 2 y^{\prime \prime } x +\left (2 x +1\right ) y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.266
13517	24816	\begin{align*} x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✗	1.266
13518	9724	\begin{align*} \left (x^{2}+y^{2}\right )^{2} {y^{\prime }}^{2}&=4 y^{2} x^{2} \\ \end{align*}	✓	✓	✓	✗	1.267
13519	15404	\begin{align*} -{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	1.267
13520	22859	\begin{align*} y^{\prime \prime } x +y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.267
13521	9557	\begin{align*} y^{\prime \prime } x +\left (x -6\right ) y^{\prime }-3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.268
13522	25357	\begin{align*} t y^{\prime \prime }+2 \left (i t -k \right ) y^{\prime }-2 i k y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	1.268
13523	25433	\begin{align*} y^{\prime }-a \left (t \right ) y&=\operatorname {Heaviside}\left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.268
13524	6053	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x&=x \\ \end{align*}	✓	✓	✓	✓	1.269
13525	7093	\begin{align*} y^{\prime \prime }+y&=\sin \left (2 x \right ) \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.269
13526	14185	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	1.269
13527	17749	\begin{align*} y^{\prime \prime }+5 y^{\prime }&=5 t^{2} \\ \end{align*}	✓	✓	✓	✓	1.269
13528	3300	\begin{align*} 4 x -2 y y^{\prime }+x {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.270
13529	18800	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.270
13530	20173	\begin{align*} y x -x^{2} y^{\prime }+y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✗	1.270
13531	20431	\begin{align*} 4 x {y^{\prime }}^{2}+4 y y^{\prime }&=y^{4} \\ \end{align*}	✓	✓	✓	✓	1.270
13532	8449	\begin{align*} T^{\prime }&=k \left (T-T_{m} \right ) \\ T \left (0\right ) &= T_{0} \\ \end{align*}	✓	✓	✓	✓	1.271
13533	16734	\begin{align*} 2 y^{\prime \prime }-7 y^{\prime }+3&=0 \\ \end{align*}	✓	✓	✓	✓	1.271
13534	20402	\begin{align*} y&=x {y^{\prime }}^{2}+y^{\prime } \\ \end{align*}	✓	✓	✓	✗	1.271
13535	7167	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+a^{3} x^{2} y&=2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.272
13536	9500	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.272
13537	9918	\begin{align*} y^{\prime \prime } x +\left (3+2 x \right ) y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.272
13538	17488	\begin{align*} y^{\prime \prime }+16 y&=\cot \left (4 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.272
13539	69	\begin{align*} y^{\prime }&=y^{2} \\ y \left (a \right ) &= b \\ \end{align*}	✓	✓	✓	✓	1.273
13540	2761	\begin{align*} x_{1}^{\prime }&=2 x_{1}-5 x_{2}+\sin \left (t \right ) \\ x_{2}^{\prime }&=x_{1}-2 x_{2}+\tan \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.273
13541	3272	\begin{align*} 2 y^{\prime \prime }&={\mathrm e}^{y} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.273
13542	7196	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.273
13543	9867	\begin{align*} 2 x \left (x +3\right ) y^{\prime \prime }-3 \left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.273
13544	21792	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.273
13545	13791	\begin{align*} x^{2} y^{\prime \prime }-2 a x y^{\prime }+\left (-b^{2} x^{2}+a \left (1+a \right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.274
13546	16049	\begin{align*} x^{\prime }&=-4 x+3 y \\ y^{\prime }&=z-y \\ z^{\prime }&=5 x-5 y \\ \end{align*}	✓	✓	✓	✓	1.274
13547	1039	\begin{align*} x_{1}^{\prime }&=11 x_{1}-x_{2}+26 x_{3}+6 x_{4}-3 x_{5} \\ x_{2}^{\prime }&=3 x_{2} \\ x_{3}^{\prime }&=-9 x_{1}-24 x_{3}-6 x_{4}+3 x_{5} \\ x_{4}^{\prime }&=3 x_{1}+9 x_{3}+5 x_{4}-x_{5} \\ x_{5}^{\prime }&=-48 x_{1}-3 x_{2}-138 x_{3}-30 x_{4}+18 x_{5} \\ \end{align*}	✓	✓	✓	✓	1.275
13548	3140	\begin{align*} 2 y^{\prime \prime }+y^{\prime }&=8 \sin \left (2 x \right )+{\mathrm e}^{-x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.275
13549	17793	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+10 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.275
13550	21592	\begin{align*} 2 x^{\prime }-3 x-2 y^{\prime }&=t \\ 2 x^{\prime }+3 x+2 y^{\prime }+8 y&=2 \\ \end{align*}	✓	✓	✓	✓	1.275
13551	23053	\begin{align*} s^{\prime \prime }&=5 t^{2}-7 t \\ s \left (0\right ) &= 0 \\ s \left (1\right ) &= {\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	1.275
13552	23449	\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }+3 y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.275
13553	9275	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=\left (x^{2}-1\right )^{2} \\ \end{align*}	✓	✓	✓	✗	1.276
13554	12431	\begin{align*} -y+\left (a +x \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.276
13555	12617	\begin{align*} y^{\prime \prime }&=\frac {\left (2 x^{2}-1\right ) y^{\prime }}{x^{3}}-\frac {2 y}{x^{4}} \\ \end{align*}	✓	✓	✓	✗	1.276
13556	14313	\begin{align*} x^{\prime \prime }+x^{\prime }+2 x&=t \sin \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.276
13557	19001	\begin{align*} x_{1}^{\prime }&=x_{1}+8 x_{2}+5 x_{3}+3 x_{4} \\ x_{2}^{\prime }&=2 x_{1}+16 x_{2}+10 x_{3}+6 x_{4} \\ x_{3}^{\prime }&=5 x_{1}-14 x_{2}-11 x_{3}-3 x_{4} \\ x_{4}^{\prime }&=-x_{1}-8 x_{2}-5 x_{3}-3 x_{4} \\ \end{align*}	✓	✓	✓	✓	1.276
