2.3.43 Problems 4201 to 4300

Table 2.617: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4201	20057	\begin{align*} y^{\prime \prime \prime }+y&=\sin \left (3 x \right )-\cos \left (\frac {x}{2}\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.231
4202	20611	\begin{align*} x^{2} y^{\prime \prime }-\left (x^{2}+2 x \right ) y^{\prime }+\left (2+x \right ) y&={\mathrm e}^{x} x^{3} \\ \end{align*}	✓	✓	✓	✗	0.231
4203	21118	\begin{align*} x^{\prime \prime }+5 x^{\prime }+6 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.231
4204	22668	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.231
4205	23283	\begin{align*} 3 y^{\prime \prime }+48 y^{\prime }+192 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.231
4206	24658	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=21 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.231
4207	24676	\begin{align*} 4 y^{\prime \prime }+y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.231
4208	412	\begin{align*} y^{\prime \prime }+9 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.232
4209	6970	\begin{align*} \left (-x^{3}+1\right ) y^{\prime }-2 \left (x +1\right ) y&=y^{{5}/{2}} \\ \end{align*}	✓	✓	✓	✓	0.232
4210	10510	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +6 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.232
4211	10823	\begin{align*} y^{\prime \prime }+\frac {y}{2 x^{4}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.232
4212	10940	\begin{align*} y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.232
4213	17649	\begin{align*} x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+5 y^{\prime } x -5 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= -1 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.232
4214	18762	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.232
4215	21168	\begin{align*} x x^{\prime \prime }-{x^{\prime }}^{2}+{\mathrm e}^{t} x^{2}&=0 \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✗	✓	✓	✗	0.232
4216	23694	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.232
4217	23807	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=x-y \\ \end{align*}	✓	✓	✓	✓	0.232
4218	24538	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=-6 x^{2}-8 x +4 \\ \end{align*}	✓	✓	✓	✓	0.232
4219	24645	\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.232
4220	25286	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} {\mathrm e}^{t} & 0\le t <1 \\ {\mathrm e}^{2 t} & 1\le t <\infty \end {array}\right . \\ \end{align*} Using Laplace transform method.	✓	✗	✓	✓	0.232
4221	418	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.233
4222	849	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.233
4223	1269	\begin{align*} y^{\prime \prime }-\left (2 \alpha -1\right ) y^{\prime }+\alpha \left (\alpha -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.233
4224	1764	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=-6 x -4 \\ \end{align*}	✓	✓	✓	✓	0.233
4225	2196	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=-2 x -2+4 \,{\mathrm e}^{x}-6 \,{\mathrm e}^{-x}+96 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.233
4226	2204	\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+9 y^{\prime \prime }+7 y^{\prime }+2 y&={\mathrm e}^{-x} \left (30+24 x \right )-{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.233
4227	2673	\begin{align*} y^{\prime \prime }+y&=t^{2} \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.233
4228	3688	\begin{align*} y^{2}-2 x +2 x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	0.233
4229	5919	\begin{align*} -\left (1-x \right ) y+\left (1-2 x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.233
4230	6718	\begin{align*} y x -x^{2} y^{\prime }+2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.233
4231	6932	\begin{align*} 4 x^{3}-\sin \left (x \right )+y^{3}-\left (y^{2}+1-3 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.233
4232	7583	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.233
4233	7824	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.233
4234	9316	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.233
4235	10243	\begin{align*} y^{\prime }+y&=\frac {1}{x^{2}} \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.233
4236	10506	\begin{align*} \left (1-x \right ) x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (-x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.233
4237	10814	\begin{align*} x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.233
4238	10927	\begin{align*} \left (1-x \right ) x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (-x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.233
4239	11170	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.233
4240	15214	\begin{align*} 4 y^{\prime \prime }+5 y^{\prime }+4 y&=3 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.233
4241	16164	\begin{align*} y^{\prime } x +\sqrt {x}&=2 \\ \end{align*}	✓	✓	✓	✓	0.233
4242	17678	\begin{align*} x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+44 y^{\prime } x +58 y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 10 \\ y^{\prime \prime }\left (1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.233
4243	18320	\begin{align*} x \left (x -1\right ) y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+2 y&=x^{2} \left (2 x -3\right ) \\ \end{align*}	✓	✓	✓	✗	0.233
4244	18773	\begin{align*} y^{\prime \prime }+2 y^{\prime }+\frac {5 y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.233
4245	18780	\begin{align*} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.233
4246	19546	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=1 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 4 \\ y^{\prime \prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.233
