2.3.61 Problems 6001 to 6100

Table 2.671: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
6001	21867	\begin{align*} y y^{\prime }&=-x {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.464
6002	22131	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.464
6003	22648	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.464
6004	24116	\begin{align*} y^{\prime }&=x +2 y \\ y \left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.464
6005	24706	\begin{align*} y^{\prime \prime \prime \prime }-y&=x^{6} \\ \end{align*}	✓	✓	✓	✓	0.464
6006	25334	\begin{align*} y^{\prime \prime }+\frac {t y^{\prime }}{-t^{2}+1}+\frac {y}{1+t}&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.464
6007	25687	\begin{align*} x^{\prime }&=x+3 y \\ y^{\prime }&=5 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.464
6008	26374	\begin{align*} x {y^{\prime }}^{2}-y y^{\prime }-y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✗	0.464
6009	913	\begin{align*} x^{\prime \prime }+4 x^{\prime }+4 x&=10 \cos \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.465
6010	1854	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +6 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.465
6011	2368	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-10 y&=0 \\ y \left (1\right ) &= 5 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.465
6012	3199	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&=x^{3}-\frac {\cos \left (2 x \right )}{2} \\ \end{align*}	✓	✓	✓	✓	0.465
6013	3947	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=10 \cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.465
6014	4492	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime }-4 y&=50 \,{\mathrm e}^{2 x}+50 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.465
6015	6013	\begin{align*} \left (-x^{2}+2\right ) y+4 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.465
6016	6779	\begin{align*} \operatorname {A4} y+\operatorname {A3} x y^{\prime }+\operatorname {A2} \,x^{2} y^{\prime \prime }+\operatorname {A1} \,x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.465
6017	8912	\begin{align*} 4 y^{\prime \prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.465
6018	9178	\begin{align*} x^{3}+x y^{3}+3 y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.465
6019	9317	\begin{align*} y^{\prime \prime }-y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.465
6020	9454	\begin{align*} y^{\prime \prime }+y^{\prime }+2 y&=t \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.465
6021	22729	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.465
6022	344	\begin{align*} 4 y+y^{\prime \prime }&=3 x \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.466
6023	875	\begin{align*} y^{\prime \prime }-4 y&=\sinh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.466
6024	3952	\begin{align*} y^{\prime \prime }+y&=6 \cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.466
6025	6410	\begin{align*} y^{b}+x^{a} y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.466
6026	7912	\begin{align*} 3 y^{2} x^{2}+4 \left (x^{3} y-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.466
6027	8192	\begin{align*} y^{\prime \prime }+4 y^{\prime }+6 y&=10 \\ \end{align*}	✓	✓	✓	✓	0.466
6028	8487	\begin{align*} \left (2+x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.466
6029	8843	\begin{align*} x_{1}^{\prime }&=-x_{1}+3 x_{2} \\ x_{2}^{\prime }&=-3 x_{1}+5 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.466
6030	8845	\begin{align*} x_{1}^{\prime }&=-2 x_{1}+x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.466
6031	9611	\begin{align*} y^{\prime }+4 y&={\mathrm e}^{-4 t} \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.466
6032	12955	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+\left (a y+b x \right ) y^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	0.466
6033	14656	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y&=3 x \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}-\sin \left (x \right ) \\ y \left (0\right ) &= {\frac {33}{40}} \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.466
6034	14978	\begin{align*} y^{\prime \prime }-2 y^{\prime } x -4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.466
6035	15970	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=x-y \\ \end{align*}	✓	✓	✓	✓	0.466
6036	16522	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.466
6037	16845	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +\lambda y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.466
6038	18899	\begin{align*} y^{\prime \prime }-8 y^{\prime }+25 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.466
6039	21536	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=3 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{-x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✓	0.466
6040	25159	\begin{align*} y^{\prime \prime \prime \prime }-y&={\mathrm e}^{t}+{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.466
6041	883	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=x \,{\mathrm e}^{3 x} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.467
6042	919	\begin{align*} x^{\prime \prime }+6 x^{\prime }+13 x&=10 \sin \left (5 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.467
6043	2029	\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.467
6044	2297	\begin{align*} y+y^{\prime }&=\frac {1}{t^{2}+1} \\ y \left (2\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.467
6045	4128	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=1 \\ \end{align*}	✓	✓	✓	✓	0.467
6046	11266	\begin{align*} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.467
6047	14729	\begin{align*} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.467
6048	14861	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=3 x-y \\ \end{align*}	✓	✓	✓	✓	0.467