13558	2864	\begin{align*} y^{\prime }&={\mathrm e}^{y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.277
13559	10209	\begin{align*} 2 x^{2} y^{\prime \prime }+2 y^{\prime } x -y x&=x^{3}+x \sin \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.277
13560	11678	\begin{align*} {y^{\prime }}^{2}+\left (y^{\prime }-y\right ) {\mathrm e}^{x}&=0 \\ \end{align*}	✓	✓	✓	✗	1.277
13561	15395	\begin{align*} y&=y^{\prime } x +\frac {1}{y^{\prime }} \\ \end{align*}	✓	✓	✓	✗	1.277
13562	15514	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.277
13563	21172	\begin{align*} t^{2} x^{\prime \prime }+t x^{\prime }+x&=t \\ \end{align*}	✓	✓	✓	✓	1.277
13564	7375	\begin{align*} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.278
13565	22627	\begin{align*} y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y x&=x \\ \end{align*}	✓	✓	✓	✗	1.278
13566	2392	\begin{align*} y^{\prime \prime }-\frac {2 \left (1+t \right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1}&=0 \\ \end{align*}	✓	✓	✓	✗	1.279
13567	19525	\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=\left (1-x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	1.279
13568	21993	\begin{align*} y^{\prime }&=5 y \\ \end{align*}	✓	✓	✓	✓	1.279
13569	393	\begin{align*} x^{\prime \prime }+6 x^{\prime }+13 x&=10 \sin \left (5 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.280
13570	862	\begin{align*} \frac {x^{\prime \prime }}{2}+3 x^{\prime }+4 x&=0 \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.280
13571	3316	\begin{align*} 4 x {y^{\prime }}^{2}+2 y^{\prime } x&=y \\ \end{align*}	✓	✓	✓	✓	1.280
13572	18952	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{5}+y&=k \delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.280
13573	809	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	1.281
13574	5970	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	1.281
13575	23447	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.281
13576	839	\begin{align*} y^{\prime \prime }-4 y&=12 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	1.282
13577	1266	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }+y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	1.282
13578	12356	\begin{align*} a^{2} y^{\prime \prime }+a \left (a^{2}-2 b \,{\mathrm e}^{-a x}\right ) y^{\prime }+b^{2} {\mathrm e}^{-2 a x} y&=0 \\ \end{align*}	✓	✓	✓	✗	1.282
13579	25703	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (-1\right ) &= 5 \\ y^{\prime }\left (-1\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	1.282
13580	6940	\begin{align*} y^{3}+x y^{2}+y+\left (x^{3}+x^{2} y+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.283
13581	14204	\begin{align*} x^{\prime }&=\frac {1+t}{\sqrt {t}} \\ x \left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	1.283
13582	18876	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=g \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	1.283
13583	19157	\begin{align*} a^{2} y^{\prime \prime }&=2 x \sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✗	✓	✗	1.283
13584	863	\begin{align*} 3 x^{\prime \prime }+30 x^{\prime }+63 x&=0 \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.284
13585	6955	\begin{align*} y^{2}-3 y x -2 x^{2}+\left (y x -x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.284
13586	8239	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.284
13587	9961	\begin{align*} 2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (1+3 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.284
13588	10261	\begin{align*} y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	1.284
13589	9391	\begin{align*} x^{3} y^{\prime \prime }+\sin \left (x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.285
13590	14120	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=\cos \left (x \right )-{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	1.285
13591	16386	\begin{align*} y^{\prime \prime } x&=y^{\prime }-2 x^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	1.285
13592	22168	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (2\right ) &= 0 \\ y^{\prime }\left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.285
13593	1258	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.286
13594	12951	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}-8 y^{3}-4 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.286
13595	14646	\begin{align*} 16 y+8 y^{\prime }+y^{\prime \prime }&=8 \,{\mathrm e}^{-2 x} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.286
13596	15609	\begin{align*} y^{\prime }&=x +y \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.286
13597	18105	\begin{align*} y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	1.286
13598	20136	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=\ln \left (y\right ) y^{2} \\ \end{align*}	✓	✓	✓	✗	1.286
13599	24266	\begin{align*} y^{\prime }&=4 x -2 y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.286
13600	4040	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+7 \,{\mathrm e}^{x} y^{\prime } x +9 \left (1+\tan \left (x \right )\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.287