2.3.3 Problems 201 to 300

Table 2.537: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
201	12733	\begin{align*} 2 x y^{\prime \prime \prime }+3 y^{\prime \prime }+a x y-b&=0 \\ \end{align*}	✗	✓	✓	✗	0.035
202	12740	\begin{align*} x^{2} y^{\prime \prime \prime }+\left (x +1\right ) y^{\prime \prime }-y&=0 \\ \end{align*}	✗	✗	✗	✗	0.035
203	15755	\begin{align*} y_{1}^{\prime }&=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}-2 x \\ y_{2}^{\prime }&=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}+5 x \\ \end{align*}	✗	✓	✓	✓	0.035
204	16932	\begin{align*} t x^{\prime }+2 x&=15 y \\ y^{\prime } t&=x \\ \end{align*}	✗	✓	✓	✓	0.035
205	16952	\begin{align*} x^{\prime }&=x y-6 y \\ y^{\prime }&=x-y-5 \\ \end{align*}	✗	✗	✗	✗	0.035
206	18402	\begin{align*} x_{1}^{\prime }&=-2 t x_{1}^{2} \\ x_{2}^{\prime }&=\frac {x_{2}+t}{t} \\ \end{align*}	✗	✓	✓	✗	0.035
207	18439	\begin{align*} x^{\prime }&=-4 x-2 y+\frac {2}{{\mathrm e}^{t}-1} \\ y^{\prime }&=6 x+3 y-\frac {3}{{\mathrm e}^{t}-1} \\ \end{align*}	✗	✓	✓	✓	0.035
208	20196	\begin{align*} x^{2} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✗	✓	✓	✗	0.035
209	21001	\begin{align*} w_{1}^{\prime }&=w_{2} \\ w_{2}^{\prime }&=\frac {a w_{1}}{z^{2}} \\ \end{align*}	✗	✓	✓	✗	0.035
210	22800	\begin{align*} x y^{\prime \prime \prime }+2 y^{\prime \prime } x -y^{\prime } x -2 y x&=1 \\ \end{align*}	✗	✓	✓	✓	0.035
211	23241	\begin{align*} y^{\prime \prime }+y y^{\prime \prime \prime \prime }&=5 \\ \end{align*}	✗	✗	✗	✗	0.035
212	23775	\begin{align*} x^{\prime }&=y^{2}-x^{2} \\ y^{\prime }&=2 x y \\ \end{align*}	✗	✓	✓	✗	0.035
213	289	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.036
214	297	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.036
215	949	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.036
216	1470	\begin{align*} \left (2-t \right ) y^{\prime \prime \prime }+\left (2 t -3\right ) y^{\prime \prime }-y^{\prime } t +y&=0 \\ \end{align*}	✗	✓	✓	✗	0.036
217	2121	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.036
218	6622	\begin{align*} y f^{\prime }\left (x \right )+2 f \left (x \right ) y^{\prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.036
219	7056	\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.036
220	12710	\begin{align*} y^{\prime \prime \prime }-a \,x^{b} y&=0 \\ \end{align*}	✗	✓	✓	✗	0.036
221	12799	\begin{align*} x^{2} y^{\prime \prime \prime \prime }+6 x y^{\prime \prime \prime }+6 y^{\prime \prime }-\lambda ^{2} y&=0 \\ \end{align*}	✗	✓	✓	✗	0.036
222	13135	\begin{align*} x^{\prime }&=x \left (y^{2}-z^{2}\right ) \\ y^{\prime }&=-y \left (z^{2}+x^{2}\right ) \\ z^{\prime }&=z \left (x^{2}+y^{2}\right ) \\ \end{align*}	✗	✓	✗	✗	0.036
223	14166	\begin{align*} y-y^{\prime } x -y^{\prime \prime }+x y^{\prime \prime \prime }&=-x^{2}+1 \\ \end{align*}	✗	✓	✓	✗	0.036
224	15129	\begin{align*} y^{\prime \prime }+y y^{\prime \prime \prime \prime }&=1 \\ \end{align*}	✗	✗	✗	✗	0.036
225	19212	\begin{align*} y^{\prime }&=1-\frac {1}{z} \\ z^{\prime }&=\frac {1}{-x +y} \\ \end{align*}	✗	✓	✓	✗	0.036
