2.3.72 Problems 7101 to 7200

Table 2.687: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
7101	6438	\begin{align*} a x y^{\prime }+{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.457
7102	7364	\begin{align*} y^{\prime } x&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.457
7103	12955	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+\left (a y+b x \right ) y^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	0.457
7104	15983	\begin{align*} x^{\prime }&=2 x+3 y \\ y^{\prime }&=x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.457
7105	16118	\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&=-3 \sin \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.457
7106	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.	✓	✓	✓	✓	0.457
7107	16953	\begin{align*} x^{\prime }&=-x+2 y \\ y^{\prime }&=2 x-y \\ \end{align*}	✓	✓	✓	✓	0.457
7108	18668	\begin{align*} x^{\prime }&=x+2 y \\ y^{\prime }&=-5 x-y \\ \end{align*}	✓	✓	✓	✓	0.457
7109	21647	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.457
7110	22783	\begin{align*} x^{2} y^{\prime \prime }-6 y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.457
7111	23825	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-y \\ \end{align*}	✓	✓	✓	✓	0.457
7112	24715	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 x^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.457
7113	25587	\begin{align*} y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{c t} \\ \end{align*}	✓	✓	✓	✓	0.457
7114	26065	\begin{align*} y_{1}^{\prime }&=3 y_{1}+6 y_{2} \\ y_{2}^{\prime }&=2 y_{1}-6 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.457
7115	26243	\begin{align*} {\mathrm e}^{y^{\prime }}&=1 \\ \end{align*}	✓	✓	✓	✓	0.457
7116	482	\begin{align*} 2 y^{\prime \prime } x +\left (-2 x^{2}+1\right ) y^{\prime }-4 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.458
7117	1938	\begin{align*} \left (x^{2}+2 x +1\right ) y^{\prime \prime }+\left (1-x \right ) y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.458
7118	6217	\begin{align*} \left (2 x +1\right ) y-x \left (2 x +1\right ) y^{\prime }+x^{2} \left (x +1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.458
7119	6281	\begin{align*} y+\left (b x +a \right )^{4} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.458
7120	7806	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.458
7121	8847	\begin{align*} x_{1}^{\prime }&=3 x_{1}-x_{2} \\ x_{2}^{\prime }&=16 x_{1}-5 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.458
7122	9320	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.458
7123	12427	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -\left (a +x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.458
7124	22688	\begin{align*} y^{\prime \prime }-4 y&=8 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.458
7125	26026	\begin{align*} y^{\prime \prime } x +\left (x^{3}-1\right ) y^{\prime }+3 x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.458
7126	2677	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{-t} \\ y \left (t_{0} \right ) &= 1 \\ y^{\prime }\left (t_{0} \right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.459
7127	4132	\begin{align*} y^{\prime \prime }+2 y&=x +{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.459
7128	5800	\begin{align*} 12 y-7 y^{\prime }+y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.459
7129	6110	\begin{align*} -2 y-2 \left (2 x +1\right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.459
7130	6950	\begin{align*} y^{2} x^{4}-y+\left (x^{2} y^{4}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.459
7131	7783	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.459
7132	10389	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.459
7133	16152	\begin{align*} y^{\prime }&=3-\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.459
7134	16746	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=10 \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.459
7135	16822	\begin{align*} y^{\prime }+\frac {2 y}{2 x -1}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.459
7136	18448	\begin{align*} x^{\prime }+y^{\prime }+y&={\mathrm e}^{-t} \\ 2 x^{\prime }+y^{\prime }+2 y&=\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.459
7137	20366	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=\cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	0.459
7138	21649	\begin{align*} y^{\prime \prime }-y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.459
7139	22732	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+y&={\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.459
7140	24723	\begin{align*} y^{\prime \prime }+y&=\cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.459
7141	3206	\begin{align*} y^{\prime \prime }-y&=x^{2} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.460
7142	3998	\begin{align*} y^{\prime \prime }+y^{\prime } x +\left (2+x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.460
7143	4518	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=8 \sin \left (t \right ) {\mathrm e}^{-t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.460
7144	8194	\begin{align*} {y^{\prime }}^{2}&=9-y^{2} \\ \end{align*}	✓	✓	✓	✓	0.460
7145	9273	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=2 x \\ \end{align*}	✓	✓	✓	✓	0.460
7146	10384	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	0.460
7147	10385	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=x +1 \\ \end{align*}	✓	✓	✓	✓	0.460
7148	14708	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.460
7149	15180	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x +1}-\frac {\left (2+x \right ) y}{x^{2} \left (x +1\right )}&=0 \\ \end{align*}	✓	✓	✓	✗	0.460
7150	19020	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }&=\frac {x_{1}}{2}-3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.460
7151	19213	\begin{align*} y^{\prime }&=-z \\ z^{\prime }&=y \\ \end{align*} With initial conditions \begin{align*} y \left (0\right ) &= 1 \\ z \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.460
