2.3.35 Problems 3401 to 3500

Table 2.601: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
3401	12954	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+1+2 x y^{2}+a y^{3}&=0 \\ \end{align*}	✗	✗	✗	✗	0.194
3402	14189	\begin{align*} y^{\prime }+8 y^{\prime \prime } x +4 x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
3403	14414	\begin{align*} 12 y-7 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
3404	14421	\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
3405	15669	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
3406	16421	\begin{align*} x y^{\prime \prime \prime }+2 y^{\prime \prime }&=6 x \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 1 \\ y^{\prime \prime }\left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.194
3407	17677	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+10 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+21 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
3408	18018	\begin{align*} x {y^{\prime }}^{2}-y^{\prime } y-y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✗	0.194
3409	19571	\begin{align*} y^{\prime \prime \prime }-\frac {y^{\prime }}{4}&=x \\ \end{align*}	✓	✓	✓	✓	0.194
3410	21665	\begin{align*} x^{\prime }+x^{2}&=0 \\ x \left (-\frac {1}{2}\right ) &= 0 \\ \end{align*} Series expansion around \(t=-{\frac {1}{2}}\).	✓	✓	✓	✓	0.194
3411	23833	\begin{align*} y^{\prime }&=t \ln \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.194
3412	24050	\begin{align*} y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }+54 y^{\prime \prime }-108 y^{\prime }+81 y&=x^{2} {\mathrm e}^{3 x} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.194
3413	24097	\begin{align*} y^{\prime } x +\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.194
3414	24924	\begin{align*} y^{\prime }&=t \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.194
3415	25096	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
3416	25323	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.194
3417	275	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.195
3418	518	\begin{align*} 36 x^{2} y^{\prime \prime }+60 y^{\prime } x +\left (9 x^{3}-5\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.195
3419	521	\begin{align*} 4 x^{2} y^{\prime \prime }-12 y^{\prime } x +\left (15+16 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.195
3420	1249	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.195
3421	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.	✓	✓	✓	✓	0.195
3422	2776	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+2 \,{\mathrm e}^{t} \\ x_{2}^{\prime }&=4 x_{1}+x_{2}-{\mathrm e}^{t} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.195
3423	3333	\begin{align*} y^{2}-2 x y^{\prime } y+{y^{\prime }}^{2} \left (x^{2}-1\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.195
3424	4119	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.195
3425	4120	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.195
3426	5639	\begin{align*} {y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+x y \left (x^{2}+y x +y^{2}\right ) y^{\prime }-x^{3} y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.195
3427	6397	\begin{align*} 2 y x +a \,x^{4} {y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=b \\ \end{align*}	✗	✗	✗	✗	0.195
3428	6692	\begin{align*} x^{3} y^{\prime \prime \prime }&=a \\ \end{align*}	✓	✓	✓	✓	0.195
3429	6851	\begin{align*} 1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.195
3430	6937	\begin{align*} y \sec \left (x \right )+\sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.195
3431	7582	\begin{align*} 2 y^{\prime \prime }+7 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.195
3432	9728	\begin{align*} x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✓	0.195
3433	10818	\begin{align*} u^{\prime \prime }+\frac {u}{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.195
3434	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*}	✓	✓	✓	✗	0.195
3435	12538	\begin{align*} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (-v^{2}+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.195
3436	19574	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.195
3437	19846	\begin{align*} y^{\prime \prime \prime \prime }-y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.195
3438	20330	\begin{align*} 2 x^{\prime \prime }+5 x^{\prime }-12 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.195
3439	22684	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.195
3440	24812	\begin{align*} y^{\prime } \left (y^{\prime } x -y+k \right )+a&=0 \\ \end{align*}	✓	✓	✓	✗	0.195
3441	25082	\begin{align*} y^{\prime \prime }+y&=4 \sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.195
3442	401	\begin{align*} y^{\prime }&=4 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.196
3443	439	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.196
3444	9606	\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.196
3445	11272	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x -\left (x^{2}+\frac {5}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.196
3446	14199	\begin{align*} t^{2} x^{\prime \prime }-6 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.196
3447	15692	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=2 \,{\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 3 \\ y^{\prime \prime }\left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	0.196
