2.3.71 Problems 7001 to 7100

Table 2.691: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
7001	22222	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.526
7002	22703	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=x +\sin \left (x \right )+\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.526
7003	22883	\begin{align*} u^{\prime }&=2 v-1 \\ v^{\prime }&=1+2 u \\ \end{align*}	✓	✓	✓	✓	0.526
7004	23715	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +9 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.526
7005	24778	\begin{align*} x {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.526
7006	1432	\begin{align*} x_{1}^{\prime }&=4 x_{1}-2 x_{2}+\frac {1}{t^{3}} \\ x_{2}^{\prime }&=8 x_{1}-4 x_{2}-\frac {1}{t^{2}} \\ \end{align*}	✓	✓	✓	✓	0.527
7007	1874	\begin{align*} \left (3 x^{2}-6 x +5\right ) y^{\prime \prime }+\left (x -1\right ) y^{\prime }+12 y&=0 \\ y \left (1\right ) &= -1 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.527
7008	2388	\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.527
7009	2390	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \\ y \left (2\right ) &= 1 \\ y^{\prime }\left (2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.527
7010	2620	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-y^{\prime } t +\alpha ^{2} y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.527
7011	2832	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2} \\ x_{2}^{\prime }&=-5 x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.527
7012	3415	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.527
7013	5872	\begin{align*} -\left (a^{2}+1\right ) y-2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.527
7014	5997	\begin{align*} \left (a^{2} x^{2}+2\right ) y-2 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.527
7015	6162	\begin{align*} -\left (-4 x^{2}+4 x +1\right ) y+4 x \left (1-2 x \right ) y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.527
7016	6438	\begin{align*} a x y^{\prime }+{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.527
7017	6539	\begin{align*} 2 y^{\prime }+2 y {y^{\prime }}^{2}+\left (x +y^{2}\right ) y^{\prime \prime }&=a \\ \end{align*}	✓	✓	✓	✗	0.527
7018	7950	\begin{align*} x {y^{\prime }}^{5}-y {y^{\prime }}^{4}+\left (x^{2}+1\right ) {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+\left (x +y^{2}\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.527
7019	7995	\begin{align*} y^{\prime \prime }-y&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.527
7020	8578	\begin{align*} \left (x -2\right ) y^{\prime }&=y x \\ y \left (0\right ) &= 4 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.527
7021	9233	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.527
7022	10290	\begin{align*} 5 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.527
7023	12843	\begin{align*} y^{\prime \prime }+d +b x y+c y+a y^{3}&=0 \\ \end{align*}	✗	✗	✗	✗	0.527
7024	14857	\begin{align*} x^{\prime }&=2 x-4 y \\ y^{\prime }&=2 x-2 y \\ \end{align*}	✓	✓	✓	✓	0.527
7025	16039	\begin{align*} x^{\prime }&=-2 x+3 y \\ y^{\prime }&=3 x-2 y \\ z^{\prime }&=-z \\ \end{align*}	✓	✓	✓	✓	0.527
7026	17755	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=3 \,{\mathrm e}^{-2 t} \\ \end{align*}	✓	✓	✓	✓	0.527
7027	19179	\begin{align*} \left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.527
7028	19559	\begin{align*} 4 y^{\prime \prime }+y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.527
7029	20116	\begin{align*} x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.527
7030	21082	\begin{align*} y^{2}+\left (y x +3 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.527
7031	25588	\begin{align*} y^{\prime \prime }-y&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.527
7032	25589	\begin{align*} y^{\prime \prime }+y&=\cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.527
7033	26118	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }&=1+x \,{\mathrm e}^{x}+2 \cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	0.527
7034	1896	\begin{align*} \left (x^{2}+3 x +3\right ) y^{\prime \prime }+\left (6+4 x \right ) y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.528
7035	3273	\begin{align*} y^{\prime \prime }&=y^{3} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= \frac {\sqrt {2}}{2} \\ \end{align*}	✓	✓	✓	✗	0.528
7036	6644	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y&=\cosh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.528
7037	8038	\begin{align*} x^{2} y^{\prime \prime }+\left (-4 x^{2}+x \right ) y^{\prime }+\left (4 x^{2}-2 x +1\right ) y&=\left (x^{2}-x +1\right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	0.528
7038	10231	\begin{align*} y^{\prime \prime }&=\left (x^{2}+3\right ) y \\ \end{align*}	✓	✓	✓	✗	0.528
7039	15432	\begin{align*} y^{\prime \prime }+6 y^{\prime }+5 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.528
7040	17483	\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&={\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	0.528
7041	19764	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.528
7042	2037	\begin{align*} 4 x^{2} \left (4 x^{2}+1\right ) y^{\prime \prime }+32 x^{3} y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.529
7043	3987	\begin{align*} y^{\prime \prime }-2 y^{\prime } x -2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.529
7044	10347	\begin{align*} y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.529
7045	14070	\begin{align*} y y^{\prime }&=\left (x -b \right ) {y^{\prime }}^{2}+a \\ \end{align*}	✓	✓	✓	✗	0.529
7046	14106	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.529
7047	14374	\begin{align*} x^{\prime }&=-3 y \\ y^{\prime }&=2 x \\ \end{align*}	✓	✓	✓	✓	0.529
7048	17398	\begin{align*} 2 y^{\prime \prime }-7 y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.529
7049	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*}	✓	✓	✓	✓	0.529
7050	18984	\begin{align*} x y^{\prime \prime \prime }-y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.529
