2.3.30 Problems 2901 to 3000

Table 2.609: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2901	10958	\begin{align*} y^{\prime \prime }-3 y^{\prime } x +\left (2 x^{2}+5\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.247
2902	10967	\begin{align*} 2 x^{2} y^{\prime \prime }+x \left (3+2 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.247
2903	10971	\begin{align*} 3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (1+3 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.247
2904	11049	\begin{align*} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (-9 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.247
2905	11087	\begin{align*} t^{2} y^{\prime \prime }+t \left (1+t \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.247
2906	11222	\begin{align*} y^{\prime \prime } x -\left (2+x \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.247
2907	14816	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.247
2908	14819	\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=4 t \,{\mathrm e}^{-3 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.247
2909	15194	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.247
2910	15203	\begin{align*} 4 y^{\prime \prime }+40 y^{\prime }+101 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.247
2911	18462	\begin{align*} x^{\prime \prime }&=1 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.247
2912	25099	\begin{align*} y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.247
2913	401	\begin{align*} y^{\prime }&=4 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.248
2914	402	\begin{align*} 2 y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.248
2915	1306	\begin{align*} 4 y^{\prime \prime }+12 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.248
2916	10582	\begin{align*} 2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.248
2917	11267	\begin{align*} y^{\prime \prime } x +\left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.248
2918	22812	\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=12 t \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.248
2919	25628	\begin{align*} y^{\prime \prime }+2 y^{\prime }+16 y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.248
2920	4488	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=15 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.249
2921	8120	\begin{align*} y^{\prime }-\frac {y}{x}&=\cos \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.249
2922	10664	\begin{align*} 2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.249
2923	10747	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.249
2924	10871	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.249
2925	10957	\begin{align*} \left (2+4 x \right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.249
2926	11085	\begin{align*} t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.249
2927	11092	\begin{align*} t^{2} y^{\prime \prime }-t \left (1+t \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.249
2928	11241	\begin{align*} y-\left (x +1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.249
2929	17631	\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.249
2930	20374	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y&=16 x^{2}+256 \\ \end{align*}	✓	✓	✓	✓	0.249
2931	22798	\begin{align*} y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+\left (1+\sin \left (x \right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.249
2932	24010	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.249
2933	1271	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -\beta \\ \end{align*}	✓	✓	✓	✗	0.250
2934	3621	\begin{align*} y^{\prime }-\frac {y}{x}&=2 \ln \left (x \right ) x^{2} \\ \end{align*}	✓	✓	✓	✓	0.250
2935	4371	\begin{align*} \left (x +1\right ) y^{\prime }-y&=x \left (x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.250
2936	5980	\begin{align*} \left (b x +a \right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.250
2937	6778	\begin{align*} a y+12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.250
2938	8634	\begin{align*} y^{\prime }-6 y&=0 \\ y \left (-1\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.250
2939	10617	\begin{align*} 9 \left (x +3\right ) x^{2} y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (4 x +3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.250
2940	10667	\begin{align*} t^{2} y^{\prime \prime }+t \left (1+t \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.250
2941	10692	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.250
2942	10702	\begin{align*} x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.250
2943	10763	\begin{align*} \left (1-x \right ) x^{2} y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.250
2944	10882	\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.250
2945	10889	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.250
2946	10923	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.250
2947	11176	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.250
2948	14779	\begin{align*} x^{\prime }+y^{\prime }+2 y&=\sin \left (t \right ) \\ x^{\prime }+y^{\prime }-x-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.250
2949	19625	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=2 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.250
2950	21533	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=3 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.250
2951	21576	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=a \sin \left (b x \right ) \\ \end{align*}	✓	✓	✓	✓	0.250
2952	21582	\begin{align*} y^{\prime \prime \prime }+y^{\prime }+y&=\sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.250
2953	22253	\begin{align*} y^{\prime \prime \prime }-y&=5 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.250
2954	24009	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.250
2955	25243	\begin{align*} -t y^{\prime \prime }+\left (-2+t \right ) y^{\prime }+y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.250
2956	1044	\begin{align*} 2 y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.251
2957	1303	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.251
2958	3611	\begin{align*} x^{2} y^{\prime }-4 y x&=x^{7} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.251
2959	10494	\begin{align*} y^{\prime \prime } x -\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.251
2960	10536	\begin{align*} y^{\prime \prime }+3 y^{\prime } x +\left (2 x^{2}+4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.251
2961	10665	\begin{align*} t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.251
2962	10699	\begin{align*} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.251
2963	10768	\begin{align*} x \left (2+x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.251
2964	11114	\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.251
2965	11206	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.251
2966	22677	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.251
2967	260	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=2 x \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	0.252
2968	8201	\begin{align*} y^{\prime }&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.252
2969	9446	\begin{align*} L i^{\prime }+R i&=E_{0} \delta \left (t \right ) \\ i \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.252
2970	10552	\begin{align*} 2 \left (x +3\right ) x^{2} y^{\prime \prime }+x \left (5 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.252
2971	10681	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.252
2972	11197	\begin{align*} x \left (2+x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.252
2973	16054	\begin{align*} x^{\prime }&=3 x \\ y^{\prime }&=-2 y \\ \end{align*}	✓	✓	✓	✓	0.252
2974	522	\begin{align*} 16 x^{2} y^{\prime \prime }-\left (-144 x^{3}+5\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.253
2975	1396	\begin{align*} y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.253
2976	1743	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.253
2977	3613	\begin{align*} y^{\prime }+\frac {2 x y}{-x^{2}+1}&=4 x \\ \end{align*}	✓	✓	✓	✓	0.253
2978	4466	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=48 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.253
2979	10672	\begin{align*} t^{2} y^{\prime \prime }-t \left (1+t \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.253
2980	10688	\begin{align*} 4 y^{\prime \prime } x -y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.253
2981	10709	\begin{align*} x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.253
2982	10727	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4}&=0 \\ \end{align*}	✓	✓	✓	✗	0.253
2983	11015	\begin{align*} 2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.253
2984	11016	\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (3 x +4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.253
2985	11084	\begin{align*} 2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.253
2986	16847	\begin{align*} y^{\prime \prime }-x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.253
2987	17248	\begin{align*} 2 t +2 y+\left (2 t +2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.253
2988	18214	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.253
2989	21201	\begin{align*} x^{\prime \prime \prime \prime }+x^{\prime \prime \prime }&=t \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.253
2990	25063	\begin{align*} y^{\prime }+2 y&=t \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.253
2991	353	\begin{align*} y^{\prime \prime }+9 y&=\sin \left (2 x \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.254
2992	413	\begin{align*} y^{\prime \prime }+y&=x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.254
2993	550	\begin{align*} x^{\prime \prime \prime \prime }+2 x^{\prime \prime }+x&={\mathrm e}^{2 t} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ x^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.254
2994	8127	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.254
2995	10680	\begin{align*} y^{\prime \prime }+y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.254
2996	10815	\begin{align*} 2 y^{\prime \prime } x +\left (x -2\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.254
2997	10853	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.254
2998	10859	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.254
2999	11028	\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.254
3000	11055	\begin{align*} 4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.254