2.3.32 Problems 3101 to 3200

Table 2.637: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
3101	11011	\begin{align*} 36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.260
3102	11234	\begin{align*} x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.260
3103	15702	\begin{align*} y^{\prime }-y&=2 \,{\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.260
3104	16055	\(\left [\begin {array}{cc} 1 & 0 \\ 2 & 3 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.260
3105	16461	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=\sqrt {x} \\ \end{align*}	✓	✓	✓	✓	0.260
3106	20763	\begin{align*} y^{\prime \prime \prime }+\cos \left (x \right ) y^{\prime \prime }-2 \sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✗	0.260
3107	22041	\begin{align*} y^{2}+x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.260
3108	22320	\begin{align*} y^{\prime \prime \prime }&=-24 \cos \left (\frac {\pi x}{2}\right ) \\ y \left (0\right ) &= -4 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	0.260
3109	24065	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{x}+{\mathrm e}^{2 x}+{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.260
3110	25512	\begin{align*} 2 t y^{\prime \prime }-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.260
3111	26159	\begin{align*} {y^{\prime }}^{2}+{\mathrm e}^{y^{\prime }}&=x \\ \end{align*}	✓	✓	✓	✗	0.260
3112	26710	\begin{align*} y^{\prime \prime }-x y^{\prime }+y&=1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.260
3113	26765	\begin{align*} x^{\prime }&=3 x \\ y^{\prime }&=3 y \\ \end{align*}	✓	✓	✓	✓	0.260
3114	27616	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.260
3115	827	\begin{align*} 2 y^{\prime \prime }-y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.261
3116	1249	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.261
3117	7368	\begin{align*} y^{\prime \prime }&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.261
3118	10095	\begin{align*} y^{\prime \prime }-y^{\prime }-y x -x^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✗	0.261
3119	10513	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.261
3120	10693	\begin{align*} x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.261
3121	11012	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (-x +3\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.261
3122	11120	\begin{align*} x^{2} y^{\prime \prime }+x \left (-x +3\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.261
3123	11125	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.261
3124	15100	\begin{align*} x^{\prime \prime \prime \prime }+x&=t^{3} \\ \end{align*}	✓	✓	✓	✓	0.261
3125	16132	\begin{align*} y^{\prime \prime }+4 y&=8 \\ y \left (0\right ) &= 11 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.261
3126	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.	✓	✓	✓	✓	0.261
3127	16459	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=9 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.261
3128	19635	\begin{align*} y^{\prime \prime }-y^{\prime }&=t^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.261
3129	26815	\begin{align*} x^{\prime }+x&=2 \sin \left (t \right ) \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.261
3130	26842	\begin{align*} x^{\prime \prime \prime }+x^{\prime \prime }-2 x&={\mathrm e}^{t} t \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= {\frac {21}{25}} \\ x^{\prime \prime }\left (0\right ) &= -{\frac {28}{25}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.261
3131	27061	\begin{align*} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.261
3132	27638	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.261
3133	1466	\begin{align*} x y^{\prime \prime \prime }-y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.262
3134	1488	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.262
3135	7165	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.262
3136	7270	\begin{align*} y^{\prime \prime }+\left (1+2 i\right ) y^{\prime }+\left (-1+i\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.262
3137	10337	\begin{align*} t y^{\prime }+y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.262
3138	10611	\begin{align*} x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.262
3139	11051	\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.262
3140	11063	\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.262
3141	14113	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=4+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.262
3142	16777	\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.262
3143	17612	\begin{align*} t y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }&=\frac {45}{8 t^{{7}/{2}}} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 1 \\ y^{\prime \prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.262
3144	326	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.263
3145	1252	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.263
3146	2186	\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+13 y^{\prime \prime }+12 y^{\prime }+4 y&={\mathrm e}^{-x} \left (\left (4-x \right ) \cos \left (x \right )-\left (5+x \right ) \sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.263
3147	3414	\begin{align*} {y^{\prime }}^{2}-3 y^{\prime }+2&=0 \\ \end{align*}	✓	✓	✓	✓	0.263