226	19216	\begin{align*} y^{\prime }&=\frac {z^{2}}{y} \\ z^{\prime }&=\frac {y^{2}}{z} \\ \end{align*}	✗	✓	✓	✓	0.036
227	21925	\begin{align*} x^{\prime \prime }&=1 \\ x^{\prime }+x+y^{\prime \prime }-9 y+z^{\prime }+z&=0 \\ 5 x+z^{\prime \prime }-4 z&=2 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ z \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ z^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✗	✓	✓	✗	0.036
228	23265	\begin{align*} y^{\left (5\right )}&=0 \\ \end{align*}	✓	✓	✓	✓	0.036
229	23819	\begin{align*} x^{\prime }&=x-x y \\ y^{\prime }&=-y+x y \\ \end{align*}	✗	✓	✓	✗	0.036
230	23935	\begin{align*} y y^{\prime }&=-x \\ y z^{\prime }&=2 \\ \end{align*}	✗	✓	✓	✗	0.036
231	24088	\begin{align*} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✓	✓	✗	0.036
232	24089	\begin{align*} \left (-x^{4}+1\right ) y^{\prime \prime \prime }-24 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✓	✓	✗	0.036
233	24092	\begin{align*} x^{2} y^{\prime \prime \prime }-y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✓	✓	✗	0.036
234	24094	\begin{align*} x^{4} y^{\prime \prime \prime }-\frac {x^{2} y^{\prime }}{x +1}+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.036
235	25392	\begin{align*} y_{1}^{\prime }&=\frac {y_{1}}{t}+1 \\ y_{2}^{\prime }&=\frac {y_{2}}{t}+t \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (1\right ) &= 1 \\ y_{2} \left (1\right ) &= 2 \\ \end{align*}	✗	✓	✓	✗	0.036
236	283	\begin{align*} 9 y^{\prime \prime \prime }+12 y^{\prime \prime }+4 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.037
237	2112	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.037
238	2141	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.037
239	2793	\begin{align*} x^{\prime }&=\cos \left (y\right ) \\ y^{\prime }&=\sin \left (x\right )-1 \\ \end{align*}	✗	✓	✓	✗	0.037
240	4557	\begin{align*} x^{\prime \prime }+2 x-2 y^{\prime }&=0 \\ 3 x^{\prime }+y^{\prime \prime }-8 y&=240 \,{\mathrm e}^{t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✗	✓	✓	✓	0.037
241	6678	\begin{align*} a \,x^{2} y-6 y^{\prime }+x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.037
242	6683	\begin{align*} a \,x^{2} y+6 y^{\prime }+6 y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.037
243	12729	\begin{align*} x y^{\prime \prime \prime }+3 y^{\prime \prime }-a \,x^{2} y&=0 \\ \end{align*}	✗	✓	✓	✗	0.037
244	12834	\begin{align*} \left (x -a \right )^{5} \left (x -b \right )^{5} y^{\left (5\right )}-c y&=0 \\ \end{align*}	✗	✗	✗	✗	0.037
245	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*}	✗	✓	✓	✗	0.037
246	15132	\begin{align*} y^{\prime \prime \prime }+y x&=\cosh \left (x \right ) \\ \end{align*}	✗	✓	✓	✗	0.037
247	15733	\begin{align*} y_{1}^{\prime }&=\frac {2 y_{1}}{x}-\frac {y_{2}}{x^{2}}-3+\frac {1}{x}-\frac {1}{x^{2}} \\ y_{2}^{\prime }&=2 y_{1}+1-6 x \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (1\right ) &= -2 \\ y_{2} \left (1\right ) &= -5 \\ \end{align*}	✗	✓	✓	✗	0.037
248	16444	\begin{align*} y y^{\prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime }&=y \\ \end{align*}	✗	✗	✗	✗	0.037
249	21235	\begin{align*} x^{\prime }+t y&=-1 \\ x^{\prime }+y^{\prime }&=2 \\ \end{align*}	✗	✓	✓	✓	0.037
