2.3.36 Problems 3501 to 3600

Table 2.645: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
3501	22712	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=3 x^{2}-4 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.286
3502	23281	\begin{align*} y^{\prime \prime }-7 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.286
3503	23826	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-x-y \\ \end{align*}	✓	✓	✓	✓	0.286
3504	26462	\begin{align*} \left (x -1\right ) y^{\prime \prime \prime }+2 y^{\prime \prime }&=\frac {x +1}{2 x^{2}} \\ \end{align*}	✓	✓	✓	✗	0.286
3505	26712	\begin{align*} y^{\prime \prime }&=x^{2} y-y^{\prime } \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.286
3506	1082	\begin{align*} y^{\prime \prime }+x y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.287
3507	9110	\begin{align*} y^{\prime }-y x&=0 \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.287
3508	10530	\begin{align*} \left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.287
3509	10682	\begin{align*} \left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.287
3510	10945	\begin{align*} y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.287
3511	10964	\begin{align*} 12 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.287
3512	12287	\begin{align*} y^{\prime \prime }-2 y-4 x^{2} {\mathrm e}^{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.287
3513	16489	\begin{align*} y^{\prime \prime }+2 y^{\prime }-24 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.287
3514	16791	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{-3 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.287
3515	18261	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime }&=x +2 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.287
3516	19752	\begin{align*} y^{\prime \prime }+12 y&=7 y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.287
3517	20558	\begin{align*} x y^{\prime \prime \prime }-x y^{\prime \prime }-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.287
3518	23314	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.287
3519	3347	\begin{align*} y^{\prime \prime }+\frac {{y^{\prime }}^{2}}{2}-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.288
3520	16488	\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.288
3521	16781	\begin{align*} y^{\prime \prime }-9 y&=24 \,{\mathrm e}^{-3 t} \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.288
3522	17650	\begin{align*} x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+17 x y^{\prime }-17 y&=0 \\ y \left (1\right ) &= -2 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.288
3523	19866	\begin{align*} 4 y^{\prime }+5 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=-\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.288
3524	20112	\begin{align*} y x -x^{2} y^{\prime }+2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.288
3525	21911	\begin{align*} y^{\prime \prime }-4 y&=0 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.288
3526	27639	\begin{align*} y^{\prime \prime }+y&=4 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.288
3527	7366	\begin{align*} y^{\prime \prime }&=-4 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.289
3528	10743	\begin{align*} x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.289
3529	11141	\begin{align*} x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.289
3530	13175	\(\left [\begin {array}{cc} 5 & -4 \\ 3 & -2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.289
3531	17649	\begin{align*} x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+5 x y^{\prime }-5 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= -1 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.289
3532	18465	\begin{align*} x^{\prime \prime }+x^{\prime }&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.289
3533	23698	\begin{align*} y^{\prime \prime }-y x&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.289
3534	25509	\begin{align*} y^{\prime }&=-\frac {y}{2 t} \\ \end{align*}	✓	✓	✓	✓	0.289
3535	26364	\begin{align*} x&=\sin \left (y^{\prime }\right )+y^{\prime } \\ \end{align*}	✓	✓	✓	✗	0.289
3536	27575	\begin{align*} x^{2} y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	0.289
3537	27782	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.289
3538	3641	\begin{align*} y \left (x^{2}-y^{2}\right )-x \left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.290
3539	3793	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=\sqrt {x}\, \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.290
3540	10527	\begin{align*} y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.290
3541	10701	\begin{align*} x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.290
3542	10780	\begin{align*} 2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.290
3543	10926	\begin{align*} \left (x +2\right ) y^{\prime \prime }+x y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.290
3544	11072	\begin{align*} y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1}&=0 \\ \end{align*}	✓	✓	✓	✗	0.290
3545	13142	\(\left [\begin {array}{cc} 10 & -9 \\ 6 & -5 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.290
3546	17678	\begin{align*} x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+44 x y^{\prime }+58 y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 10 \\ y^{\prime \prime }\left (1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.290
3547	18571	\begin{align*} 2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.290
3548	19824	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.290
