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	26493	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.079
302	6609	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.080
303	7058	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-11 y^{\prime \prime }-12 y^{\prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.080
304	18462	\begin{align*} x^{\prime \prime }&=1 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.080
305	21786	\begin{align*} x^{\prime }&=-x+y^{2} \\ y^{\prime }&=x^{2}-y \\ \end{align*}	✗	✓	✗	✗	0.080
306	23114	\begin{align*} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.080
307	23782	\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{1}^{3} \\ \end{align*}	✗	✓	✓	✗	0.080
308	304	\begin{align*} 3 y^{\prime \prime \prime }-2 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.081
309	3891	\begin{align*} x_{1}^{\prime }&=t \cot \left (t^{2}\right ) x_{1}+\frac {t \cos \left (t^{2}\right ) x_{3}}{2} \\ x_{2}^{\prime }&=\frac {x_{2}}{t}-x_{3}+2-t \sin \left (t \right ) \\ x_{3}^{\prime }&=\csc \left (t^{2}\right ) x_{1}+x_{2}-x_{3}+1-\cos \left (t \right ) t \\ \end{align*}	✗	✗	✗	✗	0.081
310	4142	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.081
311	18420	\begin{align*} x^{\prime \prime }&=x^{2}+y \\ y^{\prime }&=-2 x x^{\prime }+x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✗	✓	✗	✗	0.081
312	19211	\begin{align*} y^{\prime }&=\frac {y^{2}}{z} \\ z^{\prime }&=\frac {y}{2} \\ \end{align*}	✗	✓	✓	✗	0.081
313	19224	\begin{align*} x^{\prime } t -x-3 y&=t \\ t y^{\prime }-x+y&=0 \\ \end{align*}	✗	✓	✓	✓	0.081
314	21782	\begin{align*} x^{\prime }&=-x^{2}-y \\ y^{\prime }&=x \\ \end{align*}	✗	✓	✓	✗	0.081
315	23816	\begin{align*} x^{\prime }&=x^{2}-x \\ y^{\prime }&=-3 y+x y \\ \end{align*}	✗	✓	✓	✓	0.081
316	23819	\begin{align*} x^{\prime }&=x-x y \\ y^{\prime }&=-y+x y \\ \end{align*}	✗	✓	✓	✗	0.081
317	25156	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.081
318	26794	\begin{align*} 2 y^{\prime \prime \prime }+7 y^{\prime \prime }+7 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.081
319	286	\begin{align*} y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.082
320	303	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-54 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.082
321	7063	\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.082
322	7065	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.082
323	10283	\begin{align*} f \left (x \right ) \sin \left (x \right ) y x y^{\prime } \pi &=0 \\ \end{align*}	✓	✓	✓	✓	0.082
324	15674	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.082
325	18146	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.082
326	18166	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=3 \\ \end{align*}	✓	✓	✓	✓	0.082
327	18186	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.082
328	18469	\begin{align*} x^{\prime \prime }-2 x^{\prime }+2 x&=2 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.082
329	18715	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=x-\frac {x^{3}}{5}-\frac {y}{5} \\ \end{align*}	✗	✗	✗	✗	0.082
330	19531	\begin{align*} y^{\prime \prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.082
331	21316	\begin{align*} x^{\prime }&=-x+y+y^{2} \\ y^{\prime }&=-2 y-x^{2} \\ \end{align*}	✗	✗	✗	✗	0.082
332	21508	\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+24 y^{\prime \prime }+32 y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.082
333	21785	\begin{align*} x^{\prime }&=x^{2} \\ y^{\prime }&=2 y^{2}-x y \\ \end{align*}	✗	✓	✓	✓	0.082
334	22122	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.082
335	23798	\begin{align*} x^{\prime }&=y+x^{2}-x y \\ y^{\prime }&=-2 x+3 y+y^{2} \\ \end{align*}	✗	✗	✗	✗	0.082
