2.3.85 Problems 8401 to 8500

Table 2.743: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
8401	3882	\begin{align*} x_{1}^{\prime }&=3 x_{1} \\ x_{2}^{\prime }&=3 x_{2}-x_{3} \\ x_{3}^{\prime }&=x_{2}+x_{3} \\ \end{align*}	✓	✓	✓	✓	0.618
8402	7137	\begin{align*} 2 y^{\prime \prime }&={\mathrm e}^{y} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	0.618
8403	16981	\begin{align*} y^{\prime }&=x \sin \left (x^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.618
8404	18652	\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.618
8405	20645	\begin{align*} y^{\prime \prime }-y&=\frac {2}{1+{\mathrm e}^{x}} \\ \end{align*}	✓	✓	✓	✓	0.618
8406	21207	\begin{align*} x^{\prime }&=3 x-y \\ y^{\prime }&=x+3 y \\ \end{align*}	✓	✓	✓	✓	0.618
8407	21709	\begin{align*} y^{\prime }+2 y&=\cos \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.618
8408	22642	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.618
8409	23573	\begin{align*} x_{1}^{\prime }&=3 x_{1}-2 x_{2}+1 \\ x_{2}^{\prime }&=x_{1}+t \\ \end{align*}	✓	✓	✓	✓	0.618
8410	24631	\begin{align*} y^{\prime \prime }-4 y&=8 x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.618
8411	25609	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=t \,{\mathrm e}^{c t} \\ \end{align*}	✓	✓	✓	✓	0.618
8412	27129	\(\left [\begin {array}{ccc} 1 & 3 & 0 \\ 3 & 0 & 1 \\ 0 & 1 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.618
8413	1006	\begin{align*} x_{1}^{\prime }&=x_{2}+2 x_{3} \\ x_{2}^{\prime }&=-5 x_{1}-3 x_{2}-7 x_{3} \\ x_{3}^{\prime }&=x_{1} \\ \end{align*}	✓	✓	✓	✓	0.619
8414	1384	\begin{align*} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.619
8415	3733	\begin{align*} y^{\prime \prime }-16 y&=20 \cos \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.619
8416	3863	\begin{align*} x_{1}^{\prime }&=3 x_{1}+x_{2} \\ x_{2}^{\prime }&=-x_{1}+5 x_{2} \\ x_{3}^{\prime }&=4 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.619
8417	4130	\begin{align*} y^{\prime \prime }+y&=x^{3}+x \\ \end{align*}	✓	✓	✓	✓	0.619
8418	5956	\begin{align*} x^{2} y^{\prime \prime }&=12 y \\ \end{align*}	✓	✓	✓	✓	0.619
8419	8967	\begin{align*} y^{\prime \prime }+\left (x -1\right )^{2} y^{\prime }-\left (x -1\right ) y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.619
8420	10402	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.619
8421	10425	\begin{align*} y^{\prime \prime }-\frac {2 y}{x^{2}}&=x \,{\mathrm e}^{-\sqrt {x}} \\ \end{align*}	✓	✓	✓	✓	0.619
8422	14150	\begin{align*} x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.619
8423	18379	\begin{align*} y^{\prime }-2 y x&=0 \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.619
8424	18431	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=-2 x+4 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.619
8425	21777	\begin{align*} x^{\prime }&=2 x-7 y \\ y^{\prime }&=3 x-8 y \\ \end{align*}	✓	✓	✓	✓	0.619
8426	24890	\begin{align*} y^{\prime \prime }&={\mathrm e}^{x} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.619
8427	25521	\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{c t} \\ \end{align*}	✓	✓	✓	✓	0.619
8428	26611	\begin{align*} y^{\prime \prime }-y^{\prime }-5 y&=1 \\ y \left (\infty \right ) &= -{\frac {1}{5}} \\ \end{align*}	✓	✓	✓	✓	0.619
8429	347	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=x \,{\mathrm e}^{3 x} \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.620
8430	2624	\begin{align*} y^{\prime \prime }+t y^{\prime }+{\mathrm e}^{t} y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.620
8431	3719	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=3 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.620
8432	4561	\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2} \\ x_{2}^{\prime }&=-4 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.620
8433	5793	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.620
8434	9714	\begin{align*} {y^{\prime }}^{2} x +\left (1-x^{2} y\right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.620
