2.3.130 Problems 12901 to 13000

Table 2.809: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
12901	11723	\begin{align*} y^{\prime }-1&=0 \\ \end{align*}	✓	✓	✓	✓	1.209
12902	455	\begin{align*} y^{\prime \prime } x +\sin \left (x \right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.210
12903	3825	\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=-b x_{1}-a x_{2} \\ \end{align*}	✓	✓	✓	✓	1.210
12904	4585	\begin{align*} x_{1}^{\prime }&=2 x_{1}-x_{2}-x_{3}+2 \,{\mathrm e}^{2 t} \\ x_{2}^{\prime }&=3 x_{1}-2 x_{2}-3 x_{3} \\ x_{3}^{\prime }&=-x_{1}+x_{2}+2 x_{3} \\ \end{align*}	✓	✓	✓	✓	1.210
12905	4684	\begin{align*} y^{\prime }&=\sin \left (x \right ) \left (2 \sec \left (x \right )^{2}-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✗	1.210
12906	5139	\begin{align*} x \left (y+2\right ) y^{\prime }+a x&=0 \\ \end{align*}	✓	✓	✓	✓	1.210
12907	6478	\begin{align*} 2 y y^{\prime \prime }&=8 y^{3}-2 y^{2} \left (f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )-3 f \left (x \right ) y y^{\prime }+{y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	1.210
12908	16699	\begin{align*} \left (x +1\right ) y^{\prime \prime }+y^{\prime } x -y&=\left (x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✗	1.210
12909	18828	\begin{align*} y^{\prime \prime }+y^{\prime }+4 y&=2 \sinh \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.210
12910	18864	\begin{align*} y^{\prime \prime }+4 y&=3 \sec \left (2 t \right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.210
12911	20144	\begin{align*} y^{\prime \prime } y^{\prime \prime \prime }&=2 \\ \end{align*}	✓	✓	✓	✗	1.210
12912	20387	\begin{align*} y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✓	1.210
12913	25954	\begin{align*} y^{\prime \prime }+5 y^{\prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.210
12914	2830	\begin{align*} x_{1}^{\prime }&=2 x_{2} \\ x_{2}^{\prime }&=-2 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	1.211
12915	5979	\begin{align*} -a^{2} y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.211
12916	9899	\begin{align*} 4 \left (x -4\right )^{2} y^{\prime \prime }+\left (x -4\right ) \left (x -8\right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=4\).	✓	✓	✓	✓	1.211
12917	12965	\begin{align*} 3 y y^{\prime \prime }-5 {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.211
12918	14284	\begin{align*} x^{\prime \prime }-2 x^{\prime }&=0 \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.211
12919	19364	\begin{align*} y^{\prime \prime } x +y^{\prime }&=4 x \\ \end{align*}	✓	✓	✓	✓	1.211
12920	8983	\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.212
12921	9768	\begin{align*} \left (1+y\right ) y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.213
12922	12464	\begin{align*} x^{2} y^{\prime \prime }-\left (x^{2}-2 x \right ) y^{\prime }-\left (3 x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.213
12923	15068	\begin{align*} x^{\prime \prime }+x&=\sin \left (t \right )-\cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.213
12924	16479	\begin{align*} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.213
12925	19005	\begin{align*} x_{1}^{\prime }&=-2 x_{1}+2 x_{2}+x_{3} \\ x_{2}^{\prime }&=-2 x_{1}+2 x_{2}+2 x_{3} \\ x_{3}^{\prime }&=2 x_{1}-3 x_{2}-3 x_{3} \\ \end{align*}	✓	✓	✓	✓	1.213
12926	20535	\begin{align*} y^{\prime \prime }&=x +\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.213
12927	21635	\begin{align*} \left (x -1\right ) y^{\prime \prime }+y^{\prime } x +\frac {y}{x}&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	1.213
12928	14661	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{x} x^{4}+x^{3} {\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	1.214
12929	14876	\begin{align*} x^{\prime }&=\sec \left (t \right )^{2} \\ x \left (\frac {\pi }{4}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.214
12930	4140	\begin{align*} y^{\prime \prime }+2 n y^{\prime }+n^{2} y&=A \cos \left (p x \right ) \\ y \left (0\right ) &= 9 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.215
12931	4541	\begin{align*} x^{\prime }-x-2 y&={\mathrm e}^{t} \\ -4 x+y^{\prime }-3 y&=1 \\ \end{align*}	✓	✓	✓	✓	1.215
12932	11778	\begin{align*} y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (-1+a \right ) b +a \,x^{2}+\left (1-a \right ) y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.215
12933	262	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.216