3448	19123	\begin{align*} y&=y^{\prime } x +y^{\prime }-{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.196
3449	19443	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.196
3450	19814	\begin{align*} \left (x^{2}-2 y x \right ) y^{\prime }+x^{2}-3 y x +2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.196
3451	21287	\begin{align*} x^{\prime }-x&=k \delta \left (t \right ) \\ x \left (0\right ) &= a \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.196
3452	24522	\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=20 \\ \end{align*}	✓	✓	✓	✓	0.196
3453	25092	\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.196
3454	1757	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=\frac {4}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.197
3455	5497	\begin{align*} x^{2} {y^{\prime }}^{2}&=\left (x -y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.197
3456	5637	\begin{align*} {y^{\prime }}^{3}+\left (2 x -y^{2}\right ) {y^{\prime }}^{2}-2 y^{2} y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
3457	6951	\begin{align*} y \left (2 x +y^{3}\right )-x \left (2 x -y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.197
3458	8186	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
3459	10756	\begin{align*} 2 y^{\prime \prime } x -y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
3460	10859	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.197
3461	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*}	✓	✓	✓	✗	0.197
3462	11029	\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*}	✓	✓	✓	✗	0.197
3463	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*}	✓	✓	✓	✗	0.197
3464	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*}	✓	✓	✓	✗	0.197
3465	11101	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.197
3466	11183	\begin{align*} 2 y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.197
3467	11267	\begin{align*} y^{\prime \prime } x +\left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.197
3468	12798	\begin{align*} 6 y^{\prime \prime }+6 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
3469	13926	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{x}-b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.197
3470	14576	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
3471	14657	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }-4 y&=8 x^{2}+3-6 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 7 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.197
3472	15486	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
3473	15508	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
3474	16488	\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
3475	16489	\begin{align*} y^{\prime \prime }+2 y^{\prime }-24 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
3476	22234	\begin{align*} y^{\prime \prime }+4 y^{\prime }+8 y&=\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.197
3477	23325	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
3478	23416	\begin{align*} x \left (1-3 x \ln \left (x \right )\right ) y^{\prime \prime }+\left (1+9 \ln \left (x \right ) x^{2}\right ) y^{\prime }-\left (3+9 x \right ) y&=0 \\ \end{align*}	✓	✓	✗	✗	0.197
3479	23420	\begin{align*} 6 y-2 y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.197
3480	23639	\begin{align*} y^{\prime \prime \prime }-27 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 6 \\ y^{\prime \prime }\left (0\right ) &= 18 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.197
3481	23824	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.197
3482	24791	\begin{align*} x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	0.197
3483	24797	\begin{align*} {y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
3484	25101	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
3485	25107	\begin{align*} y^{\prime \prime }-4 y^{\prime }-21 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.197
3486	410	\begin{align*} y^{\prime \prime }&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.198
3487	1323	\begin{align*} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.198
3488	2163	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x} \left (x^{2}+4 x +3\right ) \\ \end{align*}	✓	✓	✓	✗	0.198
3489	2209	\begin{align*} y^{\prime }+2 y^{\prime \prime }+y^{\prime \prime \prime }&=-2 \,{\mathrm e}^{-x} \left (6 x^{2}-18 x +7\right ) \\ \end{align*}	✓	✓	✓	✓	0.198
3490	2721	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime }&=t +\cos \left (t \right )+2 \,{\mathrm e}^{-2 t} \\ \end{align*}	✓	✓	✓	✓	0.198
3491	4063	\begin{align*} y^{\prime \prime }-x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.198
3492	5617	\begin{align*} {y^{\prime }}^{3}-7 y^{\prime }+6&=0 \\ \end{align*}	✓	✓	✓	✓	0.198
3493	6506	\begin{align*} -y^{\prime } y-2 x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.198
3494	7233	\begin{align*} \cos \left (x \right ) y^{\prime }+y&=\cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.198
3495	8143	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.198
3496	9228	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.198
3497	10333	\begin{align*} y^{\prime }-t y&=0 \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.198
3498	10868	\begin{align*} \left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.198
3499	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*}	✓	✓	✓	✗	0.198
3500	11265	\begin{align*} x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.198