2.3.4 Problems 301 to 400

Table 2.539: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
301	22301	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.038
302	22646	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.038
303	23440	\begin{align*} y^{\prime \prime \prime }-3 x^{2} y^{\prime }+2 y x&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✗	✓	✓	✗	0.038
304	280	\begin{align*} 5 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.039
305	297	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.039
306	604	\begin{align*} x^{\prime }&=t x-y \,{\mathrm e}^{t}+\cos \left (t \right ) \\ y^{\prime }&={\mathrm e}^{-t} x+t^{2} y-\sin \left (t \right ) \\ \end{align*}	✗	✓	✗	✗	0.039
307	944	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.039
308	4141	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.039
309	6604	\begin{align*} y^{\prime \prime \prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.039
310	6641	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.039
311	6654	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.039
312	6798	\begin{align*} 2 {y^{\prime }}^{3}+3 y^{\prime \prime }+6 y y^{\prime } y^{\prime \prime }+\left (x +y^{2}\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.039
313	8054	\begin{align*} \left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 y^{\prime } x -4 y&=8 \\ \end{align*}	✗	✓	✓	✗	0.039
314	8921	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.039
315	8927	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.039
316	12723	\begin{align*} a^{3} x^{3} y+3 a^{2} x^{2} y^{\prime }+3 a x y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.039
317	12726	\begin{align*} y^{\prime \prime \prime }+f \left (x \right ) \left (x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y\right )&=0 \\ \end{align*}	✗	✓	✓	✗	0.039
318	12734	\begin{align*} 2 x y^{\prime \prime \prime }-4 \left (x +\nu -1\right ) y^{\prime \prime }+\left (2 x +6 \nu -5\right ) y^{\prime }+\left (1-2 \nu \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	0.039
319	12753	\begin{align*} x^{2} y^{\prime \prime \prime }-\left (x^{4}-6 x \right ) y^{\prime \prime }-\left (2 x^{3}-6\right ) y^{\prime }+2 x^{2} y&=0 \\ \end{align*}	✗	✓	✓	✗	0.039
320	12789	\begin{align*} y^{\prime \prime \prime \prime }+\left (a \,x^{2}+b \lambda +c \right ) y^{\prime \prime }+\left (a \,x^{2}+\beta \lambda +\gamma \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	0.039
321	13032	\begin{align*} {y^{\prime \prime }}^{2}-a y-b&=0 \\ \end{align*}	✗	✓	✓	✗	0.039
322	13034	\begin{align*} 2 \left (x^{2}+1\right ) {y^{\prime \prime }}^{2}-x \left (x +4 y^{\prime }\right ) y^{\prime \prime }+2 \left (x +y^{\prime }\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✗	✓	✓	✗	0.039
323	13048	\begin{align*} 15 {y^{\prime }}^{3}-18 y y^{\prime } y^{\prime \prime }+4 y^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.039
324	13049	\begin{align*} 40 {y^{\prime }}^{3}-45 y y^{\prime } y^{\prime \prime }+9 y^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.039
325	13122	\begin{align*} x^{\prime }&=-y+x \left (x^{2}+y^{2}-1\right ) \\ y^{\prime }&=x+y \left (x^{2}+y^{2}-1\right ) \\ \end{align*}	✗	✗	✗	✗	0.039
326	13124	\begin{align*} \left (x^{2}+y^{2}-t^{2}\right ) x^{\prime }&=-2 t x \\ \left (x^{2}+y^{2}-t^{2}\right ) y^{\prime }&=-2 t y \\ \end{align*}	✗	✓	✓	✗	0.039
327	14344	\begin{align*} x^{\prime \prime \prime }+x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.039
328	17824	\begin{align*} x^{\prime }&=x^{2} \\ y^{\prime }&={\mathrm e}^{t} \\ \end{align*}	✗	✓	✓	✗	0.039
329	18378	\begin{align*} y^{\prime \prime \prime }+x \sin \left (y\right )&=0 \\ y \left (0\right ) &= \frac {\pi }{2} \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✗	✓	✗	✗	0.039
330	18973	\begin{align*} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+4 y&=\cos \left (t \right ) \\ \end{align*}	✗	✗	✗	✗	0.039
331	19211	\begin{align*} y^{\prime }&=\frac {y^{2}}{z} \\ z^{\prime }&=\frac {y}{2} \\ \end{align*}	✗	✓	✓	✗	0.039
332	19212	\begin{align*} y^{\prime }&=1-\frac {1}{z} \\ z^{\prime }&=\frac {1}{y-x} \\ \end{align*}	✗	✓	✓	✗	0.039
