2.3.43 Problems 4201 to 4300

Table 2.659: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4201	10460	\begin{align*} x^{\prime }&=3 x+y \\ y^{\prime }&=-x+y \\ \end{align*}	✓	✓	✓	✓	0.339
4202	10506	\begin{align*} x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.339
4203	10521	\begin{align*} \left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.339
4204	12981	\begin{align*} a y y^{\prime }-2 {y^{\prime }}^{2} x +x y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.339
4205	13168	\(\left [\begin {array}{cc} 0 & 24 \\ -6 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.339
4206	17201	\begin{align*} 3 t y^{2}+y^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.339
4207	17385	\begin{align*} 8 y^{\prime \prime }+6 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.339
4208	17412	\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.339
4209	17418	\begin{align*} y^{\prime \prime }-6 y^{\prime }-16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.339
4210	19460	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.339
4211	19737	\begin{align*} \sec \left (\theta \right )^{2}&=\frac {m s^{\prime }}{k} \\ \end{align*}	✓	✓	✓	✓	0.339
4212	23710	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.339
4213	25679	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.339
4214	26123	\begin{align*} x^{\prime }&=-x+2 y \\ y^{\prime }&=2 x-y \\ \end{align*}	✓	✓	✓	✓	0.339
4215	9111	\begin{align*} y^{\prime }-2 y x&=6 x \,{\mathrm e}^{x^{2}} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.340
4216	9228	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.340
4217	10013	\begin{align*} \frac {y^{\prime }}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	0.340
4218	12719	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-a^{2} y^{\prime }+2 a^{2} y-\sinh \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.340
4219	13169	\(\left [\begin {array}{cc} 0 & -4 \\ 36 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.340
4220	16970	\begin{align*} y^{\prime \prime }-12 y^{\prime }+40 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.340
4221	17417	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.340
4222	23718	\begin{align*} 6 y-2 x y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.340
4223	26943	\begin{align*} y^{\prime \prime }-14 y^{\prime }+49 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.340
4224	1370	\begin{align*} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.341
4225	1457	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.341
4226	7691	\begin{align*} x \left (x -1\right )^{2} y^{\prime \prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.341
4227	12817	\begin{align*} \left ({\mathrm e}^{x}+2 x \right ) y^{\prime \prime \prime \prime }+4 \left ({\mathrm e}^{x}+2\right ) y^{\prime \prime \prime }+6 \,{\mathrm e}^{x} y^{\prime \prime }+4 \,{\mathrm e}^{x} y^{\prime }+y \,{\mathrm e}^{x}-\frac {1}{x^{5}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.341
4228	14710	\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-6 x y^{\prime }+18 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.341
4229	17390	\begin{align*} 4 y^{\prime \prime }+21 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.341
4230	18297	\begin{align*} x^{2} y^{\prime \prime \prime }&=2 y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.341
4231	20412	\begin{align*} \left (1+{y^{\prime }}^{2}\right ) x&=1 \\ \end{align*}	✓	✓	✓	✓	0.341
4232	23380	\begin{align*} x^{2} y^{\prime \prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.341
4233	26936	\begin{align*} y^{\prime \prime }-2 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.341
4234	384	\begin{align*} x^{\prime \prime }+4 x&=5 \sin \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.342
4235	1271	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -\beta \\ \end{align*}	✓	✓	✓	✗	0.342
4236	1419	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+\frac {5 x_{2}}{2} \\ x_{2}^{\prime }&=-\frac {5 x_{1}}{2}+2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.342
4237	13166	\(\left [\begin {array}{cc} 0 & -3 \\ 12 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.342
4238	16181	\begin{align*} y^{\prime }&=\sin \left (\frac {x}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.342
4239	17410	\begin{align*} 6 y^{\prime \prime }+5 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.342
4240	21867	\begin{align*} y y^{\prime }&=-{y^{\prime }}^{2} x \\ \end{align*}	✓	✓	✓	✓	0.342
4241	22239	\begin{align*} y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.342
4242	23271	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.342
4243	23357	\begin{align*} y^{\prime \prime }+9 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.342
4244	26196	\begin{align*} y^{\prime }&=1-x \\ \end{align*}	✓	✓	✓	✓	0.342
4245	26623	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime \prime }-12 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.342
4246	26763	\begin{align*} x^{\prime }&=3 x-y \\ y^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.342
4247	1458	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.343
4248	3620	\begin{align*} 1-y \sin \left (x \right )-\cos \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.343
4249	3880	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2} \\ x_{2}^{\prime }&=2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.343
