2.3.62 Problems 6101 to 6200

Table 2.667: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
6101	23419	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.395
6102	23973	\begin{align*} y^{\prime \prime }-5 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.395
6103	23999	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=x^{4} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.395
6104	1403	\begin{align*} x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.396
6105	6432	\begin{align*} y y^{\prime \prime }&=-y^{2} x^{2}+\ln \left (y\right ) y^{2}+{y^{\prime }}^{2} \\ \end{align*}	✗	✓	✓	✗	0.396
6106	7140	\begin{align*} y y^{\prime }-2 x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.396
6107	7883	\begin{align*} x +\cos \left (x \right ) y+\sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.396
6108	9497	\begin{align*} y^{\prime \prime }-y^{\prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.396
6109	17833	\begin{align*} x^{\prime \prime }-3 x^{\prime }+4 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.396
6110	19567	\begin{align*} 12 y-7 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{2 x} \left (x^{3}-5 x^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.396
6111	19782	\begin{align*} y^{\prime \prime \prime } y^{\prime }-3 {y^{\prime \prime }}^{2}+3 y^{\prime \prime } {y^{\prime }}^{2}-2 {y^{\prime }}^{4}-x {y^{\prime }}^{5}&=0 \\ \end{align*}	✗	✓	✗	✗	0.396
6112	20143	\begin{align*} y^{\prime \prime } x +y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.396
6113	20365	\begin{align*} y^{\prime \prime }+4 y^{\prime }-12 y&=\left (x -1\right ) {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.396
6114	20519	\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 y^{\prime } x +2 y&=x^{2}+3 x -4 \\ \end{align*}	✓	✓	✓	✓	0.396
6115	22131	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.396
6116	24536	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.396
6117	25549	\begin{align*} y^{\prime \prime }+y&=10 \,{\mathrm e}^{-3 t} \\ \end{align*}	✓	✓	✓	✓	0.396
6118	25641	\begin{align*} y^{\prime \prime }+B y^{\prime }+C y&=\delta \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.396
6119	1855	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.397
6120	6285	\begin{align*} a y-x^{5} y^{\prime }+x^{6} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.397
6121	7233	\begin{align*} \cos \left (x \right ) y^{\prime }+y&=\cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.397
6122	7995	\begin{align*} y^{\prime \prime }-y&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.397
6123	8005	\begin{align*} y^{\prime \prime }-y&=\sin \left (2 x \right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.397
6124	9351	\begin{align*} y^{\prime }-y&=2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.397
6125	10074	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.397
6126	14576	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.397
6127	16786	\begin{align*} y^{\prime \prime }+4 y&=\sin \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.397
6128	18113	\begin{align*} y^{\prime \prime }&=2 y y^{\prime } \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	0.397
6129	21230	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=2 y+z \\ z^{\prime }&=x+z \\ \end{align*}	✓	✓	✓	✓	0.397
6130	22262	\begin{align*} w^{\prime }-w-2 y&=1 \\ y^{\prime }-4 w-3 y&=-1 \\ \end{align*} With initial conditions \begin{align*} y \left (0\right ) &= 2 \\ w \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.397
6131	24459	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.397
6132	24596	\begin{align*} y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.397
6133	25368	\begin{align*} y_{1}^{\prime }&=-y_{1} \\ y_{2}^{\prime }&=3 y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.397
6134	25514	\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.397
6135	869	\begin{align*} y^{\prime \prime }+16 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.398
6136	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*}	✓	✓	✓	✓	0.398
6137	1380	\begin{align*} \left (-x^{2}+4\right ) y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.398
6138	1527	\begin{align*} y^{\prime }&=-x \,{\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.398
6139	2226	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=12 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.398
6140	2551	\begin{align*} y^{\prime \prime }-6 y^{\prime }+y&=0 \\ y \left (2\right ) &= 1 \\ y^{\prime }\left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.398
6141	4087	\begin{align*} \left (-y^{\prime } x +y\right )^{2}&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.398
6142	6100	\begin{align*} x \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.398
6143	8944	\begin{align*} y^{\prime \prime }+9 y&=x^{2} {\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.398
6144	9349	\begin{align*} y^{\prime }+y&=1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.398
6145	13162	\(\left [\begin {array}{cccc} 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 2 & 0 \\ 0 & 0 & 0 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.398
6146	13197	\(\left [\begin {array}{cccc} 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.398
6147	14950	\begin{align*} x^{\prime \prime \prime \prime }-5 x^{\prime \prime }+4 x&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.398
6148	15092	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=x \,{\mathrm e}^{x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.398
