2.3.30 Problems 2901 to 3000

Table 2.591: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2901	9889	\begin{align*} 8 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.219
2902	10575	\begin{align*} 6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.219
2903	11210	\begin{align*} 2 x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (2 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.219
2904	17587	\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }-14 y^{\prime }-104 y&=-111 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.219
2905	19641	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.219
2906	22235	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{-t} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.219
2907	25629	\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.219
2908	1049	\begin{align*} 2 \left (x +1\right ) y^{\prime }&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.220
2909	9178	\begin{align*} x^{3}+x y^{3}+3 y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.220
2910	11285	\begin{align*} y^{\prime \prime }-\frac {y}{4 x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.220
2911	12917	\begin{align*} y y^{\prime \prime }-a x&=0 \\ \end{align*}	✗	✗	✗	✗	0.220
2912	15939	\begin{align*} y^{\prime }&=t^{2} \left (t^{2}+1\right ) \\ \end{align*}	✓	✓	✓	✓	0.220
2913	17201	\begin{align*} 3 t y^{2}+y^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.220
2914	17572	\begin{align*} y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 16 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime \prime }\left (0\right ) &= 0 \\ y^{\left (5\right )}\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.220
2915	17581	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.220
2916	20901	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=\infty \).	✗	✗	✓	✓	0.220
2917	22839	\begin{align*} y^{\prime }+y&=x^{2} \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.220
2918	3342	\begin{align*} y^{\prime }&=\cos \left (x \right )+\sin \left (y\right ) \\ y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\ \end{align*} Series expansion around \(x=\frac {\pi }{2}\).	✓	✓	✓	✓	0.221
2919	5497	\begin{align*} x^{2} {y^{\prime }}^{2}&=\left (x -y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.221
2920	8339	\begin{align*} y^{\prime }&=\left (x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.221
2921	8533	\begin{align*} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.221
2922	10150	\begin{align*} x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.221
2923	10299	\begin{align*} y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.221
2924	10731	\begin{align*} 4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.221
2925	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*}	✓	✓	✓	✗	0.221
2926	11083	\begin{align*} 2 t^{2} y^{\prime \prime }-y^{\prime } t +\left (1+t \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.221
2927	13168	\(\left [\begin {array}{cc} 0 & 24 \\ -6 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.221
2928	14664	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=x \,{\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.221
2929	14874	\begin{align*} z^{\prime }&={\mathrm e}^{-2 x} x \\ \end{align*}	✓	✓	✓	✓	0.221
2930	20702	\begin{align*} y^{\prime \prime \prime }+y&=\left ({\mathrm e}^{x}+1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.221
2931	7233	\begin{align*} \cos \left (x \right ) y^{\prime }+y&=\cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.222
2932	7912	\begin{align*} 3 y^{2} x^{2}+4 \left (x^{3} y-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.222
2933	11197	\begin{align*} x \left (2+x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.222
2934	11235	\begin{align*} 4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.222
2935	14523	\begin{align*} y^{2} {\mathrm e}^{2 x}+\left (y \,{\mathrm e}^{2 x}-2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.222
2936	15047	\begin{align*} y&=y^{\prime } x +{y^{\prime }}^{2} \\ y \left (2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.222
2937	15689	\begin{align*} y^{\left (6\right )}-12 y^{\left (5\right )}+63 y^{\prime \prime \prime \prime }-18 y^{\prime \prime \prime }+315 y^{\prime \prime }-300 y^{\prime }+125 y&={\mathrm e}^{x} \left (48 \cos \left (x \right )+96 \sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.222
2938	17758	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }+5 y&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.222
2939	21270	\begin{align*} x^{\prime \prime }+t x^{\prime }+x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.222
2940	24010	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.222
2941	415	\begin{align*} 2 y^{\prime } x&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.223
2942	6762	\begin{align*} 3 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.223
2943	8072	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.223
2944	8142	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.223
2945	8737	\begin{align*} x^{3} \left (y^{\prime }-x \right )&=y^{2} \\ \end{align*}	✓	✓	✓	✓	0.223
2946	11727	\begin{align*} x^{2} {y^{\prime }}^{2}+3 y y^{\prime } x +2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.223
2947	21191	\begin{align*} x^{\prime \prime \prime \prime }+2 x^{\prime \prime }-4 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.223
2948	21906	\begin{align*} y^{\prime }-y^{2}-x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.223
2949	23096	\begin{align*} 4 x^{\prime }+2 y^{\prime }+3 x&=E \sin \left (t \right ) \\ 4 x+2 x^{\prime }+3 y&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.223
