2.3.136 Problems 13501 to 13600

Table 2.803: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
13501	6286	\begin{align*} y+3 x^{5} y^{\prime }+x^{6} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.860
13502	9590	\begin{align*} y^{\prime \prime } x -\left (2+x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.860
13503	15550	\begin{align*} y^{\prime }&=\sqrt {\left (y+2\right ) \left (y-1\right )} \\ \end{align*}	✓	✓	✓	✓	0.860
13504	16410	\begin{align*} -y^{\prime }+y^{\prime \prime } x&=6 x^{5} \\ \end{align*}	✓	✓	✓	✓	0.860
13505	19606	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.860
13506	21661	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +\lambda \left (1+\lambda \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.860
13507	22718	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=\sin \left (3 x \right )+x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.860
13508	8216	\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (\frac {\pi }{6}\right ) &= {\frac {1}{2}} \\ x^{\prime }\left (\frac {\pi }{6}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.861
13509	9211	\begin{align*} y^{\prime \prime } x -3 y^{\prime }&=5 x \\ \end{align*}	✓	✓	✓	✓	0.861
13510	9545	\begin{align*} 3 y^{\prime \prime } x +\left (-x +2\right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.861
13511	10144	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.861
13512	2430	\begin{align*} t^{2} y^{\prime \prime }-5 t y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.862
13513	2640	\begin{align*} \left ({\mathrm e}^{t}-1\right ) y^{\prime \prime }+{\mathrm e}^{t} y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✗	0.862
13514	3352	\begin{align*} x^{2} \left (x +4\right ) y^{\prime \prime }+7 y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.862
13515	7566	\begin{align*} x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+2&=0 \\ \end{align*}	✓	✓	✓	✗	0.862
13516	9431	\begin{align*} 2 y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.862
13517	12433	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +\left (a \,x^{m}+b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.862
13518	15434	\begin{align*} y^{\prime \prime }-3 y^{\prime }&=2-6 x \\ \end{align*}	✓	✓	✓	✓	0.862
13519	17511	\begin{align*} y^{\prime \prime }+y&=\sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.862
13520	5538	\begin{align*} 3 x^{4} {y^{\prime }}^{2}-y x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.863
13521	13697	\begin{align*} y^{\prime \prime }+\left (2 x^{2}+a \right ) y^{\prime }+\left (x^{4}+a \,x^{2}+b +2 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.863
13522	14320	\begin{align*} x^{\prime \prime }+3025 x&=\cos \left (45 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.863
13523	20643	\begin{align*} 4 y+y^{\prime \prime }&=4 \tan \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.863
13524	25087	\begin{align*} y^{\prime \prime }-3 y^{\prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.863
13525	25475	\begin{align*} y^{\prime }&=-y^{2}+y \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	0.863
13526	7445	\begin{align*} u^{\prime }&=\alpha \left (1-u\right )-\beta u \\ \end{align*}	✓	✓	✓	✓	0.864
13527	18150	\begin{align*} y^{\prime \prime }+7 y^{\prime }&={\mathrm e}^{-7 x} \\ \end{align*}	✓	✓	✓	✓	0.864
13528	21300	\begin{align*} x^{\prime \prime }+2 h x^{\prime }+k^{2} x&=0 \\ \end{align*}	✓	✓	✓	✓	0.864
13529	23001	\begin{align*} y^{\prime \prime }-4 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.864
13530	1296	\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.865
13531	3261	\begin{align*} y^{\prime } y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.865
13532	15485	\begin{align*} 2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.865
13533	21163	\begin{align*} x^{\prime \prime }-\frac {x^{\prime }}{t}&=0 \\ x \left (1\right ) &= 0 \\ x^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.865
13534	23108	\begin{align*} m s^{\prime \prime }&=\frac {g \,t^{2}}{2} \\ \end{align*}	✓	✓	✓	✓	0.865
