2.3.104 Problems 10301 to 10400

Table 2.781: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
10301	643	\begin{align*} x_{1}^{\prime }&=3 x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }&=-5 x_{1}-3 x_{2}-x_{3} \\ x_{3}^{\prime }&=5 x_{1}+5 x_{2}+3 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.638
10302	1006	\begin{align*} x_{1}^{\prime }&=x_{2}+2 x_{3} \\ x_{2}^{\prime }&=-5 x_{1}-3 x_{2}-7 x_{3} \\ x_{3}^{\prime }&=x_{1} \\ \end{align*}	✓	✓	✓	✓	0.638
10303	1899	\begin{align*} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y&=0 \\ y \left (-1\right ) &= 1 \\ y^{\prime }\left (-1\right ) &= -1 \\ \end{align*} Series expansion around \(x=-1\).	✓	✓	✓	✓	0.638
10304	2003	\begin{align*} x^{2} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+x \left (7 x^{2}+6 x +3\right ) y^{\prime }+\left (-3 x^{2}+6 x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.638
10305	3797	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=4 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.638
10306	4433	\begin{align*} 2 {y^{\prime }}^{3}-3 {y^{\prime }}^{2}+x&=y \\ \end{align*}	✓	✓	✗	✗	0.638
10307	7381	\begin{align*} y^{\prime }&=4 y^{2}-3 y+1 \\ \end{align*}	✓	✓	✓	✓	0.638
10308	7839	\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.638
10309	8062	\begin{align*} x^{\prime }-y^{\prime }+y&=-{\mathrm e}^{t} \\ x+y^{\prime }-y&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.638
10310	9076	\begin{align*} x \left (x^{2}-4\right ) y^{\prime }&=1 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.638
10311	9464	\begin{align*} x^{\prime }&=4 x-2 y \\ y^{\prime }&=5 x+2 y \\ \end{align*}	✓	✓	✓	✓	0.638
10312	9794	\begin{align*} x^{2} y^{\prime \prime }&=\left (3 x -2 y^{\prime }\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.638
10313	10083	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x -x^{3}+2&=0 \\ \end{align*}	✓	✓	✓	✗	0.638
10314	16058	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=-2 x-y \\ \end{align*}	✓	✓	✓	✓	0.638
10315	16102	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=t^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.638
10316	16606	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=27 \,{\mathrm e}^{6 x} \\ \end{align*}	✓	✓	✓	✓	0.638
10317	16828	\begin{align*} \left (-x^{3}+2\right ) y^{\prime }-3 x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.638
10318	17820	\begin{align*} x^{\prime \prime }+\frac {x^{\prime }}{10}+x&=3 \cos \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.638
10319	19841	\begin{align*} y^{\prime \prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.638
10320	20346	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{\frac {5 x}{2}} \\ \end{align*}	✓	✓	✓	✓	0.638
10321	22495	\begin{align*} {y^{\prime \prime \prime }}^{2}&={y^{\prime \prime }}^{3} \\ \end{align*}	✓	✓	✓	✓	0.638
10322	24488	\begin{align*} x^{\prime \prime }+2 b x^{\prime }+k^{2} x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= v_{0} \\ \end{align*}	✓	✓	✓	✓	0.638
10323	26025	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } x -2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.638
10324	3263	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.639
10325	3836	\begin{align*} x_{1}^{\prime }&=x_{1}-2 x_{2} \\ x_{2}^{\prime }&=5 x_{1}-5 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.639
10326	4105	\begin{align*} y^{\prime }&={\mathrm e}^{x} \sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.639
10327	5766	\begin{align*} \frac {\left (a +b \right ) y}{x^{2}}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.639
10328	10527	\begin{align*} y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.639
10329	14648	\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=18 \,{\mathrm e}^{-2 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.639
10330	16511	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&=0 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	0.639
10331	16635	\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=6 \,{\mathrm e}^{-5 x} \\ \end{align*}	✓	✓	✓	✓	0.639
10332	20419	\begin{align*} \left (y-y^{\prime } x \right ) \left (y^{\prime }-1\right )&=y^{\prime } \\ \end{align*}	✓	✓	✓	✗	0.639
10333	20899	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.639
10334	23982	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=x^{2}-2 x +1 \\ \end{align*}	✓	✓	✓	✓	0.639
