2.3.34 Problems 3301 to 3400

Table 2.611: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
3301	1307	\begin{align*} y^{\prime \prime }-2 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.224
3302	1466	\begin{align*} x y^{\prime \prime \prime }-y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.224
3303	1772	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.224
3304	2364	\begin{align*} 6 y^{\prime \prime }-7 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.224
3305	3308	\begin{align*} x&={y^{\prime }}^{2}+y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.224
3306	4159	\begin{align*} y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y&=\cos \left (3+2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.224
3307	4495	\begin{align*} y^{\prime \prime \prime \prime }-18 y^{\prime \prime }+81 y&=72 \,{\mathrm e}^{3 x}+729 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.224
3308	10685	\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.224
3309	11215	\begin{align*} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.224
3310	11295	\begin{align*} y^{\prime \prime }&=\left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (x -1\right )^{2}}+\frac {3}{16 \left (x -1\right ) x}\right ) y \\ \end{align*}	✓	✓	✓	✓	0.224
3311	12724	\begin{align*} y^{\prime \prime \prime }-\sin \left (x \right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y-\ln \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	0.224
3312	17600	\begin{align*} y^{\prime \prime \prime }-13 y^{\prime }+12 y&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.224
3313	20887	\begin{align*} \left (x +1\right ) y^{\prime }&=y p \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.224
3314	21109	\begin{align*} x^{\prime \prime }+2 x^{\prime }+2 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.224
3315	21665	\begin{align*} x^{\prime }+x^{2}&=0 \\ x \left (-\frac {1}{2}\right ) &= 0 \\ \end{align*} Series expansion around \(t=-{\frac {1}{2}}\).	✓	✓	✓	✓	0.224
3316	22736	\begin{align*} 2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.224
3317	23348	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 3 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.224
3318	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*}	✓	✓	✓	✗	0.225
3319	2546	\begin{align*} y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.225
3320	5891	\begin{align*} -\left (x +1\right ) y+y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.225
3321	10940	\begin{align*} y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.225
3322	21206	\begin{align*} x^{\prime }&=a x+y \\ y^{\prime }&=a y \\ \end{align*}	✓	✓	✓	✓	0.225
3323	24047	\begin{align*} y^{\prime \prime \prime }+y&={\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.225
3324	353	\begin{align*} y^{\prime \prime }+9 y&=\sin \left (2 x \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.226
3325	1079	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.226
3326	5933	\begin{align*} f \left (x \right ) y+\left (2+f \left (x \right ) x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.226
3327	10926	\begin{align*} \left (2+x \right ) y^{\prime \prime }+y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.226
3328	13146	\(\left [\begin {array}{cc} 8 & -10 \\ 2 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.226
3329	17581	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.226
3330	19996	\begin{align*} {y^{\prime }}^{2}-9 y^{\prime }+18&=0 \\ \end{align*}	✓	✓	✓	✓	0.226
3331	20036	\begin{align*} y^{\prime \prime }+3 y^{\prime }-54 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.226
3332	21874	\begin{align*} y^{\prime \prime }-12 y^{\prime }+35 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.226
3333	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.	✓	✓	✓	✓	0.226
3334	23992	\begin{align*} y^{\prime \prime \prime }-y&=1 \\ \end{align*}	✓	✓	✓	✓	0.226
3335	404	\begin{align*} y^{\prime }&=y x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.227
3336	442	\begin{align*} y^{\prime \prime }+y^{\prime } x -2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.227
3337	1057	\begin{align*} 2 y^{\prime } x&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.227
3338	2169	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{2 x} \left (18 x^{2}+33 x +13\right ) \\ \end{align*}	✓	✓	✓	✓	0.227
3339	3573	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.227
3340	3938	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=10 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.227
3341	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.	✓	✓	✓	✓	0.227
3342	4370	\begin{align*} y^{\prime }&=\left (\sin \left (x \right )^{2}-y\right ) \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.227
3343	5957	\begin{align*} a y+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.227
3344	7957	\begin{align*} y&=y^{\prime } x -2 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.227
3345	8628	\begin{align*} y^{\prime \prime }+7 y^{\prime }+12 y&=21 \,{\mathrm e}^{3 t} \\ y \left (0\right ) &= {\frac {7}{2}} \\ y^{\prime }\left (0\right ) &= -10 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.227
3346	10606	\begin{align*} 3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.227
3347	10644	\begin{align*} x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.227
3348	10840	\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*}	✓	✓	✓	✗	0.227
3349	11047	\begin{align*} x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.227
