2.3.51 Problems 5001 to 5100

Table 2.675: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5001	980	\begin{align*} x_{1}^{\prime }&=-50 x_{1}+20 x_{2} \\ x_{2}^{\prime }&=100 x_{1}-60 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.397
5002	2441	\begin{align*} t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(t=2\).	✗	✗	✓	✗	0.397
5003	2567	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.397
5004	3171	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.397
5005	6616	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime \prime }&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.397
5006	7077	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.397
5007	8794	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.397
5008	8932	\begin{align*} y^{\prime \prime }-2 i y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.397
5009	9882	\begin{align*} 9 x^{2} y^{\prime \prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.397
5010	19970	\begin{align*} {y^{\prime }}^{3}+2 {y^{\prime }}^{2} x -y^{2} {y^{\prime }}^{2}-2 x y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.397
5011	23069	\begin{align*} y^{\prime \prime }-11 y^{\prime }+30 y&={\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	0.397
5012	23111	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.397
5013	24097	\begin{align*} x y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.397
5014	408	\begin{align*} \left (x -1\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.398
5015	1423	\begin{align*} x_{1}^{\prime }&=-\frac {5 x_{1}}{2}+\frac {3 x_{2}}{2} \\ x_{2}^{\prime }&=-\frac {3 x_{1}}{2}+\frac {x_{2}}{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 3 \\ x_{2} \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.398
5016	1736	\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.398
5017	2376	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.398
5018	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 \(t=0\).	✓	✓	✓	✓	0.398
5019	2513	\begin{align*} 2 t y^{3}+3 t^{2} y^{2} y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.398
5020	3418	\begin{align*} y^{\prime }&={\mathrm e}^{2 t} t \\ \end{align*}	✓	✓	✓	✓	0.398
5021	4121	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.398
5022	7104	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=12 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.398
5023	7362	\begin{align*} y^{\prime }&=3 x^{2} y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.398
5024	8076	\begin{align*} y^{\prime \prime }+x^{2} y&=x^{2}+x +1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.398
5025	8163	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.398
5026	10332	\begin{align*} t y^{\prime }+y&=t \\ y \left (0\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✗	✓	0.398
5027	11738	\begin{align*} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.398
5028	12917	\begin{align*} y y^{\prime \prime }-a x&=0 \\ \end{align*}	✗	✗	✗	✗	0.398
5029	16373	\begin{align*} y^{\prime }+2 x&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.398
5030	17992	\begin{align*} {y^{\prime }}^{2}-2 x y^{\prime }-8 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.398
5031	18372	\begin{align*} y^{\prime }&=\frac {-x +y}{x +y} \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✗	✓	0.398
5032	20181	\begin{align*} x^{2} y^{\prime \prime }-2 \left (x^{2}+x \right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.398
5033	20748	\begin{align*} -2 y+2 x y^{\prime }-x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x^{2}+3 x \\ \end{align*}	✓	✓	✓	✓	0.398
5034	20881	\begin{align*} y^{\prime }&=y \\ y \left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.398
5035	20921	\begin{align*} x^{\prime }&=2 x+3 y+2 \sin \left (2 t \right ) \\ y^{\prime }&=-3 x+2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.398
5036	20934	\begin{align*} x^{\prime }&=-4 x-y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.398
5037	23036	\begin{align*} x^{\prime \prime }-6 x^{\prime }-7 x&=4 z -7 \\ \end{align*}	✓	✓	✓	✓	0.398
5038	25226	\begin{align*} 4 t^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.398
5039	25442	\begin{align*} y^{\prime }&=A \cos \left (\omega t \right )+B \sin \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	0.398
5040	26118	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }&=1+x \,{\mathrm e}^{x}+2 x \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.398
5041	407	\begin{align*} 2 \left (x +1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.399
5042	1380	\begin{align*} \left (-x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.399
5043	1422	\begin{align*} x_{1}^{\prime }&=x_{1}-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1}-7 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 3 \\ x_{2} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.399
5044	1930	\begin{align*} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.399
5045	2670	\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&={\mathrm e}^{2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.399
5046	3189	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=x^{2}-8 \\ \end{align*}	✓	✓	✓	✓	0.399
5047	3301	\begin{align*} 2 x^{2} y+{y^{\prime }}^{2}&=x^{3} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.399
5048	3403	\begin{align*} y^{\prime }&=2 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.399
5049	6637	\begin{align*} -3 y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&={\mathrm e}^{-x}+3 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.399
5050	9314	\begin{align*} y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.399
5051	16402	\begin{align*} 3 y y^{\prime \prime }&=2 {y^{\prime }}^{2} \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✗	0.399