336	23817	\begin{align*} x^{\prime }&=-x+x y \\ y^{\prime }&=y+\left (x^{2}+y^{2}\right )^{2} \\ \end{align*}	✗	✗	✗	✗	0.082
337	23818	\begin{align*} x^{\prime }&=2 x+y^{2} \\ y^{\prime }&=3 y-x^{2} \\ \end{align*}	✗	✗	✗	✗	0.082
338	26489	\begin{align*} y^{\prime \prime \prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.082
339	26497	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.082
340	13079	\begin{align*} x^{\prime }&=x \cos \left (t \right ) \\ y^{\prime }&=x \,{\mathrm e}^{-\sin \left (t \right )} \\ \end{align*}	✗	✓	✓	✓	0.083
341	15423	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.083
342	18983	\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.083
343	21507	\begin{align*} y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+18 y^{\prime \prime }-20 y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.083
344	21733	\begin{align*} y^{\prime }&=-\sqrt {1-y^{2}} \\ x^{\prime }&=x+2 y \\ \end{align*}	✗	✓	✓	✓	0.083
345	21781	\begin{align*} x^{\prime }&=8 x-y^{2} \\ y^{\prime }&=6 x^{2}-6 y \\ \end{align*}	✗	✗	✗	✗	0.083
346	22301	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.083
347	26500	\begin{align*} 2 y^{\prime \prime \prime }-3 y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.083
348	15681	\begin{align*} y^{\prime \prime \prime \prime }+\left (-3-i\right ) y^{\prime \prime \prime }+\left (4+3 i\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.084
349	16486	\begin{align*} y^{\prime \prime \prime }-9 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.084
350	18165	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.084
351	20676	\begin{align*} x^{\prime } t +y&=0 \\ t y^{\prime }+x&=0 \\ \end{align*}	✗	✓	✓	✓	0.084
352	21780	\begin{align*} x^{\prime }&=\sin \left (x\right )-4 y \\ y^{\prime }&=\sin \left (2 x\right )-5 y \\ \end{align*}	✗	✗	✗	✗	0.084
353	21784	\begin{align*} x^{\prime }&=2 x y \\ y^{\prime }&=3 y^{2}-x^{2} \\ \end{align*}	✗	✓	✓	✗	0.084
354	23778	\begin{align*} x^{\prime }&=x-x y \\ y^{\prime }&=-y+x y \\ \end{align*}	✗	✓	✓	✗	0.084
355	23796	\begin{align*} x^{\prime }&=5 x-6 y+x y \\ y^{\prime }&=6 x-7 y-x y \\ \end{align*}	✗	✗	✗	✗	0.084
356	23800	\begin{align*} x^{\prime }&=-x-x^{2}+y^{2} \\ y^{\prime }&=-y+2 x y \\ \end{align*}	✗	✓	✗	✗	0.084
357	25172	\begin{align*} y_{1}^{\prime \prime }+2 y_{1}^{\prime }+6 y_{1}&=5 y_{2} \\ y_{2}^{\prime \prime }-2 y_{2}^{\prime }+6 y_{2}&=9 y_{1} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 0 \\ y_{1}^{\prime }\left (0\right ) &= 0 \\ y_{2} \left (0\right ) &= 6 \\ y_{2}^{\prime }\left (0\right ) &= 6 \\ \end{align*}	✗	✓	✓	✓	0.084
358	25536	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.084
359	26496	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.084
360	26778	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.084
361	26790	\begin{align*} y^{\prime \prime \prime \prime }+\alpha y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.084
362	26791	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+\alpha y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.084
363	26793	\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+\alpha y^{\prime \prime }+2 y^{\prime }+\beta y&=0 \\ \end{align*}	✓	✓	✓	✓	0.084
364	935	\begin{align*} 5 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.085
365	943	\begin{align*} y^{\prime \prime \prime \prime }&=16 y \\ \end{align*}	✓	✓	✓	✓	0.085
366	944	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.085
367	13058	\begin{align*} y^{\prime \prime \prime }&=f \left (y\right ) \\ \end{align*}	✗	✗	✗	✗	0.085
368	18588	\begin{align*} \frac {y^{\prime }}{-\sin \left (y\right )+\frac {x}{y}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.085