10335	26550	\begin{align*} y^{\prime \prime }-2 k y^{\prime }+k^{2} y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.639
10336	27193	\begin{align*} x_{1}^{\prime }&=2 x_{1}-7 x_{2} \\ x_{2}^{\prime }&=5 x_{1}-10 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.639
10337	7096	\begin{align*} y^{\prime \prime }+9 y&=8 \cos \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= -1 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.640
10338	9478	\begin{align*} x^{\prime }&=3 x-5 y \\ y^{\prime }&=-x+2 y \\ \end{align*}	✓	✓	✓	✓	0.640
10339	14115	\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.640
10340	15459	\begin{align*} x^{\prime }&=-4 x-10 y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.640
10341	19204	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.640
10342	22275	\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=6 x_{1}+4 \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (1\right ) &= 0 \\ x_{2} \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.640
10343	458	\begin{align*} y^{\prime \prime } x +x^{2} y^{\prime }+\left ({\mathrm e}^{x}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.641
10344	987	\begin{align*} x_{1}^{\prime }&=3 x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }&=-5 x_{1}-3 x_{2}-x_{3} \\ x_{3}^{\prime }&=5 x_{1}+5 x_{2}+3 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.641
10345	1016	\begin{align*} x_{1}^{\prime }&=-19 x_{1}+12 x_{2}+84 x_{3} \\ x_{2}^{\prime }&=5 x_{2} \\ x_{3}^{\prime }&=-8 x_{1}+4 x_{2}+33 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.641
10346	2010	\begin{align*} 4 x^{2} y^{\prime \prime }+2 x \left (x^{2}+x +4\right ) y^{\prime }+\left (3 x^{2}+5 x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.641
10347	9796	\begin{align*} x^{4} y^{\prime \prime }&=y^{\prime } \left (y^{\prime }+x^{3}\right ) \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.641
10348	10265	\begin{align*} y^{\prime }&=a x +y \\ \end{align*}	✓	✓	✓	✓	0.641
10349	13186	\(\left [\begin {array}{ccc} 3 & -3 & 1 \\ 2 & -2 & 1 \\ 0 & 0 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.641
10350	14313	\begin{align*} x^{\prime \prime }+x^{\prime }+2 x&=t \sin \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.641
10351	15007	\begin{align*} x^{\prime }&=-11 x-2 y \\ y^{\prime }&=13 x-9 y \\ \end{align*}	✓	✓	✓	✓	0.641
10352	15110	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=y^{\prime } \\ \end{align*}	✓	✓	✓	✗	0.641
10353	17354	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	0.641
10354	17427	\begin{align*} y^{\prime \prime }-y&=2 t -4 \\ \end{align*}	✓	✓	✓	✓	0.641
10355	18096	\begin{align*} y^{\prime \prime } x&=y^{\prime }+x^{2} \\ \end{align*}	✓	✓	✓	✓	0.641
10356	18430	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=x-3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.641
10357	19764	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.641
10358	21776	\begin{align*} \left ({y^{\prime }}^{2}-y^{2}\right ) {\mathrm e}^{y^{\prime }}-x {y^{\prime }}^{2}+x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.641
10359	23500	\begin{align*} y^{\prime \prime }-y&=4 \cosh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.641
10360	26129	\begin{align*} x^{\prime }-x&=1 \\ x \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.641
10361	27044	\begin{align*} x^{\prime }+y^{\prime }-x&=\cos \left (t \right ) \\ x^{\prime }+2 y^{\prime }&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.641
10362	878	\begin{align*} y^{\prime \prime }+9 y&=2 \cos \left (3 x \right )+3 \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.642
10363	1920	\begin{align*} \left (x^{2}+4 x +4\right ) y^{\prime \prime }+\left (4 x +8\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.642
10364	2607	\begin{align*} y^{\prime \prime }+y&=\cos \left (2 t \right ) \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.642
10365	2730	\begin{align*} x_{1}^{\prime }&=7 x_{1}-x_{2}+6 x_{3} \\ x_{2}^{\prime }&=-10 x_{1}+4 x_{2}-12 x_{3} \\ x_{3}^{\prime }&=-2 x_{1}+x_{2}-x_{3} \\ \end{align*}	✓	✓	✓	✓	0.642
10366	3184	\begin{align*} y^{\prime \prime }+2 n^{2} y^{\prime }+n^{4} y&=\sin \left (x k \right ) \\ \end{align*}	✓	✓	✓	✓	0.642
