2.3.47 Problems 4601 to 4700

Table 2.667: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4601	1045	\begin{align*} y^{\prime }+2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.368
4602	1450	\begin{align*} x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.368
4603	2417	\begin{align*} y^{\prime \prime }+t^{2} y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.368
4604	2721	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime }&=t +\cos \left (t \right )+2 \,{\mathrm e}^{-2 t} \\ \end{align*}	✓	✓	✓	✓	0.368
4605	4520	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=54 t \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.368
4606	8121	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.368
4607	12412	\begin{align*} x^{2} y^{\prime \prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.368
4608	15810	\begin{align*} y^{\prime }&=t^{2}+1 \\ \end{align*}	✓	✓	✓	✓	0.368
4609	20899	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.368
4610	23324	\begin{align*} 2 y^{\prime \prime }+14 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.368
4611	23666	\begin{align*} y^{\prime }&=3 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.368
4612	27098	\(\left [\begin {array}{ccc} -14 & 1 & 0 \\ 0 & 2 & 0 \\ 1 & 0 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.368
4613	27683	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (2\right ) &= 1 \\ y^{\prime }\left (2\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.368
4614	963	\begin{align*} x_{1}^{\prime }&=6 x_{1} \\ x_{2}^{\prime }&=-3 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.369
4615	6939	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.369
4616	13200	\(\left [\begin {array}{ccccc} 2 & 1 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 & 0 \\ 0 & 0 & 2 & 0 & 0 \\ 0 & 0 & 0 & 2 & 1 \\ 0 & 0 & 0 & 0 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.369
4617	14402	\begin{align*} x^{\prime }&=2 x \\ y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.369
4618	22093	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.369
4619	23336	\begin{align*} 9 y^{\prime \prime }-6 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.369
4620	23353	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (-1\right ) &= {\mathrm e} \\ \end{align*}	✓	✓	✓	✓	0.369
4621	23595	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=-3 x+6 y \\ \end{align*}	✓	✓	✓	✓	0.369
4622	23708	\begin{align*} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.369
4623	23790	\begin{align*} x^{\prime }&=-3 x+4 y \\ y^{\prime }&=-2 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.369
4624	26131	\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=3 x-4 y \\ \end{align*}	✓	✓	✓	✓	0.369
4625	27063	\begin{align*} y^{\prime }-x^{3} y&=4 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.369
4626	27540	\begin{align*} x^{2} y^{\prime \prime \prime }&={y^{\prime \prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.369
4627	8533	\begin{align*} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.370
4628	16819	\begin{align*} y^{\prime \prime \prime \prime }-16 y&=\delta \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.370
4629	17661	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 x y^{\prime }&=-8 \\ \end{align*}	✓	✓	✓	✓	0.370
4630	23318	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.370
4631	23445	\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.370
4632	23779	\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=-x_{1} \\ \end{align*}	✓	✓	✓	✓	0.370
4633	27753	\begin{align*} y^{\prime }&=y^{2}-x \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.370
4634	404	\begin{align*} y^{\prime }&=y x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.371
4635	1046	\begin{align*} y^{\prime }&=x^{2} y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.371
4636	1047	\begin{align*} \left (x -2\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.371
4637	1069	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.371
4638	1461	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.371
4639	3763	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=36 \,{\mathrm e}^{2 x} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.371
4640	8892	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.371
4641	10495	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.371
4642	10738	\begin{align*} y^{\prime \prime }+n^{2} y&=\frac {6 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.371
4643	17698	\begin{align*} y^{\prime \prime }+\left (y^{2}-1\right ) y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✗	✗	0.371
4644	18757	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.371
4645	19201	\begin{align*} -2 y+2 x y^{\prime }-x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x^{3}+3 x \\ \end{align*}	✓	✓	✓	✓	0.371
4646	21475	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.371
4647	21482	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.371
4648	23433	\begin{align*} y^{\prime \prime }+x y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.371
4649	23606	\begin{align*} x^{\prime }&=3 x-2 y \\ y^{\prime }&=2 x-y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= -1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.371
4650	23707	\begin{align*} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.371