369	20991	\begin{align*} x^{\prime }&=x \cos \left (t \right )-\sin \left (t \right ) y \\ y^{\prime }&=\sin \left (t \right ) x+\cos \left (t \right ) y \\ \end{align*}	✗	✓	✓	✓	0.085
370	21001	\begin{align*} w_{1}^{\prime }&=w_{2} \\ w_{2}^{\prime }&=\frac {a w_{1}}{z^{2}} \\ \end{align*}	✗	✓	✓	✗	0.085
371	21188	\begin{align*} x^{\prime \prime \prime \prime }-x^{\prime \prime }&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.085
372	21238	\begin{align*} t^{2} x^{\prime }-y&=1 \\ y^{\prime }-2 x&=0 \\ \end{align*}	✗	✓	✓	✗	0.085
373	21779	\begin{align*} x^{\prime }&=x+4 y-y^{2} \\ y^{\prime }&=6 x-y+2 x y \\ \end{align*}	✗	✗	✗	✗	0.085
374	23815	\begin{align*} x^{\prime }&=-2 x+y-x^{2}+2 y^{2} \\ y^{\prime }&=3 x+2 y+x^{2} y^{2} \\ \end{align*}	✗	✗	✗	✗	0.085
375	25912	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.085
376	26490	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+10 y^{\prime \prime }+12 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.085
377	306	\begin{align*} 9 y^{\prime \prime \prime }+11 y^{\prime \prime }+4 y^{\prime }-14 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.086
378	15675	\begin{align*} 36 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }-11 y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.086
379	15680	\begin{align*} y^{\prime \prime \prime }+\left (-3-4 i\right ) y^{\prime \prime }+\left (-4+12 i\right ) y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.086
380	16397	\begin{align*} y^{\prime \prime \prime }&=y^{\prime \prime } \\ \end{align*}	✓	✓	✓	✓	0.086
381	16972	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.086
382	18468	\begin{align*} x^{\prime \prime }+6 x^{\prime }&=12 t +2 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.086
383	19530	\begin{align*} y^{\prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.086
384	21252	\begin{align*} x^{\prime }&=x-4 x y \\ y^{\prime }&=-2 y+x y \\ \end{align*}	✗	✓	✓	✗	0.086
385	22258	\begin{align*} z^{\prime \prime }+y^{\prime }&=\cos \left (t \right ) \\ y^{\prime \prime }-z&=\sin \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ z \left (0\right ) &= -1 \\ z^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✗	✓	✓	✓	0.086
386	22496	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.086
387	23575	\begin{align*} x^{\prime } t&=3 x-2 y \\ t y^{\prime }&=x+y-t^{2} \\ \end{align*}	✗	✓	✓	✓	0.086
388	25142	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.086
389	26487	\begin{align*} y^{\left (6\right )}+2 y^{\left (5\right )}+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.086
390	937	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.087
391	4454	\begin{align*} y^{\left (6\right )}-64 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.087
392	16971	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.087
393	18708	\begin{align*} x^{\prime }&=x-x y \\ y^{\prime }&=y+2 x y \\ \end{align*}	✗	✓	✓	✗	0.087
394	22121	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.087
395	23797	\begin{align*} x^{\prime }&=3 x-2 y+\left (x^{2}+y^{2}\right )^{2} \\ y^{\prime }&=4 x-y+\left (x^{2}-y^{2}\right )^{5} \\ \end{align*}	✗	✗	✗	✗	0.087
396	25925	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.087
397	16533	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.088
398	18422	\begin{align*} x^{\prime }&=-\frac {1}{y} \\ y^{\prime }&=\frac {1}{x} \\ \end{align*}	✗	✓	✓	✓	0.088
399	18710	\begin{align*} x^{\prime }&=x-x^{2}-x y \\ y^{\prime }&=\frac {y}{2}-\frac {y^{2}}{4}-\frac {3 x y}{4} \\ \end{align*}	✗	✗	✗	✗	0.088
400	21250	\begin{align*} x^{\prime }&=2 x-7 x y-a x \\ y^{\prime }&=-y+4 x y-a y \\ \end{align*}	✗	✓	✗	✗	0.088