13535	23467	\begin{align*} y^{\prime \prime }+y^{\prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.865
13536	1509	\begin{align*} y^{\prime \prime }+2 y^{\prime }+3 y&=\sin \left (t \right )+\delta \left (t -3 \pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.866
13537	2732	\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2}+3 x_{3}+6 x_{4} \\ x_{2}^{\prime }&=3 x_{1}+6 x_{2}+9 x_{3}+18 x_{4} \\ x_{3}^{\prime }&=5 x_{1}+10 x_{2}+15 x_{3}+30 x_{4} \\ x_{4}^{\prime }&=7 x_{1}+14 x_{2}+21 x_{3}+42 x_{4} \\ \end{align*}	✓	✓	✓	✓	0.866
13538	3174	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2} \\ \end{align*}	✓	✓	✓	✓	0.866
13539	3383	\begin{align*} \left (-x^{2}+x \right ) y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.866
13540	8293	\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\ y \left (-6\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	0.866
13541	20507	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -20 y&=\left (x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.866
13542	3816	\begin{align*} x_{1}^{\prime }&=-2 x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }&=x_{1}-x_{2}+3 x_{3} \\ x_{3}^{\prime }&=-x_{2}-3 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.867
13543	20536	\begin{align*} y^{\prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.867
13544	21564	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}&=2 \\ \end{align*}	✓	✓	✓	✓	0.867
13545	25230	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.867
13546	1456	\begin{align*} x_{1}^{\prime }&=-x_{1}-x_{2}-1 \\ x_{2}^{\prime }&=2 x_{1}-x_{2}+5 \\ \end{align*}	✓	✓	✓	✓	0.868
13547	3356	\begin{align*} \left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-y^{\prime } x +\left (1-x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.868
13548	7602	\begin{align*} 3 y^{\prime }-7 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.868
13549	12997	\begin{align*} \left (1+y^{2}\right ) y^{\prime \prime }-3 y {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.868
13550	23369	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.868
13551	25446	\begin{align*} z^{\prime }+4 i z&={\mathrm e}^{8 i t} \\ \end{align*}	✓	✓	✓	✓	0.868
13552	1293	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.869
13553	4483	\begin{align*} y^{\prime \prime }-y^{\prime }&={\mathrm e}^{x} \left (x^{2}+10\right ) \\ \end{align*}	✓	✓	✓	✓	0.869
13554	7175	\begin{align*} x^{2} \left (1-4 x \right ) y^{\prime \prime }+\left (\left (1-n \right ) x -\left (6-4 n \right ) x^{2}\right ) y^{\prime }+n \left (1-n \right ) x y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.869
13555	9052	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.869
13556	16749	\begin{align*} -y^{\prime }+y^{\prime \prime } x&=-3 x {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✓	0.869
13557	22284	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.869
13558	22306	\begin{align*} x^{\prime \prime }&=t^{2}-4 t +8 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	0.869
13559	25220	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.869
13560	9880	\begin{align*} 2 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.870
13561	19010	\begin{align*} x_{1}^{\prime }&=\frac {4 x_{1}}{3}+\frac {4 x_{2}}{3}-\frac {11 x_{3}}{3} \\ x_{2}^{\prime }&=-\frac {16 x_{1}}{3}-\frac {x_{2}}{3}+\frac {14 x_{3}}{3} \\ x_{3}^{\prime }&=3 x_{1}-2 x_{2}-2 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.870
13562	20651	\begin{align*} \left (x^{2}+a \right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.870
13563	1746	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.871
13564	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*}	✓	✓	✓	✗	0.871
13565	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 \(x=2\).	✓	✓	✓	✓	0.871
13566	13694	\begin{align*} y^{\prime \prime }+a \left (-b^{2}+x^{2}\right ) y^{\prime }-a \left (x +b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.871
13567	18034	\begin{align*} y&={y^{\prime }}^{2}-y^{\prime } x +x \\ \end{align*}	✓	✓	✓	✗	0.871
