2.3.35 Problems 3401 to 3500

Table 2.613: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
3401	10941	\begin{align*} \left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.230
3402	11141	\begin{align*} y^{\prime \prime } x +\left (x +n \right ) y^{\prime }+\left (n +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.230
3403	11161	\begin{align*} u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.230
3404	13148	\(\left [\begin {array}{cc} 19 & -10 \\ 21 & -10 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.230
3405	15013	\begin{align*} x^{\prime }&=7 x-4 y \\ y^{\prime }&=x+3 y \\ \end{align*}	✓	✓	✓	✓	0.230
3406	15217	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }+17 y&=17 t -1 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.230
3407	17410	\begin{align*} 6 y^{\prime \prime }+5 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.230
3408	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*}	✓	✓	✓	✓	0.230
3409	19185	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.230
3410	21032	\begin{align*} {\mathrm e}^{x^{\prime }}&=x \\ x \left (t_{0} \right ) &= a \\ \end{align*}	✓	✓	✓	✓	0.230
3411	22681	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.230
3412	25226	\begin{align*} 4 t^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.230
3413	1053	\begin{align*} y^{\prime \prime }&=4 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.231
3414	1764	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=-6 x -4 \\ \end{align*}	✓	✓	✓	✓	0.231
3415	4114	\begin{align*} x +\left (2-x +2 y\right ) y^{\prime }&=x y \left (y^{\prime }-1\right ) \\ \end{align*}	✓	✓	✓	✓	0.231
3416	5947	\begin{align*} -y-2 y^{\prime }+4 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.231
3417	6942	\begin{align*} y-3 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.231
3418	7942	\begin{align*} x^{2} {y^{\prime }}^{2}+y y^{\prime } x -6 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.231
3419	8142	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.231
3420	15701	\begin{align*} y^{\prime }&={\mathrm e}^{x} \\ y \left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.231
3421	19825	\begin{align*} y^{\prime \prime }+2 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.231
3422	20388	\begin{align*} x +y {y^{\prime }}^{2}&=\left (y x +1\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.231
3423	6216	\begin{align*} y-x \left (x +1\right ) y^{\prime }+\left (1-x \right ) x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.232
3424	7041	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.232
3425	7238	\begin{align*} y^{\prime }+y \tanh \left (x \right )&=2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.232
3426	8037	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+1\right )^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.232
3427	10743	\begin{align*} y^{\prime \prime } x +3 y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.232
3428	10746	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.232
3429	15211	\begin{align*} y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= 5 \\ y^{\prime \prime \prime }\left (0\right ) &= 19 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.232
3430	20538	\begin{align*} x^{3} y^{\prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.232
3431	22677	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.232
3432	25936	\begin{align*} y^{\prime \prime }-4 y&=8 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.232
3433	169	\begin{align*} y&=y^{\prime } x -\frac {{y^{\prime }}^{2}}{4} \\ \end{align*}	✓	✓	✓	✓	0.233
3434	329	\begin{align*} y^{\prime \prime }-4 y&=\cosh \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.233
3435	3620	\begin{align*} 1-\sin \left (x \right ) y-\cos \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.233
3436	6944	\begin{align*} 2 y x +x^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.233
3437	7259	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.233
3438	7265	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.233
3439	10583	\begin{align*} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.233
3440	10605	\begin{align*} 4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.233
3441	10797	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +30 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.233
3442	16055	\(\left [\begin {array}{cc} 1 & 0 \\ 2 & 3 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.233
3443	17390	\begin{align*} 4 y^{\prime \prime }+21 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.233
3444	17598	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }-11 y^{\prime }+30 y&={\mathrm e}^{4 t} \\ \end{align*}	✓	✓	✓	✓	0.233
3445	18114	\begin{align*} 3 y^{\prime } y^{\prime \prime }&=2 y \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	0.233
3446	18741	\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.233
3447	20883	\begin{align*} \left (x +1\right ) y^{\prime }&=y p \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.233
3448	20928	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.233
3449	21133	\begin{align*} x^{\prime \prime }+x&=3 t^{2}+t \\ \end{align*}	✓	✓	✓	✓	0.233
3450	21710	\begin{align*} y^{\prime }+b y&=1 \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.233