8435	16039	\begin{align*} x^{\prime }&=-2 x+3 y \\ y^{\prime }&=3 x-2 y \\ z^{\prime }&=-z \\ \end{align*}	✓	✓	✓	✓	0.620
8436	19974	\begin{align*} 4 y^{2} {y^{\prime }}^{2}+2 \left (1+3 x \right ) x y y^{\prime }+3 x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.620
8437	20031	\begin{align*} 4 {y^{\prime }}^{2}&=9 x \\ \end{align*}	✓	✓	✓	✓	0.620
8438	24783	\begin{align*} {y^{\prime }}^{2}-y^{\prime } x y \left (x +y\right )+x^{3} y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.620
8439	27175	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+6 \,{\mathrm e}^{3 t} \\ x_{2}^{\prime }&=x_{1}+x_{2}+4 \\ \end{align*}	✓	✓	✓	✓	0.620
8440	895	\begin{align*} y^{\prime \prime }-4 y&=\sinh \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.621
8441	1342	\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=\frac {{\mathrm e}^{t}}{t^{2}+1} \\ \end{align*}	✓	✓	✓	✗	0.621
8442	1640	\begin{align*} x^{2} y^{\prime }+2 y x&=y^{3} \\ y \left (1\right ) &= \frac {\sqrt {2}}{2} \\ \end{align*}	✓	✓	✓	✓	0.621
8443	3174	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2} \\ \end{align*}	✓	✓	✓	✓	0.621
8444	3689	\begin{align*} 4 \,{\mathrm e}^{2 x}+2 y x -y^{2}+\left (x -y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.621
8445	8412	\begin{align*} 1+{x^{\prime }}^{2}&=\frac {a}{y} \\ \end{align*}	✓	✓	✓	✓	0.621
8446	9469	\begin{align*} x^{\prime }&=7 x+6 y \\ y^{\prime }&=2 x+6 y \\ \end{align*}	✓	✓	✓	✓	0.621
8447	9639	\begin{align*} y^{\prime \prime }+y&=\sin \left (t \right )+t \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.621
8448	9719	\begin{align*} y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.621
8449	10080	\begin{align*} y^{\prime \prime }-x y^{\prime }-y x -2 x&=0 \\ \end{align*}	✓	✓	✓	✗	0.621
8450	10479	\begin{align*} y^{\prime \prime }+x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.621
8451	12957	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+b -4 \left (x^{2}+a \right ) y^{2}-8 x y^{3}-3 y^{4}&=0 \\ \end{align*}	✗	✗	✗	✗	0.621
8452	17606	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=\sec \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.621
8453	17695	\begin{align*} \left (2 x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-3 y&=0 \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.621
8454	17752	\begin{align*} y^{\prime \prime }-9 y&=\frac {1}{1+{\mathrm e}^{3 t}} \\ \end{align*}	✓	✓	✓	✓	0.621
8455	17825	\begin{align*} x_{1}^{\prime }&=-3 x_{1} \\ x_{2}^{\prime }&=1 \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= -1 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.621
8456	18451	\begin{align*} x^{\prime }&=5 x+4 y \\ y^{\prime }&=x+2 y \\ \end{align*}	✓	✓	✓	✓	0.621
8457	18793	\begin{align*} y^{\prime \prime }+6 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.621
8458	19772	\begin{align*} 2 y^{\prime }+x y^{\prime \prime }&=y x \\ \end{align*}	✓	✓	✓	✓	0.621
8459	20016	\begin{align*} y&=2 x y^{\prime }+y^{2} {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.621
8460	20604	\begin{align*} 3 y-\left (x +3\right ) y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.621
8461	23076	\begin{align*} y^{\prime \prime }-2 y^{\prime }-y&=2 \cos \left (3 x \right )-3 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.621
8462	23285	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	0.621
8463	25977	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\left (x -2\right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.621
8464	1841	\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }+\left (2-3 x \right ) y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.622
8465	1940	\begin{align*} \left (2 x^{2}-11 x +16\right ) y^{\prime \prime }+\left (x^{2}-6 x +10\right ) y^{\prime }-\left (2-x \right ) y&=0 \\ y \left (3\right ) &= 1 \\ y^{\prime }\left (3\right ) &= -2 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	0.622
8466	2284	\begin{align*} y_{1}^{\prime }&=-3 y_{1}-y_{2} \\ y_{2}^{\prime }&=y_{1}-y_{2} \\ y_{3}^{\prime }&=-y_{1}-y_{2}-2 y_{3} \\ \end{align*}	✓	✓	✓	✓	0.622