3549	20330	\begin{align*} 2 x^{\prime \prime }+5 x^{\prime }-12 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.290
3550	20611	\begin{align*} x^{2} y^{\prime \prime }-\left (x^{2}+2 x \right ) y^{\prime }+\left (x +2\right ) y&={\mathrm e}^{x} x^{3} \\ \end{align*}	✓	✓	✓	✗	0.290
3551	23356	\begin{align*} y^{\prime \prime }+20 y^{\prime }+64 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.290
3552	23759	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.290
3553	24049	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=16 \,{\mathrm e}^{2 x} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.290
3554	8631	\begin{align*} y^{\prime \prime }+\frac {y}{25}&=\frac {t^{2}}{50} \\ y \left (0\right ) &= -25 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.291
3555	10950	\begin{align*} \left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.291
3556	11162	\begin{align*} -a^{2} y+y^{\prime \prime }&=\frac {6 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.291
3557	20332	\begin{align*} 9 x^{\prime \prime }+18 x^{\prime }-16 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.291
3558	2198	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=12 \,{\mathrm e}^{-x}+9 \cos \left (2 x \right )-13 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.292
3559	3948	\begin{align*} y^{\prime \prime }+5 y^{\prime }+4 y&=20 \sin \left (2 t \right ) \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.292
3560	7909	\begin{align*} 2 y-x^{3}+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.292
3561	11010	\begin{align*} 9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.292
3562	13139	\(\left [\begin {array}{cc} 5 & -6 \\ 3 & -4 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.292
3563	13140	\(\left [\begin {array}{cc} 8 & -6 \\ 3 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.292
3564	15264	\begin{align*} y^{\prime \prime \prime }&=2 y^{\prime \prime }-4 y^{\prime }+\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.292
3565	15970	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=x-y \\ \end{align*}	✓	✓	✓	✓	0.292
3566	20039	\begin{align*} 9 y^{\prime \prime }+18 y^{\prime }-16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.292
3567	23645	\begin{align*} y^{\prime \prime \prime }-y&=-1 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -2 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.292
3568	24046	\begin{align*} y^{\prime \prime }+y&=x \sin \left (x \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.292
3569	27569	\begin{align*} y y^{\prime \prime }&={y^{\prime }}^{2}+15 y^{2} \sqrt {x} \\ \end{align*}	✗	✓	✓	✗	0.292
3570	238	\begin{align*} 2 y^{\prime \prime }-y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.293
3571	369	\begin{align*} y^{\prime \prime }-4 y&=\sinh \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.293
3572	8183	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.293
3573	11001	\begin{align*} x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.293
3574	13207	\begin{align*} y^{\prime }&=a y^{2}+b x +c \\ \end{align*}	✓	✓	✓	✗	0.293
3575	14697	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.293
3576	15741	\(\left [\begin {array}{cc} -3 & -1 \\ 2 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.293
3577	19640	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.293
3578	20538	\begin{align*} x^{3} y^{\prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.293
3579	20761	\begin{align*} \left (x^{2}+x +1\right ) y^{\prime \prime \prime }+\left (3+6 x \right ) y^{\prime \prime }+6 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.293
3580	20987	\begin{align*} y^{\prime }&=x^{3}+y^{3} \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.293
3581	23027	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.293
3582	23333	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.293
3583	23804	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.293
3584	23808	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=-x+y \\ \end{align*}	✓	✓	✓	✓	0.293
3585	26454	\begin{align*} {y^{\prime \prime }}^{2}-y^{\prime } y^{\prime \prime \prime }&=\frac {{y^{\prime }}^{2}}{x^{2}} \\ \end{align*}	✗	✓	✓	✗	0.293
3586	26622	\begin{align*} x^{2} y^{\prime \prime \prime }&=2 y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.293
3587	26719	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.293
3588	27013	\begin{align*} y^{\prime }-9 y&=t \\ y \left (0\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.293
3589	411	\begin{align*} y^{\prime \prime }&=4 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.294
3590	1070	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.294
3591	3559	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.294
3592	4159	\begin{align*} y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y&=\cos \left (2 x +3\right ) \\ \end{align*}	✓	✓	✓	✓	0.294
3593	8188	\begin{align*} x^{2} y^{\prime \prime \prime }-3 x y^{\prime \prime }+3 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.294
3594	10304	\begin{align*} y {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.294
3595	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*}	✓	✓	✓	✗	0.294
3596	10623	\begin{align*} 9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.294
3597	11071	\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.294
3598	11205	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.294
3599	14099	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=2 \,{\mathrm e}^{-x}-x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.294
3600	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*}	✓	✓	✓	✓	0.294