3451	22242	\begin{align*} y^{\prime }+2 y&=0 \\ y \left (1\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.233
3452	24116	\begin{align*} y^{\prime }&=x +2 y \\ y \left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.233
3453	24865	\begin{align*} x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.233
3454	412	\begin{align*} y^{\prime \prime }+9 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.234
3455	1054	\begin{align*} y^{\prime \prime }+9 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.234
3456	1491	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.234
3457	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*}	✓	✓	✓	✓	0.234
3458	2556	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.234
3459	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*}	✓	✓	✓	✓	0.234
3460	6156	\begin{align*} -\left (a^{2}-x \right ) y+4 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.234
3461	10567	\begin{align*} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.234
3462	10568	\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*}	✓	✓	✓	✗	0.234
3463	10732	\begin{align*} u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.234
3464	11018	\begin{align*} \left (1-x \right ) x^{2} y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.234
3465	13177	\(\left [\begin {array}{cc} 10 & -6 \\ 12 & -7 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.234
3466	15028	\begin{align*} {y^{\prime }}^{2}+x^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	0.234
3467	17583	\begin{align*} y^{\prime \prime \prime \prime }+9 y^{\prime \prime }&=9 \,{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	0.234
3468	17587	\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }-14 y^{\prime }-104 y&=-111 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.234
3469	17735	\begin{align*} t y^{\prime \prime }+2 y^{\prime }+t y&=0 \\ \end{align*}	✓	✓	✓	✓	0.234
3470	18037	\begin{align*} {y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x}&=0 \\ \end{align*}	✓	✓	✓	✗	0.234
3471	18772	\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.234
3472	20072	\begin{align*} y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y&=\cos \left (x m \right ) \\ \end{align*}	✓	✓	✓	✓	0.234
3473	21130	\begin{align*} x^{\prime \prime }-4 x&=t \\ \end{align*}	✓	✓	✓	✓	0.234
3474	21487	\begin{align*} y^{\prime \prime }-2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.234
3475	24079	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.234
3476	6189	\begin{align*} -2 y+y^{\prime } x +x^{3} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.235
3477	9614	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=t^{3} {\mathrm e}^{2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.235
3478	10867	\begin{align*} \left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.235
3479	15417	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.235
3480	17391	\begin{align*} 7 y^{\prime \prime }+4 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.235
3481	17417	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.235
3482	18758	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.235
3483	20705	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&={\mathrm e}^{x}+\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.235
3484	431	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.236
3485	1043	\begin{align*} y^{\prime }&=4 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.236
3486	2106	\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\ y \left (-1\right ) &= -4 \\ y^{\prime }\left (-1\right ) &= -14 \\ y^{\prime \prime }\left (-1\right ) &= -20 \\ \end{align*}	✓	✓	✓	✓	0.236
3487	5953	\begin{align*} x^{2} y^{\prime \prime }&=b x +a \\ \end{align*}	✓	✓	✓	✓	0.236
3488	7788	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=2 x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.236
3489	10546	\begin{align*} 18 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.236
3490	10556	\begin{align*} x^{2} \left (4 x +3\right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (4 x +3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.236
3491	10612	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.236
3492	11226	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +30 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.236
3493	18781	\begin{align*} y^{\prime \prime }+4 y^{\prime }+\frac {25 y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.236
3494	21115	\begin{align*} x^{\prime \prime }+x^{\prime }-\beta x&=0 \\ \end{align*}	✓	✓	✓	✓	0.236
3495	23260	\begin{align*} y^{\prime \prime \prime }&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.236
3496	24439	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.236
3497	1267	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ y \left (0\right ) &= \alpha \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.237
3498	1452	\begin{align*} x_{1}^{\prime }&=-x_{1} \\ x_{2}^{\prime }&=-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.237
3499	6646	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.237
3500	6670	\begin{align*} x y^{\prime \prime \prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.237