2.3.31 Problems 3001 to 3100

Table 2.635: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
3001	11180	\begin{align*} \left (2 x -3\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.254
3002	14339	\begin{align*} x^{\prime \prime }+x^{\prime } t +x&=0 \\ \end{align*}	✓	✓	✓	✗	0.254
3003	15077	\begin{align*} y^{\prime \prime \prime \prime }-16 y&=x^{2}-{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.254
3004	16149	\begin{align*} y^{\prime \prime }+4 y&=\sin \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.254
3005	16196	\begin{align*} y^{\prime }&=\left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x <2 \\ 0 & 2\le x \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.254
3006	17706	\begin{align*} x \left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}+5 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.254
3007	18369	\begin{align*} 2 y^{\prime \prime }+4 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.254
3008	19408	\begin{align*} {\mathrm e}^{x^{2} y} \left (1+2 x^{2} y\right )+x^{3} {\mathrm e}^{x^{2} y} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.254
3009	20147	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.254
3010	25065	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.254
3011	27785	\begin{align*} y^{\prime }&=\frac {2}{y}-5 \mu x \\ y \left (1\right ) &= 2 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.254
3012	824	\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.255
3013	1309	\begin{align*} 4 y^{\prime \prime }+17 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.255
3014	7823	\begin{align*} y^{\prime \prime }-y&=\sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.255
3015	9889	\begin{align*} 8 y-8 x y^{\prime }+4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.255
3016	10636	\begin{align*} 3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.255
3017	10657	\begin{align*} \left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.255
3018	10689	\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*}	✓	✓	✓	✗	0.255
3019	10708	\begin{align*} x^{2} y^{\prime \prime }+2 x \left (x +2\right ) y^{\prime }+2 \left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.255
3020	11056	\begin{align*} 3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.255
3021	11139	\begin{align*} 2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.255
3022	11207	\begin{align*} x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.255
3023	21804	\begin{align*} \left (x -y\right ) y^{\prime }&=-x +y \\ \end{align*}	✓	✓	✓	✓	0.255
3024	22479	\begin{align*} y^{\prime \prime \prime }&=3 \sin \left (x \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.255
3025	24011	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	0.255
3026	379	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y&=8 x^{{4}/{3}} \\ \end{align*}	✓	✓	✓	✓	0.256
3027	1053	\begin{align*} y^{\prime \prime }&=4 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.256
3028	3613	\begin{align*} y^{\prime }+\frac {2 x y}{-x^{2}+1}&=4 x \\ \end{align*}	✓	✓	✓	✓	0.256
3029	7827	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.256
3030	7881	\begin{align*} x^{2}-y-x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.256
3031	10624	\begin{align*} 2 x^{2} \left (x +2\right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.256
3032	10757	\begin{align*} x y^{\prime \prime }+x y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.256
3033	10979	\begin{align*} 8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.256
3034	11142	\begin{align*} x^{4} y^{\prime \prime }+x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.256
3035	11196	\begin{align*} x \left (x +2\right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.256
3036	14954	\begin{align*} \left (-t^{2}+t \right ) x^{\prime \prime }+\left (-t^{2}+2\right ) x^{\prime }+\left (2-t \right ) x&=0 \\ \end{align*}	✓	✓	✓	✗	0.256
3037	15437	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&=2 x +3 \\ \end{align*}	✓	✓	✓	✓	0.256
3038	16814	\begin{align*} y^{\prime \prime }+4 y^{\prime }-12 y&=\delta \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.256
3039	17675	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+14 x^{3} y^{\prime \prime \prime }+55 x^{2} y^{\prime \prime }+65 x y^{\prime }+15 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.256
3040	18181	\begin{align*} y-4 y^{\prime }+6 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.256
3041	19298	\begin{align*} y+y \cos \left (y x \right )+\left (x +x \cos \left (y x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.256
3042	19633	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=4 \,{\mathrm e}^{3 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.256
3043	23431	\begin{align*} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ y \left (1\right ) &= 2 \,{\mathrm e} \\ y^{\prime }\left (1\right ) &= -3 \,{\mathrm e} \\ \end{align*}	✓	✓	✓	✗	0.256
3044	23631	\begin{align*} y^{\prime \prime }+4 y&=4 \cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.256
3045	24008	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.256
3046	27754	\begin{align*} y^{\prime }&=x +\frac {1}{y} \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.256
3047	27768	\begin{align*} y^{\prime \prime }-x y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.256
3048	1758	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	0.257