4250	10891	\begin{align*} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.343
4251	19474	\begin{align*} 16 y^{\prime \prime }-8 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.343
4252	22794	\begin{align*} i^{\prime \prime \prime \prime }+9 i^{\prime \prime }&=20 \,{\mathrm e}^{-t} \\ i \left (0\right ) &= 0 \\ i^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.343
4253	23602	\begin{align*} x^{\prime }&=-4 x+y \\ y^{\prime }&=-x-2 y \\ \end{align*}	✓	✓	✓	✓	0.343
4254	25320	\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.343
4255	26723	\begin{align*} y^{\prime \prime }+\frac {3 y^{\prime }}{x}+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.343
4256	413	\begin{align*} y^{\prime \prime }+y&=x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.344
4257	1005	\begin{align*} x_{1}^{\prime }&=x_{1}-3 x_{2} \\ x_{2}^{\prime }&=3 x_{1}+7 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.344
4258	1066	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.344
4259	1373	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+4 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.344
4260	1375	\begin{align*} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=0 \\ y \left (0\right ) &= -3 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.344
4261	9613	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.344
4262	10349	\begin{align*} x y^{\prime }+y&=x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.344
4263	10869	\begin{align*} t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{3} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.344
4264	12352	\begin{align*} 4 y^{\prime \prime }+9 y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.344
4265	16558	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.344
4266	16846	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.344
4267	23559	\begin{align*} x^{\prime }&=5 x-6 y \\ y^{\prime }&=6 x-7 y \\ \end{align*}	✓	✓	✓	✓	0.344
4268	23772	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-x-y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.344
4269	26184	\begin{align*} y^{\prime }&=x +1 \\ \end{align*}	✓	✓	✓	✓	0.344
4270	27643	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.344
4271	854	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*}	✓	✓	✓	✓	0.345
4272	1762	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{x} \sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.345
4273	2678	\begin{align*} y^{\prime \prime }+y&=\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.345
4274	8763	\begin{align*} x^{4} y^{\prime \prime \prime \prime }-x^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.345
4275	15105	\begin{align*} y^{\left (6\right )}+2 y^{\prime \prime \prime \prime }+y^{\prime \prime }&=x +{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.345
4276	15971	\begin{align*} x^{\prime }&=2 x-y \\ y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.345
4277	16515	\begin{align*} y^{\prime \prime }-4 y^{\prime }+29 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.345
4278	19469	\begin{align*} 4 y^{\prime \prime }+20 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.345
4279	20917	\begin{align*} y^{\prime \prime }-3 y^{\prime }-2 y&={\mathrm e}^{t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.345
4280	23330	\begin{align*} 2 y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.345
4281	23345	\begin{align*} y^{\prime \prime }-i y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.345
4282	23694	\begin{align*} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.345
4283	23973	\begin{align*} y^{\prime \prime }-5 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.345
4284	26728	\begin{align*} x^{\prime }+3 x+y&=0 \\ y^{\prime }+y-x&=0 \\ \end{align*}	✓	✓	✓	✓	0.345
4285	26956	\begin{align*} y^{\prime \prime }-2 \alpha y^{\prime }+\left (\alpha ^{2}-\epsilon ^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.345
4286	278	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.346
4287	1072	\begin{align*} \left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.346
4288	1459	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.346
4289	3232	\begin{align*} 4 x^{3} y^{\prime \prime \prime }+8 x^{2} y^{\prime \prime }-x y^{\prime }+y&=\ln \left (x \right )+x \\ \end{align*}	✓	✓	✓	✓	0.346
4290	3764	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=\frac {2 \,{\mathrm e}^{-x}}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✗	0.346
4291	4514	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=9 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.346
4292	10571	\begin{align*} 9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.346
4293	10605	\begin{align*} 4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.346
4294	10627	\begin{align*} x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.346
4295	12515	\begin{align*} x \left (x +1\right ) y^{\prime \prime }-\left (x -1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.346
4296	19466	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.346
4297	20837	\begin{align*} 20 y-9 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.346
4298	23702	\begin{align*} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.346
4299	23767	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.346
4300	25680	\begin{align*} 2 y^{\prime \prime }+9 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.346