12934	8414	\begin{align*} y^{\prime }&=-\frac {8 x +5}{3 y^{2}+1} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✗	1.216
12935	9559	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{t}+\lambda y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	1.216
12936	13488	\begin{align*} y^{\prime }&=f \left (x \right ) y^{2}+g^{\prime }\left (x \right ) y+a f \left (x \right ) {\mathrm e}^{2 g \left (x \right )} \\ \end{align*}	✓	✓	✓	✗	1.216
12937	20364	\begin{align*} y+y^{\prime \prime }+y^{\prime \prime \prime \prime }&=a \,x^{2}+b \,{\mathrm e}^{-x} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.216
12938	1794	\begin{align*} y^{\prime }+y^{2}+8 y+7&=0 \\ \end{align*}	✓	✓	✓	✓	1.217
12939	4546	\begin{align*} 3 x^{\prime }+2 x+y^{\prime }-6 y&=5 \,{\mathrm e}^{t} \\ 4 x^{\prime }+2 x+y^{\prime }-8 y&=5 \,{\mathrm e}^{t}+2 t -3 \\ \end{align*}	✓	✓	✓	✓	1.217
12940	6862	\begin{align*} \left (y^{2} x^{2}+y x \right ) y+\left (y^{2} x^{2}-1\right ) x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.217
12941	7639	\begin{align*} \left (x +1\right ) y^{\prime \prime }-3 y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	1.217
12942	16567	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -25 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.217
12943	19788	\begin{align*} v^{\prime \prime }+\frac {2 x v^{\prime }}{x^{2}+1}+\frac {v}{\left (x^{2}+1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	1.217
12944	22312	\begin{align*} y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.217
12945	2384	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.218
12946	4015	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -\left (2+x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.218
12947	8293	\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\ y \left (-6\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	1.218
12948	9991	\begin{align*} y^{\prime }&=1+y \\ \end{align*}	✓	✓	✓	✓	1.218
12949	14696	\begin{align*} \sin \left (x \right )^{2} y^{\prime \prime }-2 \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+\left (\cos \left (x \right )^{2}+1\right ) y&=\sin \left (x \right )^{3} \\ \end{align*}	✓	✓	✓	✗	1.218
12950	20852	\begin{align*} y^{\prime \prime }+y^{\prime }&=3 x^{2} \\ \end{align*}	✓	✓	✓	✓	1.218
12951	25052	\begin{align*} y^{\prime }&=a y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.218
12952	4550	\begin{align*} x^{\prime }-x+y&=\sec \left (t \right ) \\ -2 x+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.219
12953	4565	\begin{align*} x_{1}^{\prime }&=3 x_{1}-x_{2}+x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{2}+x_{3} \\ x_{3}^{\prime }&=4 x_{1}-x_{2}+4 x_{3} \\ \end{align*}	✓	✓	✓	✓	1.219
12954	6526	\begin{align*} x \left (x +1\right )^{2} y y^{\prime \prime }&=a \left (2+x \right ) y^{2}-2 \left (x^{2}+1\right ) y y^{\prime }+x \left (x +1\right )^{2} {y^{\prime }}^{2} \\ \end{align*}	✗	✓	✓	✗	1.219
12955	6527	\begin{align*} 3 x y^{2}-12 x^{2} y y^{\prime }+4 \left (-x^{3}+1\right ) {y^{\prime }}^{2}+8 \left (-x^{3}+1\right ) y y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	1.219
12956	13063	\begin{align*} x^{\prime }&=a x+b y \\ y^{\prime }&=c x+b y \\ \end{align*}	✓	✓	✓	✓	1.219
12957	13775	\begin{align*} x^{2} y^{\prime \prime }-\left (a^{2} x^{2}+2 a b x +b^{2}-b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.219
12958	3382	\begin{align*} \left (1-x \right ) x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-9 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.220
12959	9208	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.220
12960	10887	\begin{align*} \left (-x^{2}+4\right ) y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.220
12961	19045	\begin{align*} x_{1}^{\prime }&=-\frac {x_{1}}{2}+\frac {x_{2}}{2}-\frac {x_{3}}{2}+1 \\ x_{2}^{\prime }&=-x_{1}-2 x_{2}+x_{3}+t \\ x_{3}^{\prime }&=\frac {x_{1}}{2}+\frac {x_{2}}{2}-\frac {3 x_{3}}{2}+11 \,{\mathrm e}^{-3 t} \\ \end{align*}	✓	✓	✓	✓	1.220
12962	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*}	✓	✓	✓	✓	1.220
12963	4184	\begin{align*} y^{\prime \prime }+\frac {\left (1-x \right ) y^{\prime }}{2 x}-\frac {y}{4 x}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.221
12964	9414	\begin{align*} \left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (5 x +1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.221
12965	14180	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x&=2 \\ \end{align*}	✓	✓	✓	✓	1.221
