2.3.72 Problems 7101 to 7200

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

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
7101	2798	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=-2 x-2 y \\ \end{align*}	✓	✓	✓	✓	0.362
7102	3827	\begin{align*} x_{1}^{\prime }&=-2 x_{1}+3 x_{2} \\ x_{2}^{\prime }&=-2 x_{1}+5 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= -2 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.362
7103	5659	\begin{align*} \left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (2 x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.362
7104	6554	\begin{align*} \operatorname {a2} x \left (1-y\right ) y^{2}+\operatorname {a3} \,x^{3} y^{2} \left (1+y\right )+\left (1-y\right )^{3} \left (\operatorname {a0} +\operatorname {a1} y^{2}\right )+2 x \left (1-y\right ) y y^{\prime }-x^{2} \left (1-3 y\right ) {y^{\prime }}^{2}+2 x^{2} \left (1-y\right ) y y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.362
7105	7071	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.362
7106	7346	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=6 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.362
7107	7786	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=64 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.362
7108	8051	\begin{align*} {y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.362
7109	8484	\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.362
7110	8908	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=3 \,{\mathrm e}^{-x}+2 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.362
7111	9266	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.362
7112	9697	\begin{align*} x^{\prime }&=2 x+4 y \\ y^{\prime }&=-x+6 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= -1 \\ y \left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	0.362
7113	9836	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.362
7114	12632	\begin{align*} y^{\prime \prime }&=-\frac {a y}{\left (x^{2}-1\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	0.362
7115	14405	\begin{align*} x^{\prime }&=9 y \\ y^{\prime }&=-x \\ \end{align*}	✓	✓	✓	✓	0.362
7116	14727	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.362
7117	14728	\begin{align*} y^{\prime \prime }+8 y^{\prime } x -4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.362
7118	15246	\begin{align*} y^{\prime \prime }-7 y^{\prime }+6 y&=\delta \left (-1+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.362
7119	16030	\begin{align*} x^{\prime }&=2 x+4 y \\ y^{\prime }&=3 x+6 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.362
7120	17108	\begin{align*} y^{\prime }&=\cos \left (t \right ) \\ y \left (\frac {\pi }{2}\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.362
7121	17397	\begin{align*} y^{\prime \prime }-7 y^{\prime }+12 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.362
7122	17632	\begin{align*} x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+7 y^{\prime \prime } x +y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.362
7123	18111	\begin{align*} y^{\prime \prime \prime }+{y^{\prime \prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.362
7124	18823	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=3 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.362
7125	20047	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.362
7126	23041	\begin{align*} x^{\prime \prime }-9 x^{\prime }-10 x&=\cos \left (4 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.362
7127	25181	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=t^{2} \\ \end{align*}	✓	✓	✓	✓	0.362
7128	7790	\begin{align*} y^{\prime \prime }-5 y&=2 \,{\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	0.363
7129	8863	\begin{align*} y^{\prime }+5 y&=2 \\ \end{align*}	✓	✓	✓	✓	0.363
7130	12542	\begin{align*} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +f \left (x \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	0.363
7131	14216	\begin{align*} Q^{\prime }&=\frac {Q}{4+Q^{2}} \\ \end{align*}	✓	✓	✓	✓	0.363
7132	15500	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.363
7133	16638	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{2 x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.363
7134	16812	\begin{align*} y^{\prime \prime }-16 y&=\delta \left (t -10\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.363
7135	20413	\begin{align*} x^{2}&=a^{2} \left (1+{y^{\prime }}^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.363
7136	21644	\begin{align*} y^{\prime }&=x^{2} \\ y \left (2\right ) &= 1 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	0.363
7137	22921	\begin{align*} 2 x^{\prime }-6 x+3 y^{\prime }-2 y&=0 \\ 7 x^{\prime }+4 x+7 y^{\prime }+20 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.363
7138	23106	\begin{align*} y^{\prime \prime }-\tan \left (x \right ) y^{\prime }-\frac {\tan \left (x \right ) y}{x}&=\frac {y^{3}}{x^{3}} \\ \end{align*}	✗	✗	✗	✗	0.363
7139	23456	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.363
7140	24433	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= {\mathrm e}^{3} \\ \end{align*}	✓	✓	✓	✓	0.363
7141	24725	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.363
7142	24785	\begin{align*} \left (x -y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\ \end{align*}	✓	✓	✓	✓	0.363
7143	1924	\begin{align*} y^{\prime \prime }+5 y^{\prime } x -\left (-x^{2}+3\right ) y&=0 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.364
7144	2585	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=t \,{\mathrm e}^{3 t}+1 \\ \end{align*}	✓	✓	✓	✓	0.364
7145	5727	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{x} \left (x^{2}-1\right ) \\ \end{align*}	✓	✓	✓	✓	0.364
7146	5791	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.364
7147	7758	\begin{align*} y^{\prime \prime }+25 y&=5 x^{2}+x \\ \end{align*}	✓	✓	✓	✓	0.364
7148	8485	\begin{align*} y^{\prime \prime }+2 y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.364