250	21237	\begin{align*} x^{\prime }-t y&=1 \\ y^{\prime }-t x^{\prime }&=3 \\ \end{align*}	✗	✓	✓	✗	0.037
251	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*}	✗	✗	✗	✗	0.037
252	23275	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.037
253	23566	\begin{align*} x_{1}^{\prime }&=x_{1}+\left (1-t \right ) x_{2} \\ x_{2}^{\prime }&=\frac {x_{1}}{t}-x_{2} \\ \end{align*}	✗	✓	✓	✓	0.037
254	23584	\begin{align*} t x^{\prime }&=3 x-2 y \\ y^{\prime } t&=x+y-t^{2} \\ \end{align*} With initial conditions \begin{align*} x \left (1\right ) &= 1 \\ y \left (1\right ) &= {\frac {1}{2}} \\ \end{align*}	✗	✓	✓	✓	0.037
255	23777	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-4 \sin \left (x\right ) \\ \end{align*}	✗	✓	✓	✗	0.037
256	23818	\begin{align*} x^{\prime }&=2 x+y^{2} \\ y^{\prime }&=3 y-x^{2} \\ \end{align*}	✗	✗	✗	✗	0.037
257	25387	\begin{align*} y_{1}^{\prime }&=y_{2} t \\ y_{2}^{\prime }&=-y_{1} t \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 0 \\ \end{align*}	✗	✓	✓	✓	0.037
258	25391	\begin{align*} y_{1}^{\prime }&=y_{1}+y_{2} \\ y_{2}^{\prime }&=\frac {y_{1}}{t}+\frac {y_{2}}{t} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (1\right ) &= -3 \\ y_{2} \left (1\right ) &= 4 \\ \end{align*}	✗	✓	✓	✓	0.037
259	25649	\begin{align*} x y^{\prime \prime \prime }-{y^{\prime }}^{4}+y&=0 \\ \end{align*}	✗	✗	✗	✗	0.037
260	288	\begin{align*} y^{\prime \prime \prime \prime }&=16 y \\ \end{align*}	✓	✓	✓	✓	0.038
261	935	\begin{align*} 5 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.038
262	2788	\begin{align*} x^{\prime }&=x-x^{2}-2 x y \\ y^{\prime }&=2 y-2 y^{2}-3 x y \\ \end{align*}	✗	✗	✗	✗	0.038
263	4536	\begin{align*} x^{\prime \prime }-3 x-4 y&=0 \\ x+y^{\prime \prime }+y&=0 \\ \end{align*}	✗	✓	✓	✓	0.038
264	6618	\begin{align*} y^{\prime \prime \prime }-7 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.038
265	6635	\begin{align*} -3 y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.038
266	6662	\begin{align*} -2 y+2 y^{\prime } x -x^{2} y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.038
267	6714	\begin{align*} -6 y+6 \left (x +1\right ) y^{\prime }-3 x \left (2+x \right ) y^{\prime \prime }+x^{2} \left (3+y\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.038
268	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*}	✗	✓	✗	✗	0.038
269	8152	\begin{align*} x y^{\prime \prime \prime }-{y^{\prime }}^{4}+y&=0 \\ \end{align*}	✗	✗	✗	✗	0.038
270	12709	\begin{align*} y^{\prime \prime \prime }+y a \,x^{3}-b x&=0 \\ \end{align*}	✗	✓	✓	✗	0.038
271	12717	\begin{align*} y f^{\prime }\left (x \right )+2 f \left (x \right ) y^{\prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.038
272	12758	\begin{align*} x^{3} y^{\prime \prime \prime }+\left (4 x^{3}+\left (-4 \nu ^{2}+1\right ) x \right ) y^{\prime }+\left (4 \nu ^{2}-1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	0.038
273	12774	\begin{align*} x^{6} y^{\prime \prime \prime }+6 x^{5} y^{\prime \prime }+a y&=0 \\ \end{align*}	✗	✓	✓	✗	0.038
274	12782	\begin{align*} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.038