3049	2212	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{-2 x} \left (\left (23-2 x \right ) \cos \left (x \right )+\left (8-9 x \right ) \sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.257
3050	2218	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-x} \left (20-12 x \right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -4 \\ y^{\prime \prime }\left (0\right ) &= 7 \\ y^{\prime \prime \prime }\left (0\right ) &= -22 \\ \end{align*}	✓	✓	✓	✓	0.257
3051	8139	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.257
3052	10552	\begin{align*} 2 x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.257
3053	10601	\begin{align*} 4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.257
3054	10608	\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.257
3055	10609	\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 x y^{\prime }+\left (1+4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.257
3056	10628	\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }-\left (1+3 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.257
3057	11148	\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.257
3058	11217	\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.257
3059	23655	\begin{align*} 4 y^{\prime \prime }-3 y^{\prime }-y&=34 \sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.257
3060	27113	\(\left [\begin {array}{cc} -5 & 3 \\ 0 & 9 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.257
3061	27562	\begin{align*} y y^{\prime \prime }&=y^{\prime } \left (y^{\prime }+1\right ) \\ \end{align*}	✓	✓	✓	✗	0.257
3062	2175	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{-x} \left (\left (16+10 x \right ) \cos \left (x \right )+\left (30-10 x \right ) \sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.258
3063	3345	\begin{align*} y^{\prime \prime }+2 y y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.258
3064	3943	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=12-6 \,{\mathrm e}^{t} \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.258
3065	10593	\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.258
3066	10774	\begin{align*} \left (x +2\right ) y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.258
3067	11013	\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.258
3068	11029	\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 x y^{\prime }+\left (1+4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.258
3069	11059	\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.258
3070	11116	\begin{align*} 2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.258
3071	11128	\begin{align*} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.258
3072	14570	\begin{align*} \left (2 x +1\right ) y^{\prime \prime }-4 \left (x +1\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.258
3073	15298	\begin{align*} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.258
3074	19572	\begin{align*} y^{\prime \prime \prime \prime }&=\frac {1}{x^{3}} \\ \end{align*}	✓	✓	✓	✓	0.258
3075	22781	\begin{align*} x^{\prime \prime \prime \prime }-x&=8 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.258
3076	27089	\(\left [\begin {array}{cc} -2 & 0 \\ 1 & 4 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.258
3077	27090	\(\left [\begin {array}{cc} -5 & 0 \\ 1 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.258
3078	331	\begin{align*} 2 y^{\prime \prime }+9 y&=2 \cos \left (3 x \right )+3 \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.259
3079	378	\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.259
3080	832	\begin{align*} 35 y^{\prime \prime }-y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.259
3081	1361	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.259
3082	3611	\begin{align*} x^{2} y^{\prime }-4 y x&=x^{7} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.259
3083	9527	\begin{align*} x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.259
3084	10094	\begin{align*} y^{\prime \prime }-y^{\prime }-y x -x^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✗	0.259
3085	10599	\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.259
3086	11224	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.259
3087	18175	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.259
3088	20380	\begin{align*} {y^{\prime }}^{2}-7 y^{\prime }+12&=0 \\ \end{align*}	✓	✓	✓	✓	0.259
3089	390	\begin{align*} 2 x^{\prime \prime }+2 x^{\prime }+x&=3 \sin \left (10 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.260
3090	1056	\begin{align*} x y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.260
3091	1057	\begin{align*} 2 x y^{\prime }&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.260
3092	1787	\begin{align*} \left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✗	0.260
3093	2173	\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{-x} \left (10 x^{2}-24 x +5\right ) \\ \end{align*}	✓	✓	✓	✓	0.260
3094	3722	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=2 \,{\mathrm e}^{-x}+3 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.260
3095	7265	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.260
3096	10092	\begin{align*} y^{\prime \prime }-y^{\prime }-y x -x&=0 \\ \end{align*}	✓	✓	✓	✗	0.260
3097	10639	\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.260
3098	10725	\begin{align*} x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.260
3099	10985	\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.260
3100	11004	\begin{align*} x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.260