2.3.43 Problems 4201 to 4300

Table 2.635: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4201	5381	\begin{align*} {y^{\prime }}^{2}-7 y^{\prime }+12&=0 \\ \end{align*}	✓	✓	✓	✓	0.336
4202	11852	\begin{align*} \sin \left (y^{\prime }\right )+y^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✗	0.336
4203	15476	\begin{align*} x^{\prime }&=0 \\ y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.336
4204	16025	\begin{align*} x^{\prime }&=-3 x \\ y^{\prime }&=x-3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.336
4205	16047	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=z \\ z^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.336
4206	16140	\begin{align*} y^{\prime \prime }+3 y&=5 \delta \left (-2+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.336
4207	16937	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=2 x \\ \end{align*}	✓	✓	✓	✓	0.336
4208	18755	\begin{align*} y^{\prime \prime }+a \left (y^{\prime } x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	0.336
4209	21888	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }&=x^{3}+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.336
4210	22903	\begin{align*} x^{\prime }+x-5 y&=0 \\ y^{\prime }+4 x+5 y&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= -1 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.336
4211	23801	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=3 y \\ \end{align*}	✓	✓	✓	✓	0.336
4212	225	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.337
4213	880	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.337
4214	1005	\begin{align*} x_{1}^{\prime }&=x_{1}-3 x_{2} \\ x_{2}^{\prime }&=3 x_{1}+7 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.337
4215	2424	\begin{align*} y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.337
4216	2555	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.337
4217	5380	\begin{align*} {y^{\prime }}^{2}-5 y^{\prime }+6&=0 \\ \end{align*}	✓	✓	✓	✓	0.337
4218	5916	\begin{align*} 3 y-\left (x +3\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.337
4219	7813	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.337
4220	11003	\begin{align*} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.337
4221	11062	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.337
4222	16061	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=-2 x+y \\ \end{align*}	✓	✓	✓	✓	0.337
4223	17412	\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.337
4224	21931	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.337
4225	658	\begin{align*} y^{\prime }&=\cos \left (2 x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.338
4226	1067	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.338
4227	1072	\begin{align*} \left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.338
4228	1091	\begin{align*} \left (x^{3}+1\right ) y^{\prime \prime }+x^{4} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.338
4229	6768	\begin{align*} 12 y^{\prime \prime }+8 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.338
4230	7191	\begin{align*} 2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x}&=\sqrt {x} \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.338
4231	10461	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.338
4232	10565	\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.338
4233	10581	\begin{align*} x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.338
4234	10714	\begin{align*} 2 y^{\prime \prime } x +5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.338
4235	10987	\begin{align*} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.338
4236	14577	\begin{align*} 3 y^{\prime \prime }-14 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.338
4237	15486	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.338
4238	16005	\begin{align*} x^{\prime }&=4 x-2 y \\ y^{\prime }&=x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.338
4239	16848	\begin{align*} y^{\prime \prime }+y \,{\mathrm e}^{2 x}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.338
4240	18757	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.338
4241	19855	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.338
4242	22644	\begin{align*} 4 i^{\prime \prime }-12 i^{\prime }+9 i&=0 \\ \end{align*}	✓	✓	✓	✓	0.338
4243	25909	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.338
4244	394	\begin{align*} x^{\prime \prime }+2 x^{\prime }+26 x&=600 \cos \left (10 t \right ) \\ x \left (0\right ) &= 10 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.339
4245	1074	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.339
4246	6223	\begin{align*} -2 y+\left (1-x \right )^{2} x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.339
4247	6767	\begin{align*} 6 y^{\prime \prime }+6 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.339
4248	7234	\begin{align*} y^{\prime }+\frac {y}{\sqrt {x^{2}+1}}&=\frac {1}{x +\sqrt {x^{2}+1}} \\ \end{align*}	✓	✓	✓	✗	0.339
4249	13164	\(\left [\begin {array}{cc} 0 & 1 \\ -1 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.339
4250	13207	\begin{align*} y^{\prime }&=a y^{2}+b x +c \\ \end{align*}	✓	✓	✓	✗	0.339
4251	15208	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+29 y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 5 \\ y^{\prime \prime }\left (0\right ) &= -20 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.339