10367	4185	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{2 x}+\frac {y}{4 x}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.642
10368	8162	\begin{align*} y^{\prime }+20 y&=24 \\ \end{align*}	✓	✓	✓	✓	0.642
10369	8515	\begin{align*} 4 y^{\prime \prime } x +\frac {y^{\prime }}{2}+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.642
10370	8856	\begin{align*} y^{\prime \prime }&=2+x \\ \end{align*}	✓	✓	✓	✓	0.642
10371	11807	\begin{align*} {y^{\prime }}^{3}+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.642
10372	18436	\begin{align*} x^{\prime }+2 x-y&=-{\mathrm e}^{2 t} \\ y^{\prime }+3 x-2 y&=6 \,{\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.642
10373	18991	\begin{align*} x_{1}^{\prime }&=3 x_{1}+2 x_{2}+4 x_{3} \\ x_{2}^{\prime }&=2 x_{1}+2 x_{3} \\ x_{3}^{\prime }&=4 x_{1}+2 x_{2}+3 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.642
10374	19214	\begin{align*} y^{\prime \prime }&=x +y^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	0.642
10375	22832	\begin{align*} x^{2} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	0.642
10376	23561	\begin{align*} x^{\prime }&=3 x-2 y \\ y^{\prime }&=2 x-2 y \\ \end{align*}	✓	✓	✓	✓	0.642
10377	24767	\begin{align*} v^{\prime }-2 v+2 w^{\prime }&=2-4 \,{\mathrm e}^{2 x} \\ 2 v^{\prime }-3 v+3 w^{\prime }-w&=0 \\ \end{align*}	✓	✓	✓	✓	0.642
10378	24823	\begin{align*} {y^{\prime }}^{3}-y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.642
10379	25950	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=2 \,{\mathrm e}^{2 x}+3 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.642
10380	2741	\begin{align*} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=3 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }&=2 x_{1}+2 x_{2}+x_{3} \\ \end{align*}	✓	✓	✓	✓	0.643
10381	3853	\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=-b x_{1}-a x_{2} \\ \end{align*}	✓	✓	✓	✓	0.643
10382	4600	\begin{align*} x^{2} y^{\prime \prime }+\left (\frac {1}{2} x +x^{2}\right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.643
10383	7995	\begin{align*} y^{\prime \prime }-y&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.643
10384	8202	\begin{align*} y^{\prime \prime }&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.643
10385	8593	\begin{align*} 4 y^{\prime \prime } x +y^{\prime }+8 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.643
10386	10947	\begin{align*} y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.643
10387	16832	\begin{align*} -2 y+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.643
10388	20360	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{2 x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.643
10389	21556	\begin{align*} \left (x^{2}-3 x +1\right ) y^{\prime \prime }-\left (x^{2}-x -2\right ) y^{\prime }+\left (2 x -3\right ) y&=x \left (x^{2}-3 x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✗	0.643
10390	638	\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2}+2 x_{3} \\ x_{2}^{\prime }&=2 x_{1}+7 x_{2}+x_{3} \\ x_{3}^{\prime }&=2 x_{1}+x_{2}+7 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.644
10391	2000	\begin{align*} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.644
10392	3876	\begin{align*} x_{1}^{\prime }&=3 x_{1}+2 x_{2}-3 \,{\mathrm e}^{t} \\ x_{2}^{\prime }&=-2 x_{1}-x_{2}+6 \,{\mathrm e}^{t} t \\ \end{align*}	✓	✓	✓	✓	0.644
10393	4538	\begin{align*} y_{1}^{\prime }-2 y_{1}+3 y_{2}-3 y_{3}&=0 \\ -4 y_{1}+y_{2}^{\prime }+5 y_{2}-3 y_{3}&=0 \\ -4 y_{1}+4 y_{2}+y_{3}^{\prime }-2 y_{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.644
10394	7661	\begin{align*} 2 y-y^{\prime } x +y^{\prime \prime }&=\cos \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.644
10395	9375	\begin{align*} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.644
10396	9840	\begin{align*} y^{\prime \prime }+2 y^{\prime } x +5 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.644
10397	12363	\begin{align*} y^{\prime \prime } x -y^{\prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✓	0.644
10398	14787	\begin{align*} 2 x^{\prime }+y^{\prime }-x-y&=1 \\ x^{\prime }+y^{\prime }+2 x-y&=t \\ \end{align*}	✓	✓	✓	✓	0.644
10399	15983	\begin{align*} x^{\prime }&=2 x+3 y \\ y^{\prime }&=x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.644
10400	16865	\begin{align*} y^{\prime }+{\mathrm e}^{2 x} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.644