333	21235	\begin{align*} x^{\prime }+t y&=-1 \\ x^{\prime }+y^{\prime }&=2 \\ \end{align*}	✗	✓	✓	✓	0.039
334	22089	\begin{align*} y^{\prime \prime \prime }+\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime }+y&=5 \sin \left (x \right ) \\ \end{align*}	✗	✗	✗	✗	0.039
335	22122	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.039
336	22127	\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.039
337	22633	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-5 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.039
338	23265	\begin{align*} y^{\left (5\right )}&=0 \\ \end{align*}	✓	✓	✓	✓	0.039
339	298	\begin{align*} 2 y^{\prime \prime \prime }-y^{\prime \prime }-5 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.040
340	299	\begin{align*} y^{\prime \prime \prime }+27 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.040
341	938	\begin{align*} 9 y^{\prime \prime \prime }+12 y^{\prime \prime }+4 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.040
342	943	\begin{align*} y^{\prime \prime \prime \prime }&=16 y \\ \end{align*}	✓	✓	✓	✓	0.040
343	1470	\begin{align*} \left (2-t \right ) y^{\prime \prime \prime }+\left (2 t -3\right ) y^{\prime \prime }-t y^{\prime }+y&=0 \\ \end{align*}	✗	✓	✓	✗	0.040
344	2788	\begin{align*} x^{\prime }&=x-x^{2}-2 x y \\ y^{\prime }&=2 y-2 y^{2}-3 x y \\ \end{align*}	✗	✗	✗	✗	0.040
345	3699	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.040
346	3701	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-18 y^{\prime }-40 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.040
347	3703	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.040
348	4150	\begin{align*} y^{\prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.040
349	6614	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.040
350	6651	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.040
351	6667	\begin{align*} 4 y^{\prime \prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.040
352	6685	\begin{align*} 2 x^{3} y+\left (-2 x^{3}+6\right ) y^{\prime }+x \left (-x^{2}+6\right ) y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.040
353	6771	\begin{align*} -c^{4} y+16 \left (1+a -b \right ) \left (2+a -b \right ) y^{\prime \prime }+32 \left (2+a -b \right ) x y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.040
354	8091	\begin{align*} x^{3} \left (x +1\right ) y^{\prime \prime \prime }-\left (2+4 x \right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-\left (4+12 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✓	✓	✗	0.040
355	8092	\begin{align*} x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-\left (12 x^{2}+4\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✓	✓	✗	0.040
356	12750	\begin{align*} x^{2} y^{\prime \prime \prime }-\left (x^{2}-2 x \right ) y^{\prime \prime }-\left (x^{2}+\nu ^{2}-\frac {1}{4}\right ) y^{\prime }+\left (x^{2}-2 x +\nu ^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	0.040
357	12765	\begin{align*} x^{3} y^{\prime \prime \prime }+\left (x +3\right ) x^{2} y^{\prime \prime }+5 \left (x -6\right ) x y^{\prime }+\left (4 x +30\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	0.040
358	12803	\begin{align*} x^{3} y^{\prime \prime \prime \prime }+2 x^{2} y^{\prime \prime \prime }-y^{\prime \prime } x +y^{\prime }-a^{4} x^{3} y&=0 \\ \end{align*}	✗	✓	✓	✗	0.040
359	12807	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}-1\right ) x^{2} y^{\prime \prime }-\left (4 n^{2}-1\right ) x y^{\prime }+\left (-4 x^{4}+4 n^{2}-1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	0.040
360	13084	\begin{align*} x^{\prime }+y^{\prime }+y&=f \left (t \right ) \\ x^{\prime \prime }+y^{\prime \prime }+y^{\prime }+x+y&=g \left (t \right ) \\ \end{align*}	✗	✓	✓	✗	0.040
361	13121	\begin{align*} x^{\prime }&=x+y-x \left (x^{2}+y^{2}\right ) \\ y^{\prime }&=-x+y-y \left (x^{2}+y^{2}\right ) \\ \end{align*}	✗	✗	✗	✗	0.040
362	13129	\begin{align*} x^{\prime }&=y-z \\ y^{\prime }&=x^{2}+y \\ z^{\prime }&=x^{2}+z \\ \end{align*}	✗	✓	✓	✗	0.040
363	14090	\begin{align*} 2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.040
364	14091	\begin{align*} 4 y^{\prime \prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.040
