2.3.4 Problems 301 to 400

Table 2.581: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
301	6774	\begin{align*} -k y-\left (-a b c +x \right ) y^{\prime }+\left (a b +a c +b c +a +b +c +1\right ) x y^{\prime \prime }+\left (3+a +b +c \right ) x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.062
302	8829	\begin{align*} a^{2} y^{\prime \prime \prime \prime }&=y^{\prime \prime } \\ \end{align*}	✓	✓	✓	✓	0.062
303	8916	\begin{align*} y^{\prime \prime \prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
304	8929	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
305	12510	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-2 \left (v -1\right ) x y^{\prime }-2 v y&=0 \\ \end{align*}	✗	✓	✓	✗	0.062
306	18974	\begin{align*} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+7 t^{2} y&=0 \\ \end{align*}	✗	✗	✗	✗	0.062
307	21316	\begin{align*} x^{\prime }&=-x+y+y^{2} \\ y^{\prime }&=-2 y-x^{2} \\ \end{align*}	✗	✗	✗	✗	0.062
308	21505	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
309	22301	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.062
310	26479	\begin{align*} y^{2} y^{\prime \prime \prime }-3 y y^{\prime } y^{\prime \prime }+2 {y^{\prime }}^{3}+\frac {y \left (y y^{\prime \prime }-{y^{\prime }}^{2}\right )}{x}&=\frac {y^{3}}{x^{2}} \\ \end{align*}	✗	✓	✗	✗	0.062
311	1058	\begin{align*} x^{2} y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.063
312	3068	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
313	3073	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }-17 y^{\prime }+60 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
314	3080	\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }-2 y^{\prime }+24 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
315	3095	\begin{align*} y^{\prime \prime \prime }-7 y^{\prime \prime }+16 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
316	6610	\begin{align*} y^{\prime \prime \prime }&=y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.063
317	6619	\begin{align*} y^{\prime \prime \prime }&=a^{2} y \\ \end{align*}	✓	✓	✓	✓	0.063
318	7271	\begin{align*} y^{\prime \prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
319	13080	\begin{align*} t x^{\prime }+y&=0 \\ y^{\prime } t +x&=0 \\ \end{align*}	✗	✓	✓	✓	0.063
320	18634	\begin{align*} x^{\prime }&=-x+t y \\ y^{\prime }&=t x-y \\ \end{align*}	✗	✓	✓	✓	0.063
321	20063	\begin{align*} y^{\prime \prime \prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
322	23776	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-\sin \left (x\right ) \\ \end{align*}	✗	✓	✓	✗	0.063
323	25171	\begin{align*} y_{1}^{\prime }-2 y_{1}&=-2 y_{2} \\ y_{2}^{\prime \prime }+y_{2}^{\prime }+6 y_{2}&=4 y_{1} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 5 \\ y_{2}^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✗	✓	✓	✓	0.063
324	27625	\begin{align*} y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+9 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
325	27633	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.063
326	2119	\begin{align*} 4 y^{\prime \prime \prime }-8 y^{\prime \prime }+5 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.064
327	6759	\begin{align*} a^{4} x^{4} y+4 a^{3} x^{3} y^{\prime }+6 a^{2} x^{2} y^{\prime \prime }+4 a x y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.064
328	22895	\begin{align*} x^{\prime \prime }+y^{\prime }+x&=y+\sin \left (t \right ) \\ y^{\prime \prime }+x^{\prime }-y&=2 t^{2}-x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= -1 \\ y \left (0\right ) &= -{\frac {9}{2}} \\ y^{\prime }\left (0\right ) &= -{\frac {7}{2}} \\ \end{align*}	✗	✓	✓	✓	0.064
329	27627	\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.064
330	2120	\begin{align*} 27 y^{\prime \prime \prime }+27 y^{\prime \prime }+9 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
331	2124	\begin{align*} 16 y^{\prime \prime \prime \prime }-72 y^{\prime \prime }+81 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
332	4451	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
333	6626	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
334	7048	\begin{align*} y^{\prime \prime \prime \prime }-a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
335	8919	\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
336	9291	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
337	18124	\begin{align*} y^{\prime \prime \prime }&=3 y y^{\prime } \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= {\frac {3}{2}} \\ \end{align*}	✗	✓	✗	✗	0.065
338	18427	\begin{align*} x^{\prime }&=\cos \left (x\right )^{2} \cos \left (y\right )^{2}+\sin \left (x\right )^{2} \cos \left (y\right )^{2} \\ y^{\prime }&=-\frac {\sin \left (2 x\right ) \sin \left (2 y\right )}{2} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	0.065
339	18967	\begin{align*} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+8 y&=\cos \left (t \right ) \\ \end{align*}	✗	✗	✗	✗	0.065
340	21957	\begin{align*} y^{\prime \prime \prime \prime }+x y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-y^{\prime } x +\sin \left (y\right )&=0 \\ \end{align*}	✗	✗	✗	✗	0.065
341	22890	\begin{align*} x^{\prime \prime }+2 y^{\prime }+8 x&=32 t \\ y^{\prime \prime }+3 x^{\prime }-2 y&=60 \,{\mathrm e}^{-t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 6 \\ x^{\prime }\left (0\right ) &= 0 \\ y \left (0\right ) &= -24 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✗	✓	✓	✓	0.065
342	27626	\begin{align*} y^{\left (5\right )}-10 y^{\prime \prime \prime }+9 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.065
343	286	\begin{align*} y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
344	300	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
345	1463	\begin{align*} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y&=0 \\ \end{align*}	✗	✗	✗	✗	0.066