13568	18802	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +\frac {5 y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.871
13569	24902	\begin{align*} y^{\prime \prime }&=2 x +\left (x^{2}-y^{\prime }\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.871
13570	25214	\begin{align*} y^{\prime \prime }+\sqrt {t}\, y^{\prime }-\sqrt {t -3}\, y&=0 \\ y \left (10\right ) &= y_{1} \\ y^{\prime }\left (10\right ) &= y_{1} \\ \end{align*}	✗	✗	✗	✗	0.871
13571	1451	\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2} \\ x_{2}^{\prime }&=-5 x_{1} \\ \end{align*}	✓	✓	✓	✓	0.872
13572	1741	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\ y \left (0\right ) &= -5 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	0.872
13573	9255	\begin{align*} y^{\prime \prime }+y^{\prime }&=10 x^{4}+2 \\ \end{align*}	✓	✓	✓	✓	0.872
13574	9400	\begin{align*} 2 x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.872
13575	18566	\begin{align*} y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.872
13576	20856	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	0.872
13577	23136	\begin{align*} y^{\prime }&=\sqrt {y} \\ \end{align*}	✓	✓	✓	✓	0.872
13578	16569	\begin{align*} 3 x^{2} y^{\prime \prime }-7 y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.873
13579	18096	\begin{align*} y^{\prime \prime } x&=y^{\prime }+x^{2} \\ \end{align*}	✓	✓	✓	✓	0.873
13580	21532	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=2 \,{\mathrm e}^{x}-10 \sin \left (x \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.873
13581	21907	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.873
13582	813	\begin{align*} y^{\prime \prime }+y^{\prime }&=0 \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	0.874
13583	6077	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=-2 x +2 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	0.874
13584	7629	\begin{align*} {\mathrm e}^{x} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.874
13585	13893	\begin{align*} \left (x -a \right )^{2} \left (-b +x \right )^{2} y^{\prime \prime }-c y&=0 \\ \end{align*}	✓	✓	✓	✗	0.874
13586	16629	\begin{align*} y^{\prime \prime }+4 y^{\prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.874
13587	20133	\begin{align*} 2 x y^{\prime \prime } y^{\prime \prime \prime }&=-a^{2}+{y^{\prime \prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.874
13588	645	\begin{align*} x_{1}^{\prime }&=5 x_{1}+5 x_{2}+2 x_{3} \\ x_{2}^{\prime }&=-6 x_{1}-6 x_{2}-5 x_{3} \\ x_{3}^{\prime }&=6 x_{1}+6 x_{2}+5 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.875
13589	9407	\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.875
13590	15845	\begin{align*} y^{\prime }&={\mathrm e}^{\frac {2}{y}} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✗	✓	0.875
13591	19772	\begin{align*} y^{\prime \prime } x +2 y^{\prime }&=y x \\ \end{align*}	✓	✓	✓	✓	0.875
13592	21691	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (1-2 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.875
13593	1805	\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (2 x \right ) \sec \left (2 x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.876
13594	4461	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y&=\sin \left (2 x \right ) {\mathrm e}^{2 x}+2 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.876
13595	5687	\begin{align*} \sqrt {1+{y^{\prime }}^{2}}&=y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	0.876
13596	5754	\begin{align*} a \csc \left (x \right )^{2} y+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.876
13597	6403	\begin{align*} -x^{2} y^{\prime }+x^{3} y^{\prime \prime }&=-x^{2}+3 \\ \end{align*}	✓	✓	✓	✓	0.876
13598	9397	\begin{align*} 4 y^{\prime \prime } x +3 y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.876
13599	5636	\begin{align*} {y^{\prime }}^{3}+\left (\cot \left (x \right ) \cos \left (x \right )-y\right ) {y^{\prime }}^{2}-\left (1+y \cos \left (x \right ) \cot \left (x \right )\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.877
13600	8773	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+y x&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	0.877