2.3.61 Problems 6001 to 6100

Table 2.695: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
6001	24688	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y&=16 x^{3}+20 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.751
6002	24778	\begin{align*} x {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.751
6003	5899	\begin{align*} a \,x^{2} y+2 y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.752
6004	6676	\begin{align*} 2 y+4 y^{\prime } x -\left (-x^{2}+3\right ) y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.752
6005	14872	\begin{align*} y^{\prime }&=\frac {1}{x^{2}-1} \\ \end{align*}	✓	✓	✓	✓	0.752
6006	16945	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=4 x+24 t \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.752
6007	19555	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.752
6008	908	\begin{align*} x^{\prime \prime }+9 x&=10 \cos \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.753
6009	16580	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+9 y^{\prime } x +16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.753
6010	17522	\begin{align*} y^{\prime \prime }-16 y&=16 t \,{\mathrm e}^{-4 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.753
6011	20851	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right )^{3} \\ \end{align*}	✓	✓	✓	✓	0.753
6012	20882	\begin{align*} y^{\prime }&=2 y x -x^{3} \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.753
6013	21284	\begin{align*} x^{\prime \prime \prime \prime }+x^{\prime \prime }&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ x^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.753
6014	22579	\begin{align*} x^{4} y^{\prime \prime \prime }+1&=0 \\ \end{align*}	✓	✓	✓	✓	0.753
6015	23007	\begin{align*} 20 y^{\prime \prime }-3 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.753
6016	23243	\begin{align*} y^{\left (5\right )}-2 y^{\prime \prime \prime \prime }+y&=2 x^{2}+3 \\ \end{align*}	✓	✓	✓	✗	0.753
6017	27626	\begin{align*} y^{\left (5\right )}-10 y^{\prime \prime \prime }+9 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.753
6018	27631	\begin{align*} y^{\left (5\right )}+8 y^{\prime \prime \prime }+16 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.753
6019	638	\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2}+2 x_{3} \\ x_{2}^{\prime }&=2 x_{1}+7 x_{2}+x_{3} \\ x_{3}^{\prime }&=2 x_{1}+x_{2}+7 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.754
6020	1842	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x +2\right ) y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.754
6021	4505	\begin{align*} 4 y+y^{\prime \prime }&=2 \tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.754
6022	13169	\(\left [\begin {array}{cc} 0 & -4 \\ 36 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.754
6023	17682	\begin{align*} \left (x^{2}-4\right ) y^{\prime \prime }+16 \left (2+x \right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.754
6024	17816	\begin{align*} x^{\prime \prime }+x&=\cos \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.754
6025	19638	\begin{align*} x^{\prime }&=x+2 y \\ y^{\prime }&=3 x+2 y \\ \end{align*}	✓	✓	✓	✓	0.754
6026	23003	\begin{align*} 3 x^{\prime \prime }+19 x^{\prime }-14 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.754
6027	23005	\begin{align*} y^{\prime \prime }-9 y^{\prime }+18 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.754
6028	23334	\begin{align*} 8 y^{\prime \prime }-6 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.754
6029	2442	\begin{align*} \sin \left (t \right ) y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+\frac {y}{t}&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✗	0.755
6030	3988	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.755
6031	16163	\begin{align*} y^{\prime }&=20 \,{\mathrm e}^{-4 x} \\ \end{align*}	✓	✓	✓	✓	0.755
6032	1035	\begin{align*} x_{1}^{\prime }&=-15 x_{1}-7 x_{2}+4 x_{3} \\ x_{2}^{\prime }&=34 x_{1}+16 x_{2}-11 x_{3} \\ x_{3}^{\prime }&=17 x_{1}+7 x_{2}+5 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.756
6033	3735	\begin{align*} y^{\prime \prime }-y&=10 \,{\mathrm e}^{2 x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.756
6034	3910	\begin{align*} x_{1}^{\prime }&=-3 x_{1}-x_{2}-2 x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{3} \\ x_{3}^{\prime }&=x_{1} \\ \end{align*}	✓	✓	✓	✓	0.756
6035	7089	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.756
6036	15473	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=x+3 y \\ \end{align*}	✓	✓	✓	✓	0.756
6037	17710	\begin{align*} 5 y^{\prime \prime } x +8 y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.756
6038	22628	\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.756
6039	23380	\begin{align*} x^{2} y^{\prime \prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.756
6040	637	\begin{align*} x_{1}^{\prime }&=4 x_{1}+x_{2}+4 x_{3} \\ x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3} \\ x_{3}^{\prime }&=4 x_{1}+x_{2}+4 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.757
6041	1911	\begin{align*} \left (2 x +3\right ) y^{\prime \prime }+3 y^{\prime }-y x&=0 \\ y \left (-1\right ) &= 2 \\ y^{\prime }\left (-1\right ) &= -3 \\ \end{align*} Series expansion around \(x=-1\).	✓	✓	✓	✓	0.757
6042	3755	\begin{align*} y^{\prime \prime }-y&=2 \tanh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.757
6043	7755	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=8 \\ \end{align*}	✓	✓	✓	✓	0.757
6044	7763	\begin{align*} 2 y^{\prime \prime }-7 y^{\prime }-4 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.757
6045	13156	\(\left [\begin {array}{ccc} 3 & 6 & -2 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.757
6046	18152	\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&={\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	0.757
6047	23010	\begin{align*} 12 x^{\prime \prime }-25 x^{\prime }+12 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.757
6048	23315	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.757
6049	640	\begin{align*} x_{1}^{\prime }&=5 x_{1}+x_{2}+3 x_{3} \\ x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3} \\ x_{3}^{\prime }&=3 x_{1}+x_{2}+5 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.758