346	2122	\begin{align*} y^{\prime \prime \prime \prime }-16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
347	3067	\begin{align*} 2 y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
348	3079	\begin{align*} 4 y^{\prime \prime \prime }+2 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
349	3089	\begin{align*} 2 y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
350	4143	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
351	6588	\begin{align*} 2 \left (x -y^{\prime }\right ) y^{\prime }-x \left (x +4 y^{\prime }\right ) y^{\prime \prime }+2 \left (x^{2}+1\right ) {y^{\prime \prime }}^{2}&=2 y \\ \end{align*}	✗	✗	✗	✗	0.066
352	6607	\begin{align*} a y+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
353	6614	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
354	6618	\begin{align*} y^{\prime \prime \prime }-7 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
355	6631	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
356	6635	\begin{align*} -3 y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
357	6732	\begin{align*} y+y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
358	10298	\begin{align*} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
359	10299	\begin{align*} y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
360	10301	\begin{align*} \pi y \sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
361	18977	\begin{align*} \left (x^{2}-25\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+5 y&=0 \\ \end{align*}	✗	✗	✗	✗	0.066
362	19531	\begin{align*} y^{\prime \prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
363	21176	\begin{align*} x^{\prime \prime \prime }-x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
364	22898	\begin{align*} x^{\prime }&=x y \\ y^{\prime }&=1+y^{2} \\ z^{\prime }&=z \\ \end{align*}	✗	✓	✓	✗	0.066
365	23778	\begin{align*} x^{\prime }&=x-x y \\ y^{\prime }&=-y+x y \\ \end{align*}	✗	✓	✓	✗	0.066
366	26103	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.066
367	26772	\begin{align*} x^{\prime }&=7 x+2 \sin \left (y\right )-4 y^{4} \\ y^{\prime }&={\mathrm e}^{x}-3 y-1+\frac {5 x^{2}}{2} \\ \end{align*}	✗	✗	✗	✗	0.066
368	27592	\begin{align*} y^{2} \left (y^{\prime \prime \prime } y^{\prime }-2 {y^{\prime \prime }}^{2}\right )&={y^{\prime }}^{4} \\ \end{align*}	✗	✓	✗	✗	0.066
369	305	\begin{align*} 6 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+25 y^{\prime \prime }+20 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.067
370	306	\begin{align*} 9 y^{\prime \prime \prime }+11 y^{\prime \prime }+4 y^{\prime }-14 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.067
371	3105	\begin{align*} 2 y^{\prime \prime \prime }-3 y^{\prime \prime }+10 y^{\prime }-15 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.067
372	4147	\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.067
373	4148	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.067
374	7274	\begin{align*} y^{\prime \prime \prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.067
375	8118	\begin{align*} x^{3} y^{\prime \prime }+y&=\frac {1}{x^{4}} \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.067
376	8922	\begin{align*} y^{\prime \prime \prime }-3 i y^{\prime \prime }-3 y^{\prime }+i y&=0 \\ \end{align*}	✓	✓	✓	✓	0.067
377	8931	\begin{align*} y^{\prime \prime \prime }-i y^{\prime \prime }+y^{\prime }-i y&=0 \\ \end{align*}	✓	✓	✓	✓	0.067
378	9295	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.067
379	9303	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.067
380	10300	\begin{align*} x y \sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.067
381	25650	\begin{align*} t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y&=0 \\ \end{align*}	✗	✗	✓	✗	0.067
382	2115	\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime }-9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.068
383	6667	\begin{align*} 4 y^{\prime \prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.068
384	6730	\begin{align*} a y+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.068
385	8058	\begin{align*} \left (1+2 y+3 y^{2}\right ) y^{\prime \prime \prime }+6 y^{\prime } \left (y^{\prime \prime }+{y^{\prime }}^{2}+3 y y^{\prime \prime }\right )&=x \\ \end{align*}	✗	✓	✗	✗	0.068
386	8060	\begin{align*} y y^{\prime \prime \prime }+3 y^{\prime } y^{\prime \prime }-2 y y^{\prime \prime }-2 {y^{\prime }}^{2}+y y^{\prime }&={\mathrm e}^{2 x} \\ \end{align*}	✗	✓	✗	✗	0.068
387	10282	\begin{align*} a \sin \left (x \right ) y x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.068
388	18142	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.068
389	19530	\begin{align*} y^{\prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.068
390	23436	\begin{align*} y^{\prime \prime \prime \prime }-\ln \left (x +1\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✗	✓	✓	✗	0.068
391	24497	\begin{align*} y^{\left (5\right )}+y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.068
392	2113	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+7 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.069
393	2145	\begin{align*} y^{\prime \prime \prime \prime }+64 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.069
394	3070	\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.069
395	3075	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-7 y^{\prime \prime }-y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.069
396	3085	\begin{align*} -4 y+3 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.069
397	4449	\begin{align*} y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.069
398	6582	\begin{align*} {y^{\prime \prime }}^{2}&=a +b y \\ \end{align*}	✗	✓	✓	✗	0.069
399	6600	\begin{align*} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.069
400	6612	\begin{align*} 4 y-2 y^{\prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.069