7152	19696	\begin{align*} x^{\prime \prime }-x&=t^{2} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.460
7153	19882	\begin{align*} y^{\prime }+3 y+z&=0 \\ z^{\prime }+3 y+5 z&=0 \\ \end{align*}	✓	✓	✓	✓	0.460
7154	21233	\begin{align*} x^{\prime }&=2 x \\ y^{\prime }&=2 y+z \\ z^{\prime }&=-x-z \\ \end{align*}	✓	✓	✓	✓	0.460
7155	21293	\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=7 x-4 y \\ \end{align*}	✓	✓	✓	✗	0.460
7156	22198	\begin{align*} y^{\prime \prime }-\left (x -1\right ) y^{\prime }&=x^{2}-2 x \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✗	0.460
7157	22917	\begin{align*} x^{\prime }+4 x+3 y^{\prime }+4 y&=0 \\ x^{\prime }+2 x+2 y^{\prime }+2 y&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= -1 \\ y \left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	0.460
7158	23362	\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.460
7159	24761	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\sin \left ({\mathrm e}^{-x}\right ) \\ \end{align*}	✓	✓	✓	✓	0.460
7160	24899	\begin{align*} x^{2} y^{\prime \prime }&=\left (3 x -2 y^{\prime }\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.460
7161	454	\begin{align*} \cos \left (x \right ) y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.461
7162	838	\begin{align*} y^{\prime \prime }+y&=3 x \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.461
7163	3237	\begin{align*} x^{\prime }+5 x&=3 t^{2} \\ y+y^{\prime }&={\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	0.461
7164	3742	\begin{align*} y^{\prime \prime }-2 y^{\prime }+10 y&=24 \,{\mathrm e}^{x} \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.461
7165	4165	\begin{align*} y_{1}^{\prime }&=y_{2} \\ y_{2}^{\prime }&=3 y_{2}-2 y_{1} \\ \end{align*}	✓	✓	✓	✓	0.461
7166	7302	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{x}+6 x -5 \\ \end{align*}	✓	✓	✓	✓	0.461
7167	8496	\begin{align*} y^{\prime \prime }+\sin \left (x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.461
7168	8812	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=50 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.461
7169	9064	\begin{align*} \left (x +1\right ) y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.461
7170	9732	\begin{align*} {y^{\prime }}^{2}-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.461
7171	11714	\begin{align*} \left (x +1\right ) {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.461
7172	17447	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=-78 \cos \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.461
7173	18411	\begin{align*} x^{\prime }&=y+t \\ y^{\prime }&=x-t \\ \end{align*}	✓	✓	✓	✓	0.461
7174	18454	\begin{align*} x^{\prime }&=3 x+y+{\mathrm e}^{t} \\ y^{\prime }&=x+3 y-{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.461
7175	20607	\begin{align*} \left (-x +3\right ) y^{\prime \prime }-\left (9-4 x \right ) y^{\prime }+\left (6-3 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.461
7176	21229	\begin{align*} x^{\prime }&=x+z \\ y^{\prime }&=-y \\ z^{\prime }&=4 z \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ z \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.461
7177	21494	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.461
7178	21547	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.461
7179	22141	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.461
7180	23771	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.461
7181	24095	\begin{align*} x^{2} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.461
7182	24579	\begin{align*} y^{\prime \prime }+9 y&=4 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.461
7183	24662	\begin{align*} 4 y^{\prime \prime }-y&={\mathrm e}^{\frac {x}{2}}+12 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.461
7184	25597	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=t^{2} \\ \end{align*}	✓	✓	✓	✓	0.461
7185	2231	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+3 x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=9 x^{2} \\ y \left (1\right ) &= -7 \\ y^{\prime }\left (1\right ) &= -11 \\ y^{\prime \prime }\left (1\right ) &= -5 \\ y^{\prime \prime \prime }\left (1\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	0.462
7186	2240	\begin{align*} y_{1}^{\prime }&=-\frac {4 y_{1}}{5}+\frac {3 y_{2}}{5} \\ y_{2}^{\prime }&=-\frac {2 y_{1}}{5}-\frac {11 y_{2}}{5} \\ \end{align*}	✓	✓	✓	✓	0.462
7187	6970	\begin{align*} \left (-x^{3}+1\right ) y^{\prime }-2 \left (x +1\right ) y&=y^{{5}/{2}} \\ \end{align*}	✓	✓	✓	✓	0.462
7188	7221	\begin{align*} y y^{\prime } x -y x&=y \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.462
7189	8809	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-4 y&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.462
7190	8842	\begin{align*} x_{1}^{\prime }&=x_{1}+3 x_{2} \\ x_{2}^{\prime }&=5 x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.462
7191	8905	\begin{align*} y^{\prime \prime }+9 y&=\sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.462
7192	9031	\begin{align*} \cos \left (x \right ) \cos \left (y\right )-2 \sin \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.462
7193	17754	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=-4 \,{\mathrm e}^{-2 t} \\ \end{align*}	✓	✓	✓	✓	0.462
7194	19187	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.462
7195	20857	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\cos \left ({\mathrm e}^{x}\right ) \\ \end{align*}	✓	✓	✓	✓	0.462
7196	24708	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=24 \,{\mathrm e}^{2 x} \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.462
7197	25570	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{i \omega t} \\ \end{align*}	✓	✓	✓	✓	0.462
7198	490	\begin{align*} 2 x^{2} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.463
7199	1018	\begin{align*} x_{1}^{\prime }&=-3 x_{1}-4 x_{3} \\ x_{2}^{\prime }&=-x_{1}-x_{2}-x_{3} \\ x_{3}^{\prime }&=x_{1}+x_{3} \\ \end{align*}	✓	✓	✓	✓	0.463
7200	2423	\begin{align*} y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.463