4651	25537	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.371
4652	27712	\begin{align*} x y^{\prime \prime }-\left (x +1\right ) y^{\prime }-2 \left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.371
4653	1051	\begin{align*} 2 \left (x -1\right ) y^{\prime }&=3 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.372
4654	1086	\begin{align*} \left (4 x^{2}+16 x +17\right ) y^{\prime \prime }&=8 y \\ y \left (-2\right ) &= 1 \\ y^{\prime }\left (-2\right ) &= 0 \\ \end{align*} Series expansion around \(x=-2\).	✓	✓	✓	✓	0.372
4655	2641	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (t +1\right )}+y&=0 \\ \end{align*} Series expansion around \(t=-1\).	✗	✗	✓	✗	0.372
4656	5762	\begin{align*} a \,{\mathrm e}^{b x} y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.372
4657	7591	\begin{align*} y^{\prime \prime }-y^{\prime }-11 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.372
4658	15973	\begin{align*} x^{\prime }&=-x+2 y \\ y^{\prime }&=2 x-y \\ \end{align*}	✓	✓	✓	✓	0.372
4659	16768	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&={\mathrm e}^{2 t} \sin \left (3 t \right ) \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.372
4660	18008	\begin{align*} x&=\sin \left (y^{\prime }\right )+y^{\prime } \\ \end{align*}	✓	✓	✓	✗	0.372
4661	18744	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.372
4662	18756	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.372
4663	18766	\begin{align*} y^{\prime \prime }+2 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.372
4664	19028	\begin{align*} x_{1}^{\prime }&=\frac {x_{1}}{2}+\frac {x_{2}}{2} \\ x_{2}^{\prime }&=2 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.372
4665	22252	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.372
4666	23439	\begin{align*} y^{\prime \prime }-2 x y^{\prime }+y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.372
4667	421	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.373
4668	1761	\begin{align*} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=4 \sqrt {x}\, {\mathrm e}^{x} \left (1+4 x \right ) \\ \end{align*}	✓	✓	✓	✗	0.373
4669	7729	\begin{align*} 2 y^{\prime }+y&=y^{3} \left (x -1\right ) \\ \end{align*}	✓	✓	✓	✓	0.373
4670	10567	\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*}	✓	✓	✓	✗	0.373
4671	19027	\begin{align*} x_{1}^{\prime }&=2 x_{1}-x_{2} \\ x_{2}^{\prime }&=3 x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.373
4672	23974	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.373
4673	26360	\begin{align*} \left (1+{y^{\prime }}^{2}\right ) x&=1 \\ \end{align*}	✓	✓	✓	✓	0.373
4674	577	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.374
4675	1743	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.374
4676	1867	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	0.374
4677	2256	\begin{align*} y_{1}^{\prime }&=3 y_{1}+y_{2} \\ y_{2}^{\prime }&=-y_{1}+y_{2} \\ \end{align*}	✓	✓	✓	✓	0.374
4678	3338	\begin{align*} y^{\prime }&=\ln \left (y x \right ) \\ y \left (1\right ) &= 1 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.374
4679	7849	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.374
4680	10259	\begin{align*} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.374
4681	10420	\begin{align*} y^{\prime \prime }+x y^{\prime }+y {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.374
4682	10600	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.374
4683	11020	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.374
4684	13186	\(\left [\begin {array}{ccc} 3 & -3 & 1 \\ 2 & -2 & 1 \\ 0 & 0 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.374
4685	19019	\begin{align*} x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.374
4686	19025	\begin{align*} x_{1}^{\prime }&=5 x_{1}-x_{2} \\ x_{2}^{\prime }&=3 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.374
4687	20046	\begin{align*} y^{\prime \prime }-y&=2+5 x \\ \end{align*}	✓	✓	✓	✓	0.374
4688	20923	\begin{align*} x^{\prime }&=x-y+2 \cos \left (t \right ) \\ y^{\prime }&=x+y+3 \sin \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.374
4689	26460	\begin{align*} x^{4} y^{\prime \prime \prime }+2 x^{3} y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.374
4690	392	\begin{align*} x^{\prime \prime }+4 x^{\prime }+5 x&=10 \cos \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.375
4691	969	\begin{align*} x_{1}^{\prime }&=6 x_{1}-7 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.375
4692	1050	\begin{align*} \left (x -1\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.375
4693	1270	\begin{align*} y^{\prime \prime }+\left (3-\alpha \right ) y^{\prime }-2 \left (\alpha -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.375
4694	1630	\begin{align*} 7 x y^{\prime }-2 y&=-\frac {x^{2}}{y^{6}} \\ \end{align*}	✓	✓	✓	✗	0.375
4695	7913	\begin{align*} y \left (x +y\right )-x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.375
4696	9617	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.375
4697	10380	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.375
4698	10563	\begin{align*} 3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.375
4699	10650	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.375
4700	10726	\begin{align*} 2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x}&=0 \\ \end{align*}	✓	✓	✓	✗	0.375