6049	16183	\begin{align*} y^{\prime }&=\sin \left (\frac {x}{2}\right ) \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.467
6050	16638	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{2 x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.467
6051	18758	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.467
6052	19642	\begin{align*} x^{\prime }&=-3 x+4 y \\ y^{\prime }&=-2 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.467
6053	20508	\begin{align*} -8 y+7 y^{\prime } x -3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x^{2}+\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.467
6054	23066	\begin{align*} y^{\prime \prime }-y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.467
6055	23483	\begin{align*} y^{\prime \prime }+y&=x +{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.467
6056	23494	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\cos \left (x \right ) {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.467
6057	23504	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.467
6058	23579	\begin{align*} x_{1}^{\prime }&=4 x_{1}-x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.467
6059	24021	\begin{align*} y^{\prime \prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.467
6060	24115	\begin{align*} y^{\prime }&=2 y \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.467
6061	25995	\begin{align*} -y+y^{\prime }&={\mathrm e}^{3 t} \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.467
6062	26581	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=\cos \left (x \right ) {\mathrm e}^{-x}+x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.467
6063	925	\begin{align*} x^{\prime }&=y+z \\ y^{\prime }&=x+z \\ z^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.468
6064	1932	\begin{align*} y^{\prime \prime }+\left (x^{2}+2 x +1\right ) y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.468
6065	3686	\begin{align*} 2 x \,{\mathrm e}^{y}+\left (3 y^{2}+x^{2} {\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.468
6066	3948	\begin{align*} y^{\prime \prime }+5 y^{\prime }+4 y&=20 \sin \left (2 t \right ) \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.468
6067	6155	\begin{align*} \left (4 a^{2} x^{2}+1\right ) y+4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.468
6068	16648	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{-7 x}+2 \,{\mathrm e}^{-7 x} \\ \end{align*}	✓	✓	✓	✓	0.468
6069	17025	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.468
6070	18317	\begin{align*} y^{\prime \prime }+y^{\prime }+y \,{\mathrm e}^{-2 x}&={\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✗	0.468
6071	18374	\begin{align*} y^{\prime \prime }+y x&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.468
6072	18385	\begin{align*} y^{\prime }&={\mathrm e}^{y}+y x \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✗	✓	0.468
6073	23656	\begin{align*} y^{\prime \prime \prime }-y&=12 \sinh \left (t \right ) \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= 7 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.468
6074	25617	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.468
6075	483	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+9 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.469
6076	1895	\begin{align*} \left (2+x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.469
6077	2727	\begin{align*} x_{1}^{\prime }&=6 x_{1}-3 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.469
6078	3338	\begin{align*} y^{\prime }&=\ln \left (y x \right ) \\ y \left (1\right ) &= 1 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.469
6079	3417	\begin{align*} y^{\prime }&=t^{2}+3 \\ \end{align*}	✓	✓	✓	✓	0.469
6080	3951	\begin{align*} y^{\prime \prime }+4 y&=9 \sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.469
6081	6187	\begin{align*} x^{3} y^{\prime \prime }&=b x +a \\ \end{align*}	✓	✓	✓	✓	0.469
6082	8570	\begin{align*} y x -y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.469
6083	8795	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=1+3 x \\ \end{align*}	✓	✓	✓	✓	0.469
6084	9231	\begin{align*} y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*}	✓	✓	✓	✓	0.469
6085	9501	\begin{align*} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.469
6086	11184	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.469
6087	14792	\begin{align*} x^{\prime }&=5 x-y \\ y^{\prime }&=3 x+y \\ \end{align*}	✓	✓	✓	✓	0.469
6088	16159	\begin{align*} y^{2} y^{\prime \prime }&=8 x^{2} \\ \end{align*}	✗	✗	✗	✗	0.469
6089	16831	\begin{align*} \left (x +1\right ) y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.469
6090	17226	\begin{align*} 2 t y^{2}+2 t^{2} y y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.469
6091	18759	\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.469
6092	19578	\begin{align*} y^{\prime }&=2 y x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.469
6093	23072	\begin{align*} y^{\prime \prime }-7 y^{\prime }+2 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.469
6094	26360	\begin{align*} \left (1+{y^{\prime }}^{2}\right ) x&=1 \\ \end{align*}	✓	✓	✓	✓	0.469
6095	1860	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-5 y^{\prime } x -4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.470
6096	2030	\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*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.470
6097	7884	\begin{align*} 2 x +3 y+4+\left (3 x +4 y+5\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.470
6098	9447	\begin{align*} L i^{\prime }+R i&=E_{0} \sin \left (\omega t \right ) \\ i \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.470
6099	12511	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+2 a x y^{\prime }+a \left (-1+a \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.470
6100	14383	\begin{align*} x^{\prime }&=-3 y \\ y^{\prime }&=-2 x+y \\ \end{align*}	✓	✓	✓	✓	0.470