12966	21682	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}-2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.221
12967	23099	\begin{align*} y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.221
12968	18257	\begin{align*} y^{\prime \prime }+y&=2 \sin \left (2 x \right ) \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.222
12969	20908	\begin{align*} 2 x \left (x +1\right ) y^{\prime \prime }+3 \left (x +1\right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.222
12970	3888	\begin{align*} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=6 x_{2}-7 x_{3}+3 x_{4} \\ x_{3}^{\prime }&=3 x_{3}-x_{4} \\ x_{4}^{\prime }&=-4 x_{2}+9 x_{3}-3 x_{4} \\ \end{align*}	✓	✓	✓	✓	1.223
12971	6016	\begin{align*} 16 y-7 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.223
12972	9739	\begin{align*} {y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.223
12973	10390	\begin{align*} y^{\prime \prime }+y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	1.223
12974	16957	\begin{align*} {y^{\prime }}^{2}+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.223
12975	19046	\begin{align*} x_{1}^{\prime }&=-4 x_{1}+x_{2}+3 x_{3}+3 t \\ x_{2}^{\prime }&=-2 x_{2} \\ x_{3}^{\prime }&=-2 x_{1}+x_{2}+x_{3}+3 \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.223
12976	25698	\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (\frac {\pi }{2}\right ) &= 0 \\ x^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.223
12977	6006	\begin{align*} -5 y-3 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.224
12978	24571	\begin{align*} y^{\prime \prime }+y^{\prime }&=x +1 \\ y \left (0\right ) &= 1 \\ y \left (1\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	1.224
12979	19524	\begin{align*} \left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (2+x \right ) y&=x \left (x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✗	1.225
12980	21956	\begin{align*} t^{2} s^{\prime \prime }-t s^{\prime }&=1-\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.225
12981	25362	\begin{align*} y_{1}^{\prime }&=y_{1} \\ y_{2}^{\prime }&=2 y_{1}+y_{4} \\ y_{3}^{\prime }&=y_{4} \\ y_{4}^{\prime }&=y_{2}+2 y_{3} \\ \end{align*}	✓	✓	✓	✓	1.225
12982	4512	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	1.226
12983	4586	\begin{align*} x_{1}^{\prime }&=2 x_{1}-x_{3}+24 t \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ x_{3}^{\prime }&=3 x_{1}-x_{2}-x_{3} \\ \end{align*}	✓	✓	✓	✓	1.226
12984	6249	\begin{align*} b y+2 x^{2} \left (a +x \right ) y^{\prime }+x^{4} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.226
12985	6544	\begin{align*} 2 \left (1-y\right ) y y^{\prime \prime }&=f \left (x \right ) \left (1-y\right ) y y^{\prime }+\left (1-2 y\right ) {y^{\prime }}^{2} \\ \end{align*}	✗	✓	✓	✗	1.226
12986	16612	\begin{align*} y^{\prime \prime }+3 y^{\prime }&=26 \cos \left (\frac {x}{3}\right )-12 \sin \left (\frac {x}{3}\right ) \\ \end{align*}	✓	✓	✓	✓	1.226
12987	1796	\begin{align*} 6 y^{\prime }+6 y^{2}-y-1&=0 \\ \end{align*}	✓	✓	✓	✓	1.227
12988	8884	\begin{align*} y^{\prime }&=1+y \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.227
12989	9002	\begin{align*} 2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.227
12990	17299	\begin{align*} y^{\prime } t -y-2 \left (-y+y^{\prime } t \right )^{2}&=y^{\prime }+1 \\ \end{align*}	✓	✓	✓	✗	1.227
12991	17434	\begin{align*} y^{\prime \prime }&=3 t^{4}-2 t \\ \end{align*}	✓	✓	✓	✓	1.227
12992	20635	\begin{align*} y^{\prime \prime }+\left (\tan \left (x \right )-1\right )^{2} y^{\prime }-n \left (n -1\right ) y \sec \left (x \right )^{4}&=0 \\ \end{align*}	✓	✓	✓	✗	1.227
12993	22084	\begin{align*} y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.227
12994	22274	\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=6 x_{1}+4 \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.227
12995	1793	\begin{align*} y^{\prime }+y^{2}+5 y-6&=0 \\ \end{align*}	✓	✓	✓	✓	1.228
12996	4574	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }&=-2 x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	1.228
12997	6286	\begin{align*} y+3 x^{5} y^{\prime }+x^{6} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.228
12998	7122	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x&=1 \\ \end{align*}	✓	✓	✓	✓	1.228
12999	7902	\begin{align*} y x -2 y^{2}-\left (x^{2}-3 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.228
13000	11753	\begin{align*} y {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.228