2.3.114 Problems 11301 to 11400

Table 2.771: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
11301	2002	\begin{align*} x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.836
11302	3825	\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=-b x_{1}-a x_{2} \\ \end{align*}	✓	✓	✓	✓	0.836
11303	13108	\begin{align*} x^{\prime }&=x+y-z \\ y^{\prime }&=y+z-x \\ z^{\prime }&=x-y+z \\ \end{align*}	✓	✓	✓	✓	0.836
11304	15886	\begin{align*} y^{\prime }&=y^{2}-4 y+2 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✓	0.836
11305	16878	\begin{align*} y^{\prime \prime }-{\mathrm e}^{x} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.836
11306	18864	\begin{align*} y^{\prime \prime }+4 y&=3 \sec \left (2 t \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.836
11307	19222	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=x+{\mathrm e}^{t}+{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.836
11308	25554	\begin{align*} y^{\prime \prime }+c y&={\mathrm e}^{i \omega t} \\ \end{align*}	✓	✓	✓	✓	0.836
11309	159	\begin{align*} y^{\prime }&=f \left (a x +b y+c \right ) \\ \end{align*}	✓	✓	✓	✓	0.837
11310	7778	\begin{align*} x^{\prime \prime }+2 x^{\prime }+2 x&=85 \sin \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= -20 \\ \end{align*}	✓	✓	✓	✓	0.837
11311	12442	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.837
11312	12960	\begin{align*} 2 y y^{\prime \prime }-3 {y^{\prime }}^{2}+f \left (x \right ) y^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	0.837
11313	14100	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}} \\ \end{align*}	✓	✓	✓	✗	0.837
11314	14405	\begin{align*} x^{\prime }&=9 y \\ y^{\prime }&=-x \\ \end{align*}	✓	✓	✓	✓	0.837
11315	15978	\begin{align*} x^{\prime }&=\beta y \\ y^{\prime }&=\gamma x-y \\ \end{align*}	✓	✓	✓	✓	0.837
11316	23591	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=-x-y \\ \end{align*}	✓	✓	✓	✓	0.837
11317	23982	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=x^{2}-2 x +1 \\ \end{align*}	✓	✓	✓	✓	0.837
11318	7185	\begin{align*} x \left (-x^{2}+1\right ) y^{\prime \prime }+\left (-3 x^{2}+1\right ) y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.838
11319	9382	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +p^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.838
11320	14383	\begin{align*} x^{\prime }&=-3 y \\ y^{\prime }&=-2 x+y \\ \end{align*}	✓	✓	✓	✓	0.838
11321	70	\begin{align*} {y^{\prime }}^{2}&=4 y \\ y \left (a \right ) &= b \\ \end{align*}	✓	✓	✓	✗	0.839
11322	1253	\begin{align*} y^{\prime \prime }+5 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.839
11323	1820	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=x^{3} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	0.839
11324	2456	\begin{align*} t^{2} y^{\prime \prime }+t \left (1+t \right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.839
11325	3507	\begin{align*} z \left (1-z \right ) y^{\prime \prime }+\left (1-z \right ) y^{\prime }+\lambda y&=0 \\ \end{align*} Series expansion around \(z=0\).	✓	✓	✓	✓	0.839
11326	14794	\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=7 x+4 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 6 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.839
11327	18346	\begin{align*} x^{\prime \prime }+{x^{\prime }}^{2}+x&=0 \\ \end{align*}	✓	✓	✓	✗	0.839
11328	18363	\begin{align*} y^{\prime \prime }+y&=1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.839
11329	18641	\begin{align*} x^{\prime }&=-x+y+1 \\ y^{\prime }&=x+y-3 \\ \end{align*}	✓	✓	✓	✓	0.839
11330	20364	\begin{align*} y+y^{\prime \prime }+y^{\prime \prime \prime \prime }&=a \,x^{2}+b \,{\mathrm e}^{-x} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.839
11331	2451	\begin{align*} 2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.840
11332	4175	\begin{align*} 2 y_{1}^{\prime }+y_{2}^{\prime }-4 y_{1}-y_{2}&={\mathrm e}^{x} \\ y_{1}^{\prime }+3 y_{1}+y_{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.840
