2.3.82 Problems 8101 to 8200

Table 2.737: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
8101	10139	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.597
8102	12964	\begin{align*} 3 y y^{\prime \prime }-2 {y^{\prime }}^{2}-a \,x^{2}-b x -c&=0 \\ \end{align*}	✗	✓	✓	✗	0.597
8103	16087	\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&={\mathrm e}^{-4 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.597
8104	16645	\begin{align*} y^{\prime \prime }+y&=6 \cos \left (2 x \right )-3 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.597
8105	18210	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.597
8106	19210	\begin{align*} y^{\prime }&=y+z \\ z^{\prime }&=y+z+x \\ \end{align*}	✓	✓	✓	✓	0.597
8107	19553	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=10 x^{3} {\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.597
8108	19649	\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=4 x+5 y \\ \end{align*}	✓	✓	✓	✓	0.597
8109	24550	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.597
8110	27097	\(\left [\begin {array}{ccc} 0 & 0 & -1 \\ 0 & 0 & 1 \\ 2 & 0 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.597
8111	2393	\begin{align*} y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.598
8112	3262	\begin{align*} y^{\prime \prime }+2 {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.598
8113	3998	\begin{align*} y^{\prime \prime }+x y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.598
8114	8287	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=6 x +4 \\ y \left (1\right ) &= 4 \\ y^{\prime }\left (1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.598
8115	9499	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.598
8116	15463	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=-x-3 y \\ \end{align*} With initial conditions \begin{align*} x \left (1\right ) &= 0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.598
8117	17402	\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.598
8118	18231	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=4 x -2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.598
8119	19365	\begin{align*} \left (x^{2}+2 y^{\prime }\right ) y^{\prime \prime }+2 x y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.598
8120	21642	\begin{align*} x^{\prime \prime }-s x&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✗	0.598
8121	25546	\begin{align*} y^{\prime \prime }+y&=\delta \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.598
8122	26978	\begin{align*} y^{\prime \prime }+8 y^{\prime }+12 y&={\mathrm e}^{-x}+7 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.598
8123	767	\begin{align*} 3 x^{2} y^{3}+y^{4}+\left (3 x^{3} y^{2}+y^{4}+4 x y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.599
8124	1902	\begin{align*} x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= -2 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.599
8125	2620	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-t y^{\prime }+\alpha ^{2} y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.599
8126	7131	\begin{align*} y y^{\prime \prime }-3 {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.599
8127	7640	\begin{align*} y^{\prime \prime }-x y^{\prime }-3 y&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	0.599
8128	9254	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.599
8129	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.	✓	✓	✓	✓	0.599
8130	13673	\begin{align*} y^{\prime \prime }+a y^{\prime }+\left (b x +c \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.599
8131	15460	\begin{align*} x^{\prime }&=12 x+18 y \\ y^{\prime }&=-8 x-12 y \\ \end{align*}	✓	✓	✓	✓	0.599
8132	17451	\begin{align*} y^{\prime \prime }-7 y^{\prime }+12 y&=-2 t^{3} {\mathrm e}^{4 t} \\ \end{align*}	✓	✓	✓	✓	0.599
8133	18183	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=-2 \\ \end{align*}	✓	✓	✓	✓	0.599
8134	18283	\begin{align*} y^{\prime \prime }-y&=-2 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.599
8135	18885	\begin{align*} 9 y^{\prime \prime }+12 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.599
8136	19516	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.599
8137	21748	\begin{align*} y^{\prime }&=y-3 z \\ z^{\prime }&=2 y-4 z \\ \end{align*}	✓	✓	✓	✓	0.599
8138	24071	\begin{align*} 4 y+y^{\prime \prime }&=x -4 \\ y \left (0\right ) &= {\frac {1}{2}} \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.599
8139	25991	\begin{align*} y^{\prime }&=4 y-z \\ z^{\prime }&=2 y+z \\ \end{align*}	✓	✓	✓	✓	0.599
8140	26960	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.599
8141	17789	\begin{align*} \left (2 x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.600
8142	25598	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=t^{3} \\ \end{align*}	✓	✓	✓	✓	0.600
8143	26033	\begin{align*} x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.600
8144	27095	\(\left [\begin {array}{ccc} -2 & 1 & 0 \\ 1 & 3 & 0 \\ 0 & 0 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.600
8145	27115	\(\left [\begin {array}{ccc} 0 & 0 & 0 \\ 1 & 0 & 2 \\ 0 & 1 & 3 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.600
8146	884	\begin{align*} 4 y+y^{\prime \prime }&=2 x \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.601
8147	1339	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{-2 t}}{t^{2}} \\ \end{align*}	✓	✓	✓	✓	0.601
8148	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*}	✓	✓	✓	✓	0.601
8149	9347	\begin{align*} y^{\prime }&=2 y x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.601
8150	10426	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=x \\ \end{align*}	✓	✓	✓	✗	0.601
