2.3.34 Problems 3301 to 3400

Table 2.617: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
3301	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*}	✓	✓	✓	✗	0.275
3302	10657	\begin{align*} \left (2 t +1\right ) y^{\prime \prime }-4 \left (1+t \right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.275
3303	10932	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.275
3304	10988	\begin{align*} 2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.275
3305	11048	\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*}	✓	✓	✓	✗	0.275
3306	11217	\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.275
3307	13192	\(\left [\begin {array}{ccc} 0 & 1 & 0 \\ -1 & 2 & 0 \\ -1 & 1 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.275
3308	18261	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime }&=x +2 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.275
3309	18468	\begin{align*} x^{\prime \prime }+6 x^{\prime }&=12 t +2 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.275
3310	23007	\begin{align*} 20 y^{\prime \prime }-3 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.275
3311	1257	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.276
3312	1323	\begin{align*} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.276
3313	3370	\begin{align*} x^{3} \left (x^{2}+3\right ) y^{\prime \prime }+5 y^{\prime } x -\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.276
3314	3559	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.276
3315	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*}	✓	✓	✓	✗	0.276
3316	10636	\begin{align*} 3 \left (x +3\right ) x^{2} y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.276
3317	15191	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+37 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.276
3318	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.	✓	✓	✓	✓	0.276
3319	19752	\begin{align*} y^{\prime \prime }+12 y&=7 y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.276
3320	23008	\begin{align*} 35 y^{\prime \prime }-29 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.276
3321	23270	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.276
3322	1046	\begin{align*} y^{\prime }&=x^{2} y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.277
3323	1266	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }+y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	0.277
3324	2234	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=F \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.277
3325	6646	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.277
3326	8130	\begin{align*} y^{\prime \prime }+2 x^{3} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.277
3327	10595	\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*}	✓	✓	✓	✗	0.277
3328	10730	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9}&=0 \\ \end{align*}	✓	✓	✓	✗	0.277
3329	10952	\begin{align*} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.277
3330	10983	\begin{align*} 3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.277
3331	11022	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.277
3332	11056	\begin{align*} 3 \left (x +3\right ) x^{2} y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.277
3333	11234	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.277
3334	11274	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +4 x^{4} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.277
3335	15187	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.277
3336	448	\begin{align*} y^{\prime \prime }+\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.278
3337	1763	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=8 \,{\mathrm e}^{-x \left (2+x \right )} \\ \end{align*}	✓	✓	✓	✗	0.278
3338	3572	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.278
3339	7849	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.278
3340	10532	\begin{align*} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.278
3341	10666	\begin{align*} t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y&=0 \\ \end{align*}	✓	✓	✓	✗	0.278
3342	10708	\begin{align*} x^{2} y^{\prime \prime }+2 x \left (2+x \right ) y^{\prime }+2 \left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.278
3343	10723	\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.278
3344	11058	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.278
3345	11061	\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (4 x +1\right ) y^{\prime }-\left (49+27 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.278
3346	11088	\begin{align*} t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.278
3347	12287	\begin{align*} y^{\prime \prime }-2 y-4 x^{2} {\mathrm e}^{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.278
3348	19582	\begin{align*} y^{\prime }&=1+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.278
3349	19593	\begin{align*} x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.278
3350	20049	\begin{align*} y^{\prime \prime \prime }+y&=3+{\mathrm e}^{-x}+5 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.278
3351	23805	\begin{align*} x^{\prime }&=2 x \\ y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.278
3352	1048	\begin{align*} \left (2 x -1\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.279
3353	1050	\begin{align*} \left (x -1\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.279
3354	1258	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.279
3355	1762	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{x} \sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.279
3356	1765	\begin{align*} x^{2} y^{\prime \prime }+2 x \left (x -1\right ) y^{\prime }+\left (x^{2}-2 x +2\right ) y&=x^{3} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	0.279
3357	3685	\begin{align*} y+3 x^{2}+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.279
3358	6019	\begin{align*} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.279
3359	10609	\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 y^{\prime } x +\left (4 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.279
3360	10668	\begin{align*} t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.279
3361	11065	\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*}	✓	✓	✓	✗	0.279
3362	11098	\begin{align*} z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z}&=0 \\ \end{align*}	✓	✓	✓	✓	0.279
3363	16835	\begin{align*} y^{\prime \prime }-3 x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.279
3364	21590	\begin{align*} y^{\left (5\right )}+y^{\prime \prime }&=x^{5}-3 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.279
3365	22655	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.279
3366	23333	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.279
3367	23825	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-y \\ \end{align*}	✓	✓	✓	✓	0.279
3368	421	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.280
3369	445	\begin{align*} \left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y&=0 \\ y \left (3\right ) &= 2 \\ y^{\prime }\left (3\right ) &= 0 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	0.280
3370	585	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-9 x+6 y \\ \end{align*}	✓	✓	✓	✓	0.280
3371	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.	✓	✓	✓	✓	0.280
3372	2670	\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&={\mathrm e}^{2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.280
3373	3207	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&={\mathrm e}^{x}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.280
3374	5882	\begin{align*} 3 y-10 y^{\prime }+3 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.280
3375	9613	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.280
3376	10813	\begin{align*} y^{\prime \prime } x +3 y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.280
3377	10861	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.280
3378	11031	\begin{align*} \left (1-x \right ) x^{2} y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.280
3379	11086	\begin{align*} t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y&=0 \\ \end{align*}	✓	✓	✓	✗	0.280
3380	14635	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+2 y^{\prime \prime }&=3 \,{\mathrm e}^{-x}+6 \,{\mathrm e}^{2 x}-6 x \\ \end{align*}	✓	✓	✓	✓	0.280
3381	14820	\begin{align*} y^{\prime \prime }-8 y^{\prime }+15 y&=9 \,{\mathrm e}^{2 t} t \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.280
3382	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.	✓	✓	✓	✓	0.280
3383	20901	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=\infty \).	✗	✗	✓	✓	0.280
3384	22242	\begin{align*} y^{\prime }+2 y&=0 \\ y \left (1\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.280
3385	23334	\begin{align*} 8 y^{\prime \prime }-6 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.280
3386	25098	\begin{align*} y^{\prime \prime }+10 y^{\prime }+24 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.280
3387	436	\begin{align*} 5 y^{\prime \prime }-2 y^{\prime } x +10 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.281
3388	1397	\begin{align*} y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.281
3389	6911	\begin{align*} x +y+1+\left (2 x +2 y+2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.281
3390	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*}	✓	✓	✓	✗	0.281
3391	10705	\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.281
3392	11054	\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*}	✓	✓	✓	✗	0.281
3393	11149	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (3 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.281
3394	11173	\begin{align*} x \left (x +1\right ) y^{\prime \prime }-\left (x -1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.281
3395	11242	\begin{align*} y^{\prime \prime } x +3 y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.281
3396	12746	\begin{align*} 6 y^{\prime }+6 y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.281
3397	17365	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.281
3398	20331	\begin{align*} y^{\prime \prime }+3 y^{\prime }-54 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.281
3399	22053	\begin{align*} x y^{2}+x^{2} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.281
3400	23276	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.281