11333	16920	\begin{align*} 4 x^{2} y^{\prime \prime }+8 y^{\prime } x +\left (1-4 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.840
11334	1296	\begin{align*} t^{2} y^{\prime \prime }-4 y^{\prime } t -6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.841
11335	4604	\begin{align*} y^{\prime \prime } x +2 y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.841
11336	6254	\begin{align*} y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.841
11337	6512	\begin{align*} \left (x -y\right ) y^{\prime }+x {y^{\prime }}^{2}+x \left (x +y\right ) y^{\prime \prime }&=y \\ \end{align*}	✓	✓	✓	✗	0.841
11338	7188	\begin{align*} x \left (-x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.841
11339	16904	\begin{align*} x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+\left (9+4 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.841
11340	21104	\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.841
11341	23813	\begin{align*} x^{\prime }&=4 x+6 y \\ y^{\prime }&=-7 x-9 y \\ \end{align*}	✓	✓	✓	✓	0.841
11342	25348	\begin{align*} 2 t^{2} y^{\prime \prime }-y^{\prime } t +\left (1-t \right ) y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.841
11343	3266	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=y y^{\prime } \\ \end{align*}	✓	✓	✓	✗	0.842
11344	4388	\begin{align*} y&=2 y^{\prime } x +y^{2} {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.842
11345	5468	\begin{align*} x {y^{\prime }}^{2}+\left (a +b x -y\right ) y^{\prime }-b y&=0 \\ \end{align*}	✓	✓	✓	✗	0.842
11346	5481	\begin{align*} \left (x +1\right ) {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.842
11347	9767	\begin{align*} y^{2} y^{\prime \prime }+{y^{\prime }}^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	0.842
11348	14335	\begin{align*} x^{\prime \prime }-2 x^{\prime }+x&=\frac {{\mathrm e}^{t}}{2 t} \\ \end{align*}	✓	✓	✓	✓	0.842
11349	14860	\begin{align*} x^{\prime }&=x+7 y \\ y^{\prime }&=3 x+5 y \\ \end{align*}	✓	✓	✓	✓	0.842
11350	15469	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=-x+y \\ \end{align*}	✓	✓	✓	✓	0.842
11351	17653	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=x^{3} \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.842
11352	18100	\begin{align*} y^{\prime \prime \prime }&=\sqrt {1-{y^{\prime \prime }}^{2}} \\ \end{align*}	✓	✗	✓	✓	0.842
11353	21542	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.842
11354	21613	\begin{align*} \frac {{y^{\prime \prime }}^{2}}{{y^{\prime }}^{2}}+\frac {y y^{\prime \prime }}{y^{\prime }}-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.842
11355	24073	\begin{align*} y^{\prime \prime }-y^{\prime }-y&=\sinh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.842
11356	25227	\begin{align*} t^{2} y^{\prime \prime }-3 y^{\prime } t -21 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.842
11357	95	\begin{align*} y^{\prime } x +\left (2 x -3\right ) y&=4 x^{4} \\ \end{align*}	✓	✓	✓	✓	0.843
11358	1824	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}+3\right ) y&=x^{{7}/{2}} \\ \end{align*}	✓	✓	✓	✗	0.843
11359	20626	\begin{align*} x^{2} y^{\prime \prime }-2 n x y^{\prime }+\left (a^{2} x^{2}+n^{2}+n \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.843
11360	23846	\begin{align*} y^{\prime \prime } x -2 \left (x +1\right ) y^{\prime }+\left (2+x \right ) y&=1 \\ \end{align*}	✓	✓	✓	✗	0.843
11361	9681	\begin{align*} x^{\prime }&=-x-y \\ y^{\prime }&=\frac {3 x}{4}-\frac {3 y}{2}+3 z \\ z^{\prime }&=\frac {x}{8}+\frac {y}{4}-\frac {z}{2} \\ \end{align*}	✓	✓	✓	✓	0.844
11362	10443	\begin{align*} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-3\right ) y&={\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✗	0.844
11363	15251	\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y&=-t^{2}+2 t -10 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.844
11364	15977	\begin{align*} x^{\prime }&=-3 x+2 \pi y \\ y^{\prime }&=4 x-y \\ \end{align*}	✓	✓	✓	✓	0.844