2950	531	\begin{align*} x^{\prime \prime }+9 x&=0 \\ x \left (0\right ) &= 3 \\ x^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.224
2951	2726	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y&=t^{3} {\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.224
2952	5402	\begin{align*} {y^{\prime }}^{2}-4 \left (x +1\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.224
2953	7165	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.224
2954	10618	\begin{align*} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.224
2955	11737	\begin{align*} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}+2 y y^{\prime } x +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.224
2956	16032	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.224
2957	17586	\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-24 y^{\prime }+36 y&=108 t \\ \end{align*}	✓	✓	✓	✓	0.224
2958	21771	\begin{align*} y^{\prime } \left (y^{\prime }+y\right )&=x \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✗	0.224
2959	21865	\begin{align*} \left (x^{2}-2 y x \right ) {y^{\prime }}^{2}-\left (3 x^{2}+2 y\right ) \left (x -2 y\right ) y^{\prime }+6 x y \left (x -2 y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.224
2960	22263	\begin{align*} w^{\prime }-y&=0 \\ w+y^{\prime }+z&=1 \\ w-y+z^{\prime }&=2 \sin \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} y \left (0\right ) &= 1 \\ w \left (0\right ) &= 1 \\ z \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	0.224
2961	24533	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }&=12 \\ \end{align*}	✓	✓	✓	✓	0.224
2962	1054	\begin{align*} y^{\prime \prime }+9 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.225
2963	4087	\begin{align*} \left (-y^{\prime } x +y\right )^{2}&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.225
2964	6866	\begin{align*} 2 y x +\left (y^{2}-3 x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.225
2965	9719	\begin{align*} y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.225
2966	11224	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.225
2967	13008	\begin{align*} x y^{2} y^{\prime \prime }-a&=0 \\ \end{align*}	✗	✓	✓	✗	0.225
2968	20382	\begin{align*} {y^{\prime }}^{2}-9 y^{\prime }+18&=0 \\ \end{align*}	✓	✓	✓	✓	0.225
2969	21469	\begin{align*} {y^{\prime }}^{2} \left (x^{2}-1\right )-2 y y^{\prime } x +y^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✗	0.225
2970	7	\begin{align*} y^{\prime }&=\frac {10}{x^{2}+1} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.226
2971	8639	\begin{align*} y^{\prime \prime }+10 y^{\prime }+24 y&=144 t^{2} \\ y \left (0\right ) &= {\frac {19}{12}} \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.226
2972	11049	\begin{align*} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.226
2973	14170	\begin{align*} \left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.226
2974	14821	\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y&=20 \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= -2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.226
2975	16033	\begin{align*} x^{\prime }&=-2 y \\ y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.226
2976	17583	\begin{align*} y^{\prime \prime \prime \prime }+9 y^{\prime \prime }&=9 \,{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	0.226
2977	17608	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.226
2978	22502	\begin{align*} y&=y^{\prime } x +1+4 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.226
2979	25642	\begin{align*} y^{\prime \prime }+B y^{\prime }+C y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.226
2980	1487	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.227
2981	1772	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.227
2982	6681	\begin{align*} 4 y^{\prime }+5 y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.227
2983	8566	\begin{align*} \left (x +1\right ) y^{\prime }&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.227
2984	9711	\begin{align*} x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.227
2985	10982	\begin{align*} 4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.227
2986	11044	\begin{align*} 2 x^{2} \left (2+x \right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.227
2987	11173	\begin{align*} x \left (x +1\right ) y^{\prime \prime }-\left (x -1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.227
2988	12837	\begin{align*} y^{\prime \prime }-6 y^{2}-x&=0 \\ \end{align*}	✗	✗	✗	✗	0.227
2989	16134	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=2 \,{\mathrm e}^{t} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.227
2990	16136	\begin{align*} y^{\prime \prime }+4 y&=\cos \left (2 t \right ) \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.227
2991	17248	\begin{align*} 2 t +2 y+\left (2 t +2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.227
2992	17629	\begin{align*} x^{3} y^{\prime \prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.227
2993	18314	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -y&=1 \\ \end{align*}	✓	✓	✓	✗	0.227
2994	18906	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=18 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.227
2995	19588	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.227
2996	19996	\begin{align*} {y^{\prime }}^{2}-9 y^{\prime }+18&=0 \\ \end{align*}	✓	✓	✓	✓	0.227
2997	20380	\begin{align*} {y^{\prime }}^{2}-7 y^{\prime }+12&=0 \\ \end{align*}	✓	✓	✓	✓	0.227
2998	20454	\begin{align*} y&=y^{\prime } x -{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.227
2999	22841	\begin{align*} 2 y^{\prime }+y x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.227
3000	23996	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }+2 y^{\prime }-y&=x^{4}-2 x +1 \\ \end{align*}	✓	✓	✓	✓	0.227