8151	10472	\begin{align*} t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.601
8152	14385	\begin{align*} x^{\prime }&=-2 x-y \\ y^{\prime }&=-4 y \\ \end{align*}	✓	✓	✓	✓	0.601
8153	21493	\begin{align*} y^{\prime \prime }-2 y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.601
8154	26044	\begin{align*} y^{\prime \prime }+x y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.601
8155	507	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.602
8156	633	\begin{align*} x_{1}^{\prime }&=5 x_{1}-9 x_{2} \\ x_{2}^{\prime }&=2 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.602
8157	3144	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.602
8158	3263	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.602
8159	3807	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.602
8160	7578	\begin{align*} y^{\prime \prime }+2 y^{\prime }+4 y&=6 \cos \left (2 t \right )+8 \sin \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.602
8161	7622	\begin{align*} \left (x +1\right ) y^{\prime \prime }-x^{2} y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.602
8162	10398	\begin{align*} y^{\prime \prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	0.602
8163	10399	\begin{align*} y^{\prime \prime }+y&=x +1 \\ \end{align*}	✓	✓	✓	✓	0.602
8164	12433	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+\left (a \,x^{m}+b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.602
8165	15417	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.602
8166	16098	\begin{align*} y^{\prime \prime }+2 y&=-{\mathrm e}^{t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.602
8167	16589	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-6 \,{\mathrm e}^{4 x} \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	0.602
8168	17408	\begin{align*} y^{\prime \prime }-y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.602
8169	17430	\begin{align*} y^{\prime \prime }+y&=\cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.602
8170	17855	\begin{align*} y^{\prime }&=\left (-1+y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.602
8171	18653	\begin{align*} x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }&=\frac {3 x}{4}+\frac {5 y}{4} \\ \end{align*}	✓	✓	✓	✓	0.602
8172	19193	\begin{align*} y^{\prime \prime }-y&=\frac {{\mathrm e}^{x}-{\mathrm e}^{-x}}{{\mathrm e}^{x}+{\mathrm e}^{-x}} \\ \end{align*}	✓	✓	✓	✓	0.602
8173	20369	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \sin \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	0.602
8174	21147	\begin{align*} x^{\prime \prime }-3 x^{\prime }+2 x&=3 \,{\mathrm e}^{t} t \\ \end{align*}	✓	✓	✓	✓	0.602
8175	23988	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=1+2 x +3 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.602
8176	24665	\begin{align*} y^{\prime \prime }+16 y&=14 \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.602
8177	25943	\begin{align*} y^{\prime \prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.602
8178	3513	\begin{align*} \left (-z^{2}+1\right ) y^{\prime \prime }-z y^{\prime }+m^{2} y&=0 \\ \end{align*} Series expansion around \(z=0\).	✓	✓	✓	✓	0.603
8179	9477	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=-x+y \\ \end{align*}	✓	✓	✓	✓	0.603
8180	17440	\begin{align*} y^{\prime \prime }+2 y^{\prime }+26 y&=-338 t \\ \end{align*}	✓	✓	✓	✓	0.603
8181	19643	\begin{align*} x^{\prime }&=4 x-2 y \\ y^{\prime }&=5 x+2 y \\ \end{align*}	✓	✓	✓	✓	0.603
8182	20739	\begin{align*} {y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2}&=0 \\ \end{align*}	✓	✓	✗	✗	0.603
8183	25978	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=72 x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.603
8184	26592	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=2 \,{\mathrm e}^{x} x^{2} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.603
8185	3739	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=2 \,{\mathrm e}^{-x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.604
8186	6727	\begin{align*} 4 \cos \left (x \right ) {\mathrm e}^{-x}+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.604
8187	7136	\begin{align*} y^{\prime \prime }&=2 y y^{\prime } \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✗	0.604
8188	9274	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.604
8189	11288	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.604
8190	11717	\begin{align*} a x {y^{\prime }}^{2}+\left (b x -a y+c \right ) y^{\prime }-b y&=0 \\ \end{align*}	✓	✓	✓	✗	0.604
8191	11808	\begin{align*} {y^{\prime }}^{3}-\left (5+x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.604
8192	11835	\begin{align*} x^{2} \left (1+{y^{\prime }}^{2}\right )^{3}-a^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.604
8193	14391	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=3 x-4 y \\ \end{align*}	✓	✓	✓	✓	0.604
8194	16844	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\lambda y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.604
8195	17590	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&=\sec \left (2 t \right ) \tan \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.604
8196	18195	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=9 \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.604
8197	21942	\begin{align*} y^{\prime \prime }+x y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.604
8198	23517	\begin{align*} 4 y^{\prime \prime }+7 y^{\prime }+3 y&=5 \cos \left (t \right ) \\ y \left (0\right ) &= -3 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.604
8199	24613	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.604
8200	25093	\begin{align*} y^{\prime \prime }+8 y&=t \\ \end{align*}	✓	✓	✓	✓	0.604