3148	3941	\begin{align*} y^{\prime \prime }-y&=12 \,{\mathrm e}^{2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.263
3149	7239	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.263
3150	7828	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{-2 x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.263
3151	10718	\begin{align*} x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.263
3152	10813	\begin{align*} x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.263
3153	11061	\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (1+4 x \right ) y^{\prime }-\left (49+27 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.263
3154	11088	\begin{align*} t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.263
3155	11131	\begin{align*} x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.263
3156	11203	\begin{align*} \left (x +2\right ) y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.263
3157	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.	✓	✓	✓	✓	0.263
3158	18182	\begin{align*} y-4 y^{\prime }+6 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.263
3159	18312	\begin{align*} y^{\prime \prime }+\left (\tan \left (x \right )-2 \cot \left (x \right )\right ) y^{\prime }+2 \cot \left (x \right )^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.263
3160	20038	\begin{align*} 2 y^{\prime \prime }+5 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.263
3161	24054	\begin{align*} y^{\prime \prime }+9 y&=3 x -6 \\ y \left (0\right ) &= {\frac {1}{3}} \\ y^{\prime }\left (0\right ) &= {\frac {4}{3}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.263
3162	1250	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.264
3163	1305	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.264
3164	3944	\begin{align*} y^{\prime \prime }-y&=6 \cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.264
3165	7238	\begin{align*} y^{\prime }+y \tanh \left (x \right )&=2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.264
3166	7376	\begin{align*} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.264
3167	8626	\begin{align*} y^{\prime \prime }-\frac {y}{4}&=0 \\ y \left (0\right ) &= 12 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.264
3168	10645	\begin{align*} x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.264
3169	11007	\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.264
3170	11045	\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.264
3171	11086	\begin{align*} t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+y t&=0 \\ \end{align*}	✓	✓	✓	✗	0.264
3172	11182	\begin{align*} y-x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.264
3173	19473	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.264
3174	22784	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.264
3175	23411	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {9 y}{x^{4}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.264
3176	26711	\begin{align*} y^{\prime \prime }-\left (x^{2}+1\right ) y&=0 \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.264
3177	27120	\(\left [\begin {array}{cc} 4 & -2 \\ -2 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.264
3178	27596	\begin{align*} y y^{\prime \prime }&={y^{\prime }}^{2}+2 x y^{2} \\ \end{align*}	✗	✓	✓	✗	0.264
3179	3952	\begin{align*} y^{\prime \prime }+y&=6 \cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.265
3180	7364	\begin{align*} x y^{\prime }&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.265
3181	10101	\begin{align*} y^{\prime \prime }-2 y^{\prime }-y x -x^{3}+2&=0 \\ \end{align*}	✓	✓	✓	✗	0.265
3182	10723	\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.265
3183	11009	\begin{align*} 16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.265
3184	11030	\begin{align*} x \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.265
3185	11031	\begin{align*} x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.265
3186	11098	\begin{align*} z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z}&=0 \\ \end{align*}	✓	✓	✓	✓	0.265
3187	13192	\(\left [\begin {array}{ccc} 0 & 1 & 0 \\ -1 & 2 & 0 \\ -1 & 1 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.265
3188	19185	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.265
3189	19626	\begin{align*} y^{\prime \prime }+y^{\prime }&=3 x^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.265
3190	7043	\begin{align*} 6 y^{\prime \prime }-11 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.266
3191	7916	\begin{align*} x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.266
3192	9402	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.266
3193	10244	\begin{align*} x y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.266
3194	10607	\begin{align*} 9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.266
3195	10634	\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.266
3196	10641	\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (1+4 x \right ) y^{\prime }-\left (49+27 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.266
3197	10643	\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.266
3198	10695	\begin{align*} x^{2} y^{\prime \prime }+x \left (-x +3\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.266
3199	10846	\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x^{4} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.266
3200	11170	\begin{align*} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.266