2.3.64 Problems 6301 to 6400

Table 2.659: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
6301	20762	\begin{align*} \left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 y^{\prime } x +4 y&=\frac {2}{x^{3}} \\ \end{align*}	✓	✓	✓	✗	0.325
6302	20782	\begin{align*} y^{\prime \prime } x -\left (2 x -1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.325
6303	24705	\begin{align*} 4 y+y^{\prime \prime }&=8 \cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.325
6304	429	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.326
6305	547	\begin{align*} x^{\prime \prime \prime \prime }+x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ x^{\prime \prime \prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.326
6306	1013	\begin{align*} x_{1}^{\prime }&=x_{1}-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1}+9 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.326
6307	4064	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-6 y^{\prime } x -4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.326
6308	5946	\begin{align*} y+2 y^{\prime }+4 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.326
6309	6417	\begin{align*} f \left (x \right )^{2} y^{\prime \prime }&=-24 f \left (x \right )^{4}+\left (3 f \left (x \right )^{3}-f \left (x \right )^{2} y+3 f \left (x \right ) f^{\prime }\left (x \right )\right ) y^{\prime } \\ \end{align*}	✗	✗	✗	✗	0.326
6310	6862	\begin{align*} \left (y^{2} x^{2}+y x \right ) y+\left (y^{2} x^{2}-1\right ) x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.326
6311	8004	\begin{align*} y^{\prime \prime }+2 y&={\mathrm e}^{x}+2 \\ \end{align*}	✓	✓	✓	✓	0.326
6312	8034	\begin{align*} \left (x +1\right ) y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+\left (2+x \right ) y&=\left (x^{2}+2 x +1\right ) {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	0.326
6313	10400	\begin{align*} y^{\prime \prime }+y&=x^{2}+x +1 \\ \end{align*}	✓	✓	✓	✓	0.326
6314	10536	\begin{align*} y^{\prime \prime }+3 y^{\prime } x +\left (2 x^{2}+4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.326
6315	11668	\begin{align*} {y^{\prime }}^{2}+\left (x -2\right ) y^{\prime }-y+1&=0 \\ \end{align*}	✓	✓	✓	✓	0.326
6316	14085	\begin{align*} 4 {y^{\prime }}^{2}&=9 x \\ \end{align*}	✓	✓	✓	✓	0.326
6317	14369	\begin{align*} x^{\prime \prime }+x&=\delta \left (t -2\right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.326
6318	14391	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=3 x-4 y \\ \end{align*}	✓	✓	✓	✓	0.326
6319	16112	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.326
6320	16618	\begin{align*} y^{\prime \prime }+9 y&=9 x^{4}-9 \\ \end{align*}	✓	✓	✓	✓	0.326
6321	16642	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=10 x^{2}+4 x +8 \\ \end{align*}	✓	✓	✓	✓	0.326
6322	16738	\begin{align*} y^{\prime \prime }-9 y^{\prime }+14 y&=98 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.326
6323	17117	\begin{align*} y^{\prime }&=\frac {1}{x^{2}+1} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.326
6324	19058	\begin{align*} x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= -5 \\ x_{2} \left (0\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	0.326
6325	20479	\begin{align*} 4 {y^{\prime }}^{2} x^{2} \left (x -1\right )-4 y^{\prime } x y \left (4 x -3\right )+\left (16 x -9\right ) y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.326
6326	23046	\begin{align*} \left (1-y^{2}\right ) y^{\prime \prime }&=y^{\prime } \\ \end{align*}	✓	✓	✓	✗	0.326
6327	23247	\begin{align*} x^{2} y^{\prime \prime }-{\mathrm e}^{x} y^{\prime }-2&=0 \\ \end{align*}	✓	✓	✓	✓	0.326
6328	23809	\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=-x-2 y \\ \end{align*}	✓	✓	✓	✓	0.326
6329	24559	\begin{align*} y^{\prime \prime }+y&=12 \cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.326
6330	24792	\begin{align*} y^{2} {y^{\prime }}^{2}-a^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.326
6331	25132	\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=16 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.326
6332	25133	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{-2 t} \\ \end{align*}	✓	✓	✓	✓	0.326
6333	1010	\begin{align*} x_{1}^{\prime }&=x_{1}-2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+5 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.327
6334	1445	\begin{align*} x_{1}^{\prime }&=x_{1}-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1}-7 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.327
6335	2412	\begin{align*} y^{\prime \prime }+t y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.327
6336	3797	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=4 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.327
6337	4151	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.327
6338	5821	\begin{align*} -\left (1-x \right ) y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.327
6339	6410	\begin{align*} y^{b}+x^{a} y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.327
6340	8080	\begin{align*} y^{\prime \prime } x +y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.327
6341	9521	\begin{align*} y^{\prime \prime }-y x&=1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.327
6342	10560	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.327
6343	10891	\begin{align*} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.327
6344	16068	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.327
6345	17138	\begin{align*} -y+y^{\prime }&=10 \\ \end{align*}	✓	✓	✓	✓	0.327
6346	21865	\begin{align*} \left (x^{2}-2 y x \right ) {y^{\prime }}^{2}-\left (3 x^{2}+2 y\right ) \left (x -2 y\right ) y^{\prime }+6 x y \left (x -2 y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.327
6347	514	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.328
6348	836	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.328
6349	1417	\begin{align*} x_{1}^{\prime }&=4 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=8 x_{1}-4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.328
6350	2612	\begin{align*} \left (t^{2}+2\right ) y^{\prime \prime }-t y^{\prime }-3 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.328