8467	7091	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right )+{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.622
8468	8134	\begin{align*} x^{2} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.622
8469	8148	\begin{align*} x^{2} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.622
8470	8817	\begin{align*} y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (1+3 x \right )^{2}}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.622
8471	8848	\begin{align*} x_{1}^{\prime }&=x_{1}-2 x_{2} \\ x_{2}^{\prime }&=3 x_{1}-4 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.622
8472	9270	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.622
8473	9843	\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.622
8474	19520	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.622
8475	21469	\begin{align*} {y^{\prime }}^{2} \left (x^{2}-1\right )-2 x y y^{\prime }+y^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✗	0.622
8476	22289	\begin{align*} y^{\prime \prime }+y&=x \\ y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.622
8477	23483	\begin{align*} y^{\prime \prime }+y&=x +{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.622
8478	3162	\begin{align*} y^{\prime \prime }-2 y&=\sin \left (2 x \right ) {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.623
8479	7577	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=-50 \sin \left (5 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.623
8480	12614	\begin{align*} y^{\prime \prime }&=-\frac {\left (2 x^{2}+1\right ) y^{\prime }}{x^{3}}+\frac {y}{x^{4}} \\ \end{align*}	✓	✓	✓	✗	0.623
8481	14874	\begin{align*} z^{\prime }&={\mathrm e}^{-2 x} x \\ \end{align*}	✓	✓	✓	✓	0.623
8482	15513	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	0.623
8483	16044	\begin{align*} x^{\prime }&=-x+2 y \\ y^{\prime }&=2 x-4 y \\ z^{\prime }&=-z \\ \end{align*}	✓	✓	✓	✓	0.623
8484	16743	\begin{align*} y^{\prime \prime }-12 y^{\prime }+36 y&=3 x \,{\mathrm e}^{6 x}-2 \,{\mathrm e}^{6 x} \\ \end{align*}	✓	✓	✓	✓	0.623
8485	18789	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.623
8486	22272	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=9 x+y \\ \end{align*}	✓	✓	✓	✓	0.623
8487	25059	\begin{align*} y^{\prime }-4 y&=1 \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.623
8488	25118	\begin{align*} y^{\prime \prime }+4 y&=1+{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.623
8489	25157	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=4 \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.623
8490	454	\begin{align*} \cos \left (x \right ) y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.624
8491	1021	\begin{align*} x_{1}^{\prime }&=x_{3} \\ x_{2}^{\prime }&=-5 x_{1}-x_{2}-5 x_{3} \\ x_{3}^{\prime }&=4 x_{1}+x_{2}-2 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.624
8492	1427	\begin{align*} x_{1}^{\prime }&=-\frac {5 x_{1}}{2}+x_{2}+x_{3} \\ x_{2}^{\prime }&=x_{1}-\frac {5 x_{2}}{2}+x_{3} \\ x_{3}^{\prime }&=x_{1}+x_{2}-\frac {5 x_{3}}{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= 3 \\ x_{3} \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.624
8493	7650	\begin{align*} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=-1\).	✓	✓	✓	✓	0.624
8494	7689	\begin{align*} 2 x y^{\prime \prime }-y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.624
8495	10146	\begin{align*} y^{\prime \prime \prime }+y^{\prime }+y&=x \\ y^{\prime }\left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	0.624
8496	12897	\begin{align*} x^{2} y^{\prime \prime }&=a \left (y^{n}-y\right ) \\ \end{align*}	✗	✗	✗	✗	0.624
8497	19141	\begin{align*} {y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x}&=0 \\ \end{align*}	✓	✓	✓	✗	0.624
8498	25660	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.624
8499	25938	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.624
8500	7095	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=5 \sin \left (x \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.625