7149	8565	\begin{align*} \left (2+x \right ) y^{\prime \prime }+3 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.364
7150	8852	\begin{align*} x_{1}^{\prime }&=3 x_{1}-x_{2} \\ x_{2}^{\prime }&=4 x_{1}-2 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.364
7151	9340	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=x^{2}+2 x +2 \\ \end{align*}	✓	✓	✓	✓	0.364
7152	9475	\begin{align*} x^{\prime }&=5 x+3 y \\ y^{\prime }&=-6 x-4 y \\ \end{align*}	✓	✓	✓	✓	0.364
7153	14055	\begin{align*} {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.364
7154	14283	\begin{align*} x^{\prime \prime }-4 x^{\prime }+4 x&=0 \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.364
7155	14332	\begin{align*} x^{\prime \prime }-x&=\frac {1}{t} \\ \end{align*}	✓	✓	✓	✓	0.364
7156	16849	\begin{align*} \sin \left (x \right ) y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=\frac {\pi }{2}\).	✓	✓	✓	✓	0.364
7157	17438	\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=32 t \\ \end{align*}	✓	✓	✓	✓	0.364
7158	17828	\begin{align*} x^{\prime }&=8 x-y \\ y^{\prime }&=x+6 y \\ \end{align*}	✓	✓	✓	✓	0.364
7159	17833	\begin{align*} x^{\prime \prime }-3 x^{\prime }+4 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.364
7160	18308	\begin{align*} \left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.364
7161	22057	\begin{align*} y^{\prime }-3 y&=6 \\ \end{align*}	✓	✓	✓	✓	0.364
7162	22142	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.364
7163	22887	\begin{align*} y^{\prime }+6 y&=x^{\prime } \\ 3 x-x^{\prime }&=2 y^{\prime } \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.364
7164	23457	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.364
7165	23477	\begin{align*} y^{\prime \prime }+y&=x +2 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.364
7166	23490	\begin{align*} 4 y+y^{\prime \prime }&=4 x^{3}-8 x^{2}-14 x +7 \\ \end{align*}	✓	✓	✓	✓	0.364
7167	23701	\begin{align*} y^{\prime \prime } x -2 \left (x +1\right ) y^{\prime }+2 y&=0 \\ y \left (3\right ) &= 2 \\ y^{\prime }\left (3\right ) &= 0 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	0.364
7168	24628	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=4 x -6 \,{\mathrm e}^{-2 x}+3 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.364
7169	24737	\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=\frac {6}{1+{\mathrm e}^{-2 x}} \\ \end{align*}	✓	✓	✓	✗	0.364
7170	25136	\begin{align*} y^{\prime \prime }+3 y^{\prime }-10 y&=\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.364
7171	25307	\begin{align*} y^{\prime }-3 y&=3+\delta \left (t -2\right ) \\ y \left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.364
7172	25565	\begin{align*} y^{\prime \prime }+b y^{\prime }+c y&=f \\ \end{align*}	✓	✓	✓	✓	0.364
7173	601	\begin{align*} x^{\prime }&=-3 y \\ y^{\prime }&=3 x \\ \end{align*}	✓	✓	✓	✓	0.365
7174	612	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }&=-3 x_{1}+4 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.365
7175	922	\begin{align*} x^{\prime }&=-3 y \\ y^{\prime }&=3 x \\ \end{align*}	✓	✓	✓	✓	0.365
7176	1519	\begin{align*} y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.365
7177	2259	\begin{align*} y_{1}^{\prime }&=-13 y_{1}+16 y_{2} \\ y_{2}^{\prime }&=-9 y_{1}+11 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.365
7178	2596	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=t^{2}+t +1 \\ \end{align*}	✓	✓	✓	✓	0.365
7179	2598	\begin{align*} y^{\prime \prime }+5 y^{\prime }+4 y&=t^{2} {\mathrm e}^{7 t} \\ \end{align*}	✓	✓	✓	✓	0.365
7180	6432	\begin{align*} y y^{\prime \prime }&=-y^{2} x^{2}+\ln \left (y\right ) y^{2}+{y^{\prime }}^{2} \\ \end{align*}	✗	✓	✓	✗	0.365
7181	6491	\begin{align*} 5 y y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.365
7182	7600	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	0.365
7183	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*}	✓	✓	✓	✓	0.365
7184	8941	\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.365
7185	10015	\begin{align*} y&=x {y^{\prime }}^{2}+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.365
7186	10419	\begin{align*} y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (3+y^{2}\right ) {y^{\prime }}^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	0.365
7187	10741	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {25}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.365
7188	13156	\(\left [\begin {array}{ccc} 3 & 6 & -2 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.365
7189	14047	\begin{align*} \left (2 y^{\prime } x -y\right )^{2}&=8 x^{3} \\ \end{align*}	✓	✓	✓	✓	0.365
7190	15468	\begin{align*} x^{\prime }&=4 x-2 y \\ y^{\prime }&=3 x-y \\ \end{align*}	✓	✓	✓	✓	0.365
7191	15574	\begin{align*} y^{\prime }&=\frac {1}{x -1} \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.365
7192	16126	\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&={\mathrm e}^{-t} \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.365
7193	16740	\begin{align*} y^{\prime \prime }-9 y^{\prime }+14 y&=576 x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.365
7194	18020	\begin{align*} x&=\frac {y}{y^{\prime }}+\frac {1}{{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	0.365
7195	21210	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.365
7196	25138	\begin{align*} y^{\prime \prime }-5 y^{\prime }-6 y&=10 t \,{\mathrm e}^{4 t} \\ \end{align*}	✓	✓	✓	✓	0.365
7197	25374	\begin{align*} y_{1}^{\prime }&=3 y_{1}-4 y_{2} \\ y_{2}^{\prime }&=y_{1}-y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.365
7198	225	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.366
7199	1790	\begin{align*} \left (x^{2}-4\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=2+x \\ y \left (0\right ) &= -{\frac {1}{3}} \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	0.366
7200	4534	\begin{align*} x^{\prime }-x+3 y&=0 \\ 3 x-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.366