6351	3809	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2} \\ x_{2}^{\prime }&=2 x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.328
6352	6078	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.328
6353	8036	\begin{align*} x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+\left (x^{2}+3 x +3\right ) y&=\left (-x^{2}+6\right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	0.328
6354	9230	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (1\right ) &= {\mathrm e}^{2} \\ y^{\prime }\left (1\right ) &= 3 \,{\mathrm e}^{2} \\ \end{align*}	✓	✓	✓	✓	0.328
6355	10668	\begin{align*} t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.328
6356	10686	\begin{align*} 4 y^{\prime \prime }+y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.328
6357	15087	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=\frac {y y^{\prime }}{\sqrt {x^{2}+1}} \\ \end{align*}	✓	✓	✓	✗	0.328
6358	16110	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.328
6359	16689	\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&=6 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.328
6360	16816	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=\delta \left (t -4\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.328
6361	18655	\begin{align*} x^{\prime }&=-\frac {x}{4}-\frac {3 y}{4} \\ y^{\prime }&=\frac {x}{2}+y \\ \end{align*}	✓	✓	✓	✓	0.328
6362	19825	\begin{align*} y^{\prime \prime }+2 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.328
6363	24084	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.328
6364	24104	\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=x^{3}-x +3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.328
6365	25552	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{t} {\mathrm e}^{i t} \\ \end{align*}	✓	✓	✓	✗	0.328
6366	622	\begin{align*} x_{1}^{\prime }&=2 x_{1}+3 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.329
6367	1368	\begin{align*} \left (-x^{2}+4\right ) y^{\prime \prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.329
6368	1890	\begin{align*} y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.329
6369	2230	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x \left (x +1\right ) \\ y \left (-1\right ) &= -6 \\ y^{\prime }\left (-1\right ) &= {\frac {43}{6}} \\ y^{\prime \prime }\left (-1\right ) &= -{\frac {5}{2}} \\ \end{align*}	✓	✓	✓	✓	0.329
6370	3405	\begin{align*} y^{\prime }&={\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.329
6371	3810	\begin{align*} x_{1}^{\prime }&=2 x_{1}-3 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.329
6372	4004	\begin{align*} y^{\prime \prime }+y^{\prime } x -4 y&=6 \,{\mathrm e}^{x} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.329
6373	4383	\begin{align*} y&=y^{\prime } x +{y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.329
6374	4588	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.329
6375	5676	\begin{align*} 3 {y^{\prime }}^{5}-y^{\prime } y+1&=0 \\ \end{align*}	✓	✓	✓	✗	0.329
6376	5766	\begin{align*} \frac {\left (a +b \right ) y}{x^{2}}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
6377	6022	\begin{align*} \left (c \,x^{3}+b \right ) y+a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.329
6378	6313	\begin{align*} y \left (2 f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )+3 f \left (x \right ) y^{\prime }+y^{\prime \prime }&=2 y^{3} \\ \end{align*}	✗	✗	✗	✗	0.329
6379	7830	\begin{align*} y^{\prime \prime \prime }-y&=5 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.329
6380	8035	\begin{align*} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-10 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.329
6381	8129	\begin{align*} y^{\prime \prime } x +y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.329
6382	8494	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +8 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.329
6383	8738	\begin{align*} 2 x^{2} y^{\prime }&=y^{3}+y x \\ \end{align*}	✓	✓	✓	✓	0.329
6384	10472	\begin{align*} t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.329
6385	12412	\begin{align*} x^{2} y^{\prime \prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
6386	12899	\begin{align*} x^{2} y^{\prime \prime }-\left (2 a +b -1\right ) x y^{\prime }+\left (c^{2} b^{2} x^{2 b}+a \left (a +b \right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.329
6387	14390	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=-3 y \\ \end{align*}	✓	✓	✓	✓	0.329
6388	15259	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=1 \\ \end{align*}	✓	✓	✓	✓	0.329
6389	15985	\begin{align*} x^{\prime }&=3 x \\ y^{\prime }&=-2 y \\ \end{align*}	✓	✓	✓	✓	0.329
6390	16627	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-3 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.329
6391	16855	\begin{align*} y^{\prime }-\tan \left (x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.329
6392	16865	\begin{align*} y^{\prime }+y \,{\mathrm e}^{2 x}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.329
6393	17423	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= a \\ y^{\prime }\left (0\right ) &= b \\ \end{align*}	✓	✓	✓	✓	0.329
6394	17617	\begin{align*} 4 x^{2} y^{\prime \prime }+17 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
6395	17897	\begin{align*} \sin \left (y^{\prime }\right )&=x \\ \end{align*}	✓	✓	✓	✓	0.329
6396	18927	\begin{align*} y^{\prime \prime }+y&=\operatorname {Heaviside}\left (t -3 \pi \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.329
6397	21284	\begin{align*} x^{\prime \prime \prime \prime }+x^{\prime \prime }&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ x^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.329
6398	24072	\begin{align*} y^{\prime \prime }-4 y^{\prime }-5 y&=x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.329
6399	24584	\begin{align*} y^{\prime \prime }+6 y^{\prime }+14 y&=42 \,{\mathrm e}^{x}-7 \\ \end{align*}	✓	✓	✓	✓	0.329
6400	24625	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=20-3 x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.329