11365	19011	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }&=-8 x_{1}-5 x_{2}-3 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.844
11366	664	\begin{align*} y^{\prime }&=x -y \\ \end{align*}	✓	✓	✓	✓	0.845
11367	10363	\begin{align*} a y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.845
11368	16918	\begin{align*} x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+9 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.845
11369	18108	\begin{align*} y^{\prime \prime }+y^{\prime }+2&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.845
11370	24582	\begin{align*} y^{\prime \prime }-y^{\prime }&=42 \,{\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.845
11371	837	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.846
11372	2025	\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.846
11373	5710	\begin{align*} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.846
11374	5775	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=50 \cos \left (x \right ) \cosh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.846
11375	6849	\begin{align*} \frac {3 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.846
11376	9352	\begin{align*} y^{\prime }-y&=2 \\ \end{align*}	✓	✓	✓	✓	0.846
11377	15444	\begin{align*} y^{\prime \prime }+y&=\frac {1}{\cos \left (2 x \right )^{{3}/{2}}} \\ \end{align*}	✓	✓	✓	✗	0.846
11378	20158	\begin{align*} y^{\prime }+{y^{\prime }}^{3}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.846
11379	20743	\begin{align*} x {y^{\prime }}^{2}-2 y y^{\prime }+x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.846
11380	21096	\begin{align*} {x^{\prime }}^{2}-t x+x&=0 \\ \end{align*}	✓	✓	✓	✗	0.846
11381	25350	\begin{align*} t^{2} y^{\prime \prime }+2 y^{\prime } t -a \,t^{2} y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.846
11382	25740	\begin{align*} -y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.846
11383	7654	\begin{align*} y^{\prime \prime }+y^{\prime } t +{\mathrm e}^{t} y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.847
11384	8592	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.847
11385	9571	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}-64\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.847
11386	16907	\begin{align*} 4 x^{2} y^{\prime \prime }+8 x^{2} y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.847
11387	17721	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.847
11388	20643	\begin{align*} 4 y+y^{\prime \prime }&=4 \tan \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.847
11389	21381	\begin{align*} y^{\prime }&=2 x \\ \end{align*}	✓	✓	✓	✓	0.847
11390	22202	\begin{align*} 8 x^{2} y^{\prime \prime }+10 y^{\prime } x +\left (x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.847
11391	23563	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.847
11392	4749	\begin{align*} y^{\prime } x&=\sqrt {a^{2}-x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.848
11393	23768	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x \\ \end{align*}	✓	✓	✓	✓	0.848
11394	3163	\begin{align*} y^{\prime \prime }+9 y&=\csc \left (x \right ) \sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.849
11395	7152	\begin{align*} \left (-x^{2}+1\right ) {y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✓	0.849
11396	7637	\begin{align*} w^{\prime \prime }-x^{2} w^{\prime }+w&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.849
11397	14379	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.849
11398	15090	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=\sinh \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	0.849
11399	15285	\begin{align*} x^{\prime }&=-2 x-2 y+4 z \\ y^{\prime }&=-2 x+y+2 z \\ z^{\prime }&=-4 x-2 y+6 z+{\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.849
11400	16736	\begin{align*} y^{\prime \prime } x&=3 y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.849