3350	13178	\(\left [\begin {array}{cc} 6 & -10 \\ 2 & -3 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.227
3351	15004	\begin{align*} x^{\prime }&=-2 x+2 y \\ y^{\prime }&=x-y \\ \end{align*}	✓	✓	✓	✓	0.227
3352	15081	\begin{align*} y^{\prime \prime }+4 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.227
3353	15476	\begin{align*} x^{\prime }&=0 \\ y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.227
3354	17536	\begin{align*} 4 t^{2} y^{\prime \prime }+4 y^{\prime } t +\left (16 t^{2}-1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.227
3355	18458	\begin{align*} x^{\prime }-x&=\cos \left (t \right )-\sin \left (t \right ) \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.227
3356	19975	\begin{align*} {y^{\prime }}^{2}-7 y^{\prime }+12&=0 \\ \end{align*}	✓	✓	✓	✓	0.227
3357	21204	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=-3 y \\ \end{align*}	✓	✓	✓	✓	0.227
3358	25161	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime }+4 y^{\prime }&=4 \,{\mathrm e}^{2 t} t \\ \end{align*}	✓	✓	✓	✓	0.227
3359	26073	\begin{align*} y^{\prime }&=3 y-4 z \\ z^{\prime }&=y-z \\ \end{align*}	✓	✓	✓	✓	0.227
3360	1097	\begin{align*} y^{\prime \prime }&=y x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.228
3361	1768	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=4 x^{4} \\ \end{align*}	✓	✓	✓	✓	0.228
3362	3273	\begin{align*} y^{\prime \prime }&=y^{3} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= \frac {\sqrt {2}}{2} \\ \end{align*}	✓	✓	✓	✗	0.228
3363	3793	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=\sqrt {x}\, \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.228
3364	5882	\begin{align*} 3 y-10 y^{\prime }+3 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.228
3365	7237	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=y x +2 x \sqrt {-x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	0.228
3366	8186	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.228
3367	10562	\begin{align*} 4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.228
3368	10808	\begin{align*} 3 t \left (1+t \right ) y^{\prime \prime }+y^{\prime } t -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.228
3369	11062	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.228
3370	11268	\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*}	✓	✓	✓	✗	0.228
3371	12804	\begin{align*} 6 y^{\prime \prime } x +6 x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.228
3372	13145	\(\left [\begin {array}{cc} 7 & -6 \\ 12 & -10 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.228
3373	16461	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=\sqrt {x} \\ \end{align*}	✓	✓	✓	✓	0.228
3374	18906	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=18 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.228
3375	1627	\begin{align*} x^{2} y^{\prime }&=y^{2}+y x -x^{2} \\ \end{align*}	✓	✓	✓	✓	0.229
3376	2174	\begin{align*} y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+18 y^{\prime \prime }-20 y^{\prime }+8 y&={\mathrm e}^{2 x} \left (-5 x^{2}-8 x +3\right ) \\ \end{align*}	✓	✓	✓	✓	0.229
3377	3790	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=8 x^{4} \\ \end{align*}	✓	✓	✓	✓	0.229
3378	7717	\begin{align*} -y+y^{\prime } x&=x^{3}+3 x^{2}-2 x \\ \end{align*}	✓	✓	✓	✓	0.229
3379	8100	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +8 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.229
3380	13149	\(\left [\begin {array}{cc} 13 & -15 \\ 6 & -6 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.229
3381	13179	\(\left [\begin {array}{cc} 11 & -15 \\ 6 & -8 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.229
3382	15010	\begin{align*} x^{\prime }&=-6 x+2 y \\ y^{\prime }&=-2 x-2 y \\ \end{align*}	✓	✓	✓	✓	0.229
3383	15214	\begin{align*} 4 y^{\prime \prime }+5 y^{\prime }+4 y&=3 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.229
3384	16035	\begin{align*} y^{\prime \prime }-6 y^{\prime }-7 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.229
3385	20161	\begin{align*} x y^{\prime \prime \prime }-y^{\prime \prime } x -y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.229
3386	22243	\begin{align*} y^{\prime }+5 y&=0 \\ y \left (1\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.229
3387	24025	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.229
3388	47	\begin{align*} y^{\prime }&=64^{{1}/{3}} \left (y x \right )^{{1}/{3}} \\ \end{align*}	✓	✓	✓	✗	0.230
3389	219	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.230
3390	291	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*}	✓	✓	✓	✓	0.230
3391	413	\begin{align*} y^{\prime \prime }+y&=x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.230
3392	1303	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.230
3393	1483	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.230
3394	4471	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }-y&=44 \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.230
3395	4494	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y&=32 \,{\mathrm e}^{2 x}+16 x^{3} \\ \end{align*}	✓	✓	✓	✓	0.230
3396	6874	\begin{align*} {y^{\prime }}^{2}-5 y^{\prime }+6&=0 \\ \end{align*}	✓	✓	✓	✓	0.230
3397	7887	\begin{align*} x \sqrt {x^{2}+y^{2}}-y+\left (y \sqrt {x^{2}+y^{2}}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.230
3398	9600	\begin{align*} y+2 y^{\prime }&=0 \\ y \left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.230
3399	10591	\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*}	✓	✓	✓	✗	0.230
3400	10780	\begin{align*} 2 y^{\prime \prime } x -\left (3+2 x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.230