5052	16565	\begin{align*} 4 x^{2} y^{\prime \prime }+37 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.399
5053	24085	\begin{align*} y^{\prime \prime }+3 x^{3} y^{\prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.399
5054	2227	\begin{align*} x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y&=4 x \\ y \left (1\right ) &= 4 \\ y^{\prime }\left (1\right ) &= 4 \\ y^{\prime \prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.400
5055	10516	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }+28 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.400
5056	11715	\begin{align*} \left (1+3 x \right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9&=0 \\ \end{align*}	✓	✓	✓	✗	0.400
5057	15809	\begin{align*} y^{\prime }&=t^{2}+t \\ \end{align*}	✓	✓	✓	✓	0.400
5058	15827	\begin{align*} y^{\prime }&=-t^{2}+2 \\ \end{align*}	✓	✓	✓	✓	0.400
5059	23321	\begin{align*} y^{\prime \prime }+3 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.400
5060	23706	\begin{align*} y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+2 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.400
5061	25076	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=4 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.400
5062	423	\begin{align*} y^{\prime \prime }&=y^{\prime }+y \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.401
5063	2557	\begin{align*} y^{\prime \prime }+2 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.401
5064	4589	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.401
5065	6749	\begin{align*} -2 y+5 y^{\prime }-3 y^{\prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.401
5066	8067	\begin{align*} \left (1-x \right ) y^{\prime }&=x^{2}-y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.401
5067	10649	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.401
5068	13199	\(\left [\begin {array}{cccc} 1 & 1 & 0 & 1 \\ 0 & 1 & 1 & 1 \\ 0 & 0 & 2 & 1 \\ 0 & 0 & 0 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.401
5069	15771	\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=2 x+y \\ \end{align*}	✓	✓	✓	✓	0.401
5070	16483	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.401
5071	16496	\begin{align*} y^{\prime \prime }-8 y^{\prime }+15 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 19 \\ \end{align*}	✓	✓	✓	✓	0.401
5072	18883	\begin{align*} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y&=2 \left (t -1\right )^{2} {\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✗	0.401
5073	19244	\begin{align*} y^{\prime }&=\arcsin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.401
5074	19380	\begin{align*} y^{\prime \prime }+2 {y^{\prime }}^{2} x&=0 \\ \end{align*}	✓	✓	✓	✓	0.401
5075	19692	\begin{align*} x^{\prime \prime }-3 x^{\prime }+2 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.401
5076	21716	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=t \\ y \left (0\right ) &= -3 \\ y \left (1\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.401
5077	23046	\begin{align*} \left (1-y^{2}\right ) y^{\prime \prime }&=y^{\prime } \\ \end{align*}	✓	✓	✓	✗	0.401
5078	23355	\begin{align*} y^{\prime \prime }+6 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.401
5079	24923	\begin{align*} y^{\prime }&={\mathrm e}^{2 t}-1 \\ \end{align*}	✓	✓	✓	✓	0.401
5080	25071	\begin{align*} y^{\prime \prime }+4 y&=8 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.401
5081	25930	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.401
5082	26432	\begin{align*} y^{\prime \prime }+6 y {y^{\prime }}^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	0.401
5083	27065	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.401
5084	443	\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 \(x=1\).	✓	✓	✓	✓	0.402
5085	445	\begin{align*} \left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y&=0 \\ y \left (3\right ) &= 2 \\ y^{\prime }\left (3\right ) &= 0 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	0.402
5086	467	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.402
5087	2228	\begin{align*} x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 x y^{\prime }-18 y&=x^{3} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ y^{\prime \prime }\left (1\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	0.402
5088	3279	\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✗	✓	✗	0.402
5089	6813	\begin{align*} 40 {y^{\prime \prime \prime }}^{3}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+9 {y^{\prime \prime }}^{2} y^{\left (5\right )}&=0 \\ \end{align*}	✗	✓	✓	✗	0.402
5090	8633	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ y \left (4\right ) &= -3 \\ y^{\prime }\left (4\right ) &= -17 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.402
5091	19653	\begin{align*} x^{\prime }&=-3 x+4 y \\ y^{\prime }&=-2 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.402
5092	23809	\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=-x-2 y \\ \end{align*}	✓	✓	✓	✓	0.402
5093	25072	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=9 \,{\mathrm e}^{2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.402
5094	27673	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=\cosh \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	0.402
5095	9653	\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=\delta \left (t \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.403
5096	10290	\begin{align*} 5 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.403
5097	10573	\begin{align*} 8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.403
5098	23811	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=-x-y \\ \end{align*}	✓	✓	✓	✓	0.403
5099	25069	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=4 \,{\mathrm e}^{2 t} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.403
5100	3179	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.404