6149	15178	\begin{align*} y^{\prime \prime }+\frac {2 x y^{\prime }}{2 x -1}-\frac {4 x y}{\left (2 x -1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.398
6150	16111	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=5 \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.398
6151	16618	\begin{align*} y^{\prime \prime }+9 y&=9 x^{4}-9 \\ \end{align*}	✓	✓	✓	✓	0.398
6152	17226	\begin{align*} 2 t y^{2}+2 t^{2} y y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.398
6153	18027	\begin{align*} {y^{\prime }}^{3}-4 y y^{\prime } x +8 y^{2}&=0 \\ \end{align*}	✓	✓	✗	✗	0.398
6154	21773	\begin{align*} x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✓	0.398
6155	23357	\begin{align*} y^{\prime \prime }+9 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.398
6156	25973	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{3 x} \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.398
6157	2611	\begin{align*} y^{\prime \prime }-t y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.399
6158	3990	\begin{align*} y^{\prime \prime }+y^{\prime } x +3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.399
6159	14629	\begin{align*} 4 y^{\prime \prime \prime }-4 y^{\prime \prime }-5 y^{\prime }+3 y&=3 x^{3}-8 x \\ \end{align*}	✓	✓	✓	✓	0.399
6160	16170	\begin{align*} 1&=x^{2}-9 y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.399
6161	16336	\begin{align*} x^{2} y^{\prime }-\sqrt {x}&=3 \\ \end{align*}	✓	✓	✓	✓	0.399
6162	20387	\begin{align*} y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✓	0.399
6163	23387	\begin{align*} 3 x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+4 y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.399
6164	25647	\begin{align*} y^{\prime }&=2 \,{\mathrm e}^{2 t}-4 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.399
6165	1365	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.400
6166	3144	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.400
6167	3176	\begin{align*} y^{\prime \prime }+2 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.400
6168	6866	\begin{align*} 2 y x +\left (y^{2}-3 x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.400
6169	6932	\begin{align*} 4 x^{3}-\sin \left (x \right )+y^{3}-\left (y^{2}+1-3 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.400
6170	7089	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.400
6171	9493	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.400
6172	9599	\begin{align*} -y+y^{\prime }&=1 \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.400
6173	12842	\begin{align*} y^{\prime \prime }-2 a^{2} y^{3}+2 a b x y-b&=0 \\ \end{align*}	✗	✗	✗	✗	0.400
6174	16846	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.400
6175	17436	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=-1 \\ \end{align*}	✓	✓	✓	✓	0.400
6176	17763	\begin{align*} y^{\prime \prime }+10 y^{\prime }+16 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.400
6177	19755	\begin{align*} v^{\prime \prime }-6 v^{\prime }+13 v&={\mathrm e}^{-2 u} \\ \end{align*}	✓	✓	✓	✓	0.400
6178	20361	\begin{align*} y^{\prime \prime }-2 y^{\prime }+4 y&={\mathrm e}^{x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.400
6179	21023	\begin{align*} x^{\prime }+k x&=1 \\ \end{align*}	✓	✓	✓	✓	0.400
6180	23417	\begin{align*} y^{\prime \prime }-\left (1+\frac {3}{2 x}\right ) y^{\prime }+\frac {3 y}{2 x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.400
6181	24690	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.400
6182	24890	\begin{align*} y^{\prime \prime }&={\mathrm e}^{x} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.400
6183	233	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.401
6184	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*}	✓	✓	✓	✓	0.401
6185	3496	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=2 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.401
6186	5477	\begin{align*} x {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.401
6187	5895	\begin{align*} y^{\prime \prime } x +2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.401
6188	8578	\begin{align*} \left (x -2\right ) y^{\prime }&=y x \\ y \left (0\right ) &= 4 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.401
6189	11610	\begin{align*} \left (2 x y^{3}+y\right ) y^{\prime }+2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.401
6190	12421	\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{k}-b \left (b -1\right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.401
6191	12997	\begin{align*} \left (1+y^{2}\right ) y^{\prime \prime }-3 y {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.401
6192	16507	\begin{align*} y^{\prime \prime }-8 y^{\prime }+16 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.401
6193	17806	\begin{align*} x^{\prime \prime }+4 x^{\prime }+3 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	0.401
6194	19248	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=\arctan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.401
6195	23324	\begin{align*} 2 y^{\prime \prime }+14 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.401
6196	24933	\begin{align*} y^{\prime }&=t \,{\mathrm e}^{-t} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.401
6197	25984	\begin{align*} y^{\prime \prime }+y&=\csc \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.401
6198	148	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.402
6199	257	\begin{align*} y^{\prime \prime }+y&=3 x \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.402
6200	2596	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=t^{2}+t +1 \\ \end{align*}	✓	✓	✓	✓	0.402