365	14092	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.040
366	14094	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.040
367	14597	\begin{align*} y^{\left (5\right )}&=0 \\ \end{align*}	✓	✓	✓	✓	0.040
368	16397	\begin{align*} y^{\prime \prime \prime }&=y^{\prime \prime } \\ \end{align*}	✓	✓	✓	✓	0.040
369	16486	\begin{align*} y^{\prime \prime \prime }-9 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.040
370	16959	\begin{align*} x {y^{\prime \prime }}^{2}+2 y&=2 x \\ \end{align*}	✗	✗	✗	✗	0.040
371	16972	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.040
372	17422	\begin{align*} {y^{\prime \prime }}^{2}-2 y^{\prime \prime } y^{\prime }+y^{2}&=0 \\ \end{align*}	✗	✓	✗	✗	0.040
373	20155	\begin{align*} y^{\prime \prime \prime \prime }-a^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.040
374	20529	\begin{align*} 3 y x +\left (x^{2}+2\right ) y^{\prime }+4 y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=2 \\ \end{align*}	✗	✓	✓	✗	0.040
375	22121	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.040
376	22496	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.040
377	22659	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.040
378	22669	\begin{align*} y^{\prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.040
379	23441	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+2 y^{\prime }-x^{3} y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✗	✓	✓	✗	0.040
380	23557	\begin{align*} x_{1}^{\prime }&=2 \sin \left (t \right ) x_{1}+\ln \left (t \right ) x_{2} \\ x_{2}^{\prime }&=\frac {x_{1}}{t -2}+\frac {{\mathrm e}^{t} x_{2}}{t +1} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (3\right ) &= 0 \\ x_{2} \left (3\right ) &= 0 \\ \end{align*}	✗	✓	✗	✓	0.040
381	24096	\begin{align*} x^{2} y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.040
382	25650	\begin{align*} t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y&=0 \\ \end{align*}	✗	✗	✓	✗	0.040
383	283	\begin{align*} 9 y^{\prime \prime \prime }+12 y^{\prime \prime }+4 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.041
384	12735	\begin{align*} 2 x y^{\prime \prime \prime }+3 \left (2 a x +k \right ) y^{\prime \prime }+6 \left (a k +b x \right ) y^{\prime }+\left (3 b k +2 c x \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	0.041
385	12756	\begin{align*} 2 x \left (x -1\right ) y^{\prime \prime \prime }+3 \left (2 x -1\right ) y^{\prime \prime }+\left (2 a x +b \right ) y^{\prime }+a y&=0 \\ \end{align*}	✗	✓	✓	✗	0.041
386	12762	\begin{align*} -2 \left (x^{2}+4\right ) y+x \left (x^{2}+8\right ) y^{\prime }-4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.041
387	13095	\begin{align*} x^{\prime \prime }-a y^{\prime }+b x&=0 \\ y^{\prime \prime }+a x^{\prime }+b y&=0 \\ \end{align*}	✗	✓	✓	✓	0.041
388	13101	\begin{align*} x^{\prime \prime }-x^{\prime }+y^{\prime }&=0 \\ x^{\prime \prime }+y^{\prime \prime }-x&=0 \\ \end{align*}	✗	✓	✓	✓	0.041
389	19216	\begin{align*} y^{\prime }&=\frac {z^{2}}{y} \\ z^{\prime }&=\frac {y^{2}}{z} \\ \end{align*}	✗	✓	✓	✓	0.041
390	19224	\begin{align*} t x^{\prime }-x-3 y&=t \\ t y^{\prime }-x+y&=0 \\ \end{align*}	✗	✓	✓	✓	0.041
391	20754	\begin{align*} \left (2 x -1\right )^{3} y^{\prime \prime \prime }+\left (2 x -1\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✗	✓	✓	✗	0.041
392	21237	\begin{align*} x^{\prime }-t y&=1 \\ y^{\prime }-t x^{\prime }&=3 \\ \end{align*}	✗	✓	✓	✗	0.041
393	22111	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.041
394	22120	\begin{align*} 2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.041
395	22314	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.041
396	23275	\begin{align*} y^{\prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.041
397	25360	\begin{align*} y_{1}^{\prime }&=\sin \left (t \right ) y_{1} \\ y_{2}^{\prime }&=y_{1}+\cos \left (t \right ) y_{2} \\ \end{align*}	✗	✓	✓	✓	0.041
398	25649	\begin{align*} x y^{\prime \prime \prime }-{y^{\prime }}^{4}+y&=0 \\ \end{align*}	✗	✗	✗	✗	0.041
399	281	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+16 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.042
400	285	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.042