4247	19560	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.233
4248	20982	\begin{align*} y&=y^{\prime } x +{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.233
4249	21571	\begin{align*} 2 y^{\prime \prime }+5 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.233
4250	21867	\begin{align*} y^{\prime } y&=-x {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.233
4251	23362	\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.233
4252	23702	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.233
4253	23713	\begin{align*} y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.233
4254	24541	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=12 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.233
4255	442	\begin{align*} y^{\prime \prime }+y^{\prime } x -2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.234
4256	549	\begin{align*} x^{\prime \prime \prime \prime }+8 x^{\prime \prime }+16 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ x^{\prime \prime \prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.234
4257	1043	\begin{align*} y^{\prime }&=4 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.234
4258	1398	\begin{align*} \left (1-x \right ) y^{\prime }&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.234
4259	3064	\begin{align*} y^{\prime \prime }-2 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.234
4260	5492	\begin{align*} 4 \left (-x +2\right ) {y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✓	0.234
4261	5516	\begin{align*} x^{2} {y^{\prime }}^{2}+\left (a +b \,x^{2} y^{3}\right ) y^{\prime }+a b y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.234
4262	5523	\begin{align*} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 x y^{\prime } y+x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.234
4263	5640	\begin{align*} {y^{\prime }}^{3}-\left (y^{4}+x y^{2}+x^{2}\right ) {y^{\prime }}^{2}+x y^{2} \left (y^{4}+x y^{2}+x^{2}\right ) y^{\prime }-x^{3} y^{6}&=0 \\ \end{align*}	✓	✓	✓	✓	0.234
4264	6509	\begin{align*} a y y^{\prime }-2 x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.234
4265	7586	\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.234
4266	8625	\begin{align*} y^{\prime \prime }+9 y&=10 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.234
4267	9992	\begin{align*} y^{\prime }&=x +1 \\ \end{align*}	✓	✓	✓	✓	0.234
4268	10345	\begin{align*} y^{\prime }+\left (a t +b t \right ) y&=0 \\ y \left (-3\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.234
4269	10351	\begin{align*} y^{\prime } x +y&=\sin \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.234
4270	10933	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x +20 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.234
4271	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*}	✓	✓	✓	✗	0.234
4272	13140	\(\left [\begin {array}{cc} 8 & -6 \\ 3 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.234
4273	14070	\begin{align*} y^{\prime } y&=\left (-b +x \right ) {y^{\prime }}^{2}+a \\ \end{align*}	✓	✓	✓	✗	0.234
4274	14088	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.234
4275	16716	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.234
4276	16846	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.234
4277	17994	\begin{align*} {y^{\prime }}^{2}-\left (2 x +y\right ) y^{\prime }+x^{2}+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.234
4278	20042	\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.234
4279	22843	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.234
4280	24537	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=27 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.234
4281	24657	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=12 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.234
4282	24854	\begin{align*} x {y^{\prime }}^{2}+\left (k -x -y\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.234
4283	25670	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=12 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.234
4284	1886	\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.235
4285	5391	\begin{align*} {y^{\prime }}^{2}-\left (x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.235
4286	5436	\begin{align*} 2 {y^{\prime }}^{2}-\left (1-x \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.235
4287	8163	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.235
4288	10289	\begin{align*} y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.235
4289	10483	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.235
4290	10638	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.235
4291	10969	\begin{align*} 3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.235
4292	11268	\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*}	✓	✓	✓	✗	0.235
4293	15081	\begin{align*} y^{\prime \prime }+4 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.235
4294	18625	\begin{align*} y^{\prime } x&=-\frac {1}{\ln \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	0.235
4295	18943	\begin{align*} y^{\prime \prime }+y&=\delta \left (t -2 \pi \right ) \cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.235
4296	18951	\begin{align*} y^{\prime \prime }+y&=\delta \left (-1+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.235
4297	20161	\begin{align*} x y^{\prime \prime \prime }-y^{\prime \prime } x -y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.235
4298	23808	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=-x+y \\ \end{align*}	✓	✓	✓	✓	0.235
4299	24647	\begin{align*} 4 y^{\prime \prime }+y&={\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.235
4300	240	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.236