6050	1356	\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{4}+2 u&=0 \\ u \left (0\right ) &= 0 \\ u^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.758
6051	2664	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +\left (1+t \right ) y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✗	0.758
6052	7347	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.758
6053	12771	\begin{align*} 4 x^{4} y^{\prime \prime \prime }-4 x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }-1&=0 \\ \end{align*}	✓	✓	✓	✓	0.758
6054	20343	\begin{align*} y^{\prime \prime }-y&=2+5 x \\ \end{align*}	✓	✓	✓	✓	0.758
6055	23325	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.758
6056	1290	\begin{align*} 5 u^{\prime \prime }+2 u^{\prime }+7 u&=0 \\ u \left (0\right ) &= 2 \\ u^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.759
6057	3885	\begin{align*} x_{1}^{\prime }&=2 x_{1} \\ x_{2}^{\prime }&=x_{2}-8 x_{3} \\ x_{3}^{\prime }&=2 x_{2}-7 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.759
6058	7078	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.759
6059	12859	\begin{align*} y^{\prime \prime }+a y^{\prime }+b \,x^{v} y^{n}&=0 \\ \end{align*}	✗	✗	✗	✗	0.759
6060	16184	\begin{align*} y^{\prime }&=3 \sqrt {x +3} \\ \end{align*}	✓	✓	✓	✓	0.759
6061	19033	\begin{align*} x_{1}^{\prime }&=-3 x_{1}-9 x_{2} \\ x_{2}^{\prime }&=x_{1}-3 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 4 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.759
6062	19512	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=64 x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.759
6063	26580	\begin{align*} y^{\prime \prime \prime }-y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.759
6064	1912	\begin{align*} \left (2 x +3\right ) y^{\prime \prime }-3 y^{\prime }-\left (2+x \right ) y&=0 \\ y \left (-2\right ) &= -2 \\ y^{\prime }\left (-2\right ) &= 3 \\ \end{align*} Series expansion around \(x=-2\).	✓	✓	✓	✓	0.760
6065	3513	\begin{align*} \left (-z^{2}+1\right ) y^{\prime \prime }-z y^{\prime }+m^{2} y&=0 \\ \end{align*} Series expansion around \(z=0\).	✓	✓	✓	✓	0.760
6066	3725	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=-10 \sin \left (x \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.760
6067	3753	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right )+4 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.760
6068	7075	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=12 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.760
6069	7077	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.760
6070	9064	\begin{align*} \left (x +1\right ) y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.760
6071	9065	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.760
6072	14377	\begin{align*} x^{\prime }&=4 y \\ y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.760
6073	19892	\begin{align*} {y^{\prime }}^{2}+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.760
6074	20030	\begin{align*} y&=y^{\prime } x -{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.760
6075	23335	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.760
6076	24412	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.760
6077	12732	\begin{align*} x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 y^{\prime } x +2 y-f \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	0.761
6078	16558	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.761
6079	18226	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=\left (1+\sin \left (x \right )\right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.761
6080	364	\begin{align*} y^{\prime \prime }+9 y&=\sin \left (x \right )^{4} \\ \end{align*}	✓	✓	✓	✓	0.762
6081	986	\begin{align*} x_{1}^{\prime }&=3 x_{1}+2 x_{2}+2 x_{3} \\ x_{2}^{\prime }&=-5 x_{1}-4 x_{2}-2 x_{3} \\ x_{3}^{\prime }&=5 x_{1}+5 x_{2}+3 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.763
6082	1937	\begin{align*} \left (x^{2}+4 x +3\right ) y^{\prime \prime }-\left (-x^{2}+4 x +5\right ) y^{\prime }-\left (2+x \right ) y&=0 \\ y \left (-2\right ) &= 2 \\ y^{\prime }\left (-2\right ) &= -1 \\ \end{align*} Series expansion around \(x=-2\).	✓	✓	✓	✓	0.763
6083	2742	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{3} \\ x_{2}^{\prime }&=x_{2}-x_{3} \\ x_{3}^{\prime }&=-2 x_{1}-x_{3} \\ \end{align*}	✓	✓	✓	✓	0.763
6084	3991	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.763
6085	4161	\begin{align*} y^{\prime \prime }+9 y&=8 \sin \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= -1 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.763
6086	4180	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.763
6087	6521	\begin{align*} \left (-y+y^{\prime } x \right )^{2}+x^{2} \left (x -y\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.763
6088	8794	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.763
6089	14088	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.763
6090	14101	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.763
6091	14404	\begin{align*} x^{\prime }&=5 x-4 y \\ y^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.763
6092	15093	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 y&=1 \\ \end{align*}	✓	✓	✓	✗	0.763
6093	15740	\(\left [\begin {array}{cc} -2 & -4 \\ 1 & 3 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.763
6094	17358	\begin{align*} y^{\prime \prime }+y&=2 \cos \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.763
6095	17584	\begin{align*} y^{\prime \prime \prime }+10 y^{\prime \prime }+34 y^{\prime }+40 y&=t \,{\mathrm e}^{-4 t}+2 \,{\mathrm e}^{-3 t} \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.763
6096	18383	\begin{align*} y^{\prime \prime }&=x^{2} y-y^{\prime } \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.763
6097	18785	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.763
6098	19563	\begin{align*} y^{\prime \prime }+y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.763
6099	19656	\begin{align*} x^{\prime }&=4 x-3 y \\ y^{\prime }&=8 x-6 y \\ \end{align*}	✓	✓	✓	✓	0.763
6100	22999	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.763