7051	20360	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{2 x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.529
7052	20922	\begin{align*} x^{\prime }&=-4 x-y+{\mathrm e}^{-t} \\ y^{\prime }&=x-2 y+2 \,{\mathrm e}^{-3 t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.529
7053	21224	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=-y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= -1 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.529
7054	21911	\begin{align*} y^{\prime \prime }-4 y&=0 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.529
7055	22283	\begin{align*} y^{\prime \prime }+y&=x \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.529
7056	23758	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.529
7057	23846	\begin{align*} y^{\prime \prime } x -2 \left (x +1\right ) y^{\prime }+\left (2+x \right ) y&=1 \\ \end{align*}	✓	✓	✓	✗	0.529
7058	24601	\begin{align*} 4 y^{\prime \prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.529
7059	25282	\begin{align*} y^{\prime \prime }-a^{2} y&=f \left (t \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.529
7060	1410	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }&=-x_{1}-x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.530
7061	2781	\begin{align*} x_{1}^{\prime }&=2 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=4 x_{1}-2 x_{2}+\delta \left (t -\pi \right ) \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.530
7062	4174	\begin{align*} y_{1}^{\prime }&=1 \\ y_{2}^{\prime }&=2 y_{1} \\ \end{align*}	✓	✓	✓	✓	0.530
7063	5478	\begin{align*} x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.530
7064	9319	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.530
7065	14303	\begin{align*} x^{\prime \prime }+x^{\prime }+x&=4 t +5 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.530
7066	14990	\begin{align*} x^{\prime }&=8 x+14 y \\ y^{\prime }&=7 x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.530
7067	15482	\begin{align*} x^{\prime }&=x-5 y \\ y^{\prime }&=x-y \\ \end{align*}	✓	✓	✓	✓	0.530
7068	16510	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.530
7069	17900	\begin{align*} {\mathrm e}^{y^{\prime }}&=x \\ \end{align*}	✓	✓	✓	✓	0.530
7070	21771	\begin{align*} y^{\prime } \left (y^{\prime }+y\right )&=x \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✗	0.530
7071	21772	\begin{align*} x^{2} {y^{\prime }}^{2}+4 y y^{\prime } x +3 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.530
7072	25647	\begin{align*} y^{\prime }&=2 \,{\mathrm e}^{2 t}-4 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.530
7073	26131	\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=3 x-4 y \\ \end{align*}	✓	✓	✓	✓	0.530
7074	1344	\begin{align*} y^{\prime \prime }+4 y&=g \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.531
7075	1907	\begin{align*} \left (2 x +1\right ) y^{\prime \prime }-\left (1-2 x \right ) y^{\prime }-\left (3-2 x \right ) y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= -2 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.531
7076	2035	\begin{align*} 4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.531
7077	2043	\begin{align*} x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (-x^{2}+14\right ) y^{\prime }+2 \left (x^{2}+9\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.531
7078	2238	\begin{align*} y_{1}^{\prime }&=y_{1}+2 y_{2} \\ y_{2}^{\prime }&=2 y_{1}+y_{2} \\ \end{align*}	✓	✓	✓	✓	0.531
7079	2833	\begin{align*} x_{1}^{\prime }&=4 x_{2} \\ x_{2}^{\prime }&=-9 x_{1} \\ \end{align*}	✓	✓	✓	✓	0.531
7080	3420	\begin{align*} y^{\prime }&=\sin \left (t \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.531
7081	5617	\begin{align*} {y^{\prime }}^{3}-7 y^{\prime }+6&=0 \\ \end{align*}	✓	✓	✓	✓	0.531
7082	8055	\begin{align*} \left (2 x^{3}-1\right ) y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+6 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.531
7083	10289	\begin{align*} y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.531
7084	16861	\begin{align*} \left (x^{2}-4\right ) y^{\prime \prime }+\left (x^{2}+x -6\right ) y&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	0.531
7085	17617	\begin{align*} 4 x^{2} y^{\prime \prime }+17 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.531
7086	17789	\begin{align*} \left (2 x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x -3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.531
7087	18906	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=18 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.531
7088	19552	\begin{align*} y^{\prime \prime }-y&=x^{2} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.531
7089	24097	\begin{align*} y^{\prime } x +\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.531
7090	25093	\begin{align*} y^{\prime \prime }+8 y&=t \\ \end{align*}	✓	✓	✓	✓	0.531
7091	25592	\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{2 t} t \\ \end{align*}	✓	✓	✓	✓	0.531
7092	25978	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=72 x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.531
7093	1640	\begin{align*} x^{2} y^{\prime }+2 y x&=y^{3} \\ y \left (1\right ) &= \frac {\sqrt {2}}{2} \\ \end{align*}	✓	✓	✓	✓	0.532
7094	2389	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.532
7095	8841	\begin{align*} x_{1}^{\prime }&=3 x_{1}-18 x_{2} \\ x_{2}^{\prime }&=2 x_{1}-9 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.532
7096	13059	\begin{align*} x^{\prime }&=a x \\ y^{\prime }&=b \\ \end{align*}	✓	✓	✓	✓	0.532
7097	13903	\begin{align*} x^{n} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }-a y&=0 \\ \end{align*}	✓	✓	✗	✗	0.532
7098	16927	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.532
7099	18429	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=-x+y \\ \end{align*}	✓	✓	✓	✓	0.532
7100	20082	\begin{align*} y^{\prime \prime }-2 y^{\prime }+4 y&={\mathrm e}^{x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.532