4252	16013	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=-2 x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.339
4253	16735	\begin{align*} y^{\prime \prime }+20 y^{\prime }+100 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.339
4254	16853	\begin{align*} y^{\prime }+\cos \left (y\right )&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.339
4255	19580	\begin{align*} y^{\prime } x&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.339
4256	19640	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.339
4257	21890	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.339
4258	22492	\begin{align*} y^{\prime \prime \prime \prime }&=\ln \left (x \right ) \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ y^{\prime \prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.339
4259	23030	\begin{align*} z^{\prime \prime }+6 z^{\prime }+9 z&=0 \\ \end{align*}	✓	✓	✓	✓	0.339
4260	23363	\begin{align*} 4 y^{\prime \prime }+8 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.339
4261	23771	\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*}	✓	✓	✓	✓	0.339
4262	25537	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.339
4263	226	\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.340
4264	429	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.340
4265	657	\begin{align*} y^{\prime }&=\frac {10}{x^{2}+1} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.340
4266	1418	\begin{align*} x_{1}^{\prime }&=-\frac {3 x_{1}}{2}+x_{2} \\ x_{2}^{\prime }&=-\frac {x_{1}}{4}-\frac {x_{2}}{2} \\ \end{align*}	✓	✓	✓	✓	0.340
4267	2293	\begin{align*} y^{\prime }+\sin \left (t \right ) y&=0 \\ y \left (0\right ) &= {\frac {3}{2}} \\ \end{align*}	✓	✓	✓	✓	0.340
4268	3617	\begin{align*} y^{\prime }-\tan \left (x \right ) y&=8 \sin \left (x \right )^{3} \\ \end{align*}	✓	✓	✓	✓	0.340
4269	9029	\begin{align*} 3 \ln \left (x \right ) x^{2}+x^{2}+y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.340
4270	10464	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.340
4271	10711	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.340
4272	16834	\begin{align*} \left (x^{2}+4\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.340
4273	23443	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.340
4274	23651	\begin{align*} y^{\prime \prime }+13 y^{\prime }+36 y&=10-72 t \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.340
4275	9	\begin{align*} y^{\prime }&=\frac {1}{\sqrt {-x^{2}+1}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.341
4276	611	\begin{align*} x_{1}^{\prime }&=4 x_{1}+2 x_{2} \\ x_{2}^{\prime }&=-3 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.341
4277	624	\begin{align*} x_{1}^{\prime }&=4 x_{1}+x_{2} \\ x_{2}^{\prime }&=6 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.341
4278	816	\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 13 \\ \end{align*}	✓	✓	✓	✓	0.341
4279	896	\begin{align*} 4 y+y^{\prime \prime }&=\cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.341
4280	1083	\begin{align*} y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.341
4281	1262	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.341
4282	1786	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=4 x^{4} \\ y \left (-1\right ) &= 7 \\ y^{\prime }\left (-1\right ) &= -8 \\ \end{align*}	✓	✓	✓	✓	0.341
4283	10778	\begin{align*} x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.341
4284	10945	\begin{align*} y^{\prime \prime }+x^{6} y^{\prime }+7 y x^{5}&=0 \\ \end{align*}	✓	✓	✓	✗	0.341
4285	22843	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.341
4286	23324	\begin{align*} 2 y^{\prime \prime }+14 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.341
4287	25328	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }+2 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.341
4288	26492	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.341
4289	969	\begin{align*} x_{1}^{\prime }&=6 x_{1}-7 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.342
4290	1010	\begin{align*} x_{1}^{\prime }&=x_{1}-2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+5 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.342
4291	1073	\begin{align*} \left (-x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +16 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.342
4292	2610	\begin{align*} y^{\prime \prime }+y^{\prime } t +y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.342
4293	3060	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.342
4294	10462	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.342
4295	14088	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.342
4296	15149	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.342
4297	16031	\begin{align*} x^{\prime }&=4 x+2 y \\ y^{\prime }&=2 x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.342
4298	16709	\begin{align*} y^{\prime \prime }-12 y^{\prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.342
4299	17380	\begin{align*} y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.342
4300	20161	\begin{align*} x y^{\prime \prime \prime }-y^{\prime \prime } x -y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.342