275	12801	\begin{align*} x^{2} y^{\prime \prime \prime \prime }+8 x y^{\prime \prime \prime }+12 y^{\prime \prime }-\lambda ^{2} y&=0 \\ \end{align*}	✗	✓	✓	✗	0.038
276	12832	\begin{align*} x^{10} y^{\left (5\right )}-a y&=0 \\ \end{align*}	✗	✓	✓	✗	0.038
277	14832	\begin{align*} t^{3} x^{\prime \prime \prime }-\left (t +3\right ) t^{2} x^{\prime \prime }+2 t \left (t +3\right ) x^{\prime }-2 \left (t +3\right ) x&=0 \\ \end{align*}	✗	✓	✓	✗	0.038
278	15671	\begin{align*} y^{\prime \prime \prime \prime }-16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.038
279	18406	\begin{align*} x^{\prime }&=\frac {{\mathrm e}^{-x}}{t} \\ y^{\prime }&=\frac {x \,{\mathrm e}^{-y}}{t} \\ \end{align*}	✗	✓	✓	✓	0.038
280	18418	\begin{align*} x^{\prime \prime }+y^{\prime }+x&=0 \\ x^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✓	0.038
281	19528	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.038
282	19530	\begin{align*} y^{\prime \prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.038
283	21241	\begin{align*} x x^{\prime }+y&=2 t \\ y^{\prime }+2 x^{2}&=1 \\ \end{align*}	✗	✓	✓	✗	0.038
284	21308	\begin{align*} x^{\prime \prime \prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.038
285	21700	\begin{align*} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 y^{\prime } x -8 y&=4 \ln \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.038
286	23246	\begin{align*} 2 y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }+y x&=0 \\ \end{align*}	✗	✗	✗	✗	0.038
287	23469	\begin{align*} 3 x y^{\prime \prime \prime }-4 y x&=\cos \left (y\right ) \\ \end{align*}	✗	✗	✗	✗	0.038
288	23575	\begin{align*} t x^{\prime }&=3 x-2 y \\ y^{\prime } t&=x+y-t^{2} \\ \end{align*}	✗	✓	✓	✓	0.038
289	25145	\begin{align*} y^{\left (5\right )}+t y^{\prime \prime }-3 y&=0 \\ \end{align*}	✗	✗	✗	✗	0.038
290	25688	\begin{align*} x^{\prime \prime }&=4 y+{\mathrm e}^{t} \\ y^{\prime \prime }&=4 x-{\mathrm e}^{t} \\ \end{align*}	✗	✓	✓	✓	0.038
291	281	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+16 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.039
292	608	\begin{align*} x^{\prime }&=t x-y+{\mathrm e}^{t} z \\ y^{\prime }&=2 x+t^{2} y-z \\ z^{\prime }&={\mathrm e}^{-t} x+3 t y+t^{3} z \\ \end{align*}	✗	✗	✗	✗	0.039
293	938	\begin{align*} 9 y^{\prime \prime \prime }+12 y^{\prime \prime }+4 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.039
294	1471	\begin{align*} t^{2} \left (t +3\right ) y^{\prime \prime \prime }-3 t \left (t +2\right ) y^{\prime \prime }+6 \left (1+t \right ) y^{\prime }-6 y&=0 \\ \end{align*}	✗	✓	✓	✗	0.039
295	6609	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.039
296	6614	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.039
297	6626	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.039
298	6631	\begin{align*} y^{\prime }+2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.039
299	6672	\begin{align*} -y+y^{\prime } x -y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.039
300	6710	\begin{align*} -12 y+3 \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.039