2.3.121 Problems 12001 to 12100

Table 2.773: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
12001	21226	\begin{align*} x^{\prime }&=x+2 y+{\mathrm e}^{t} \\ y^{\prime }&=x-2 y-{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	1.923
12002	22002	\begin{align*} \sin \left (x \right )+y y^{\prime }&=0 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	1.923
12003	2590	\begin{align*} t^{2} y^{\prime \prime }-2 y&=t^{2} \\ \end{align*}	✓	✓	✓	✓	1.924
12004	8214	\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	1.924
12005	21775	\begin{align*} 2 {y^{\prime }}^{2}-2 y y^{\prime }-1&=0 \\ \end{align*}	✓	✓	✓	✓	1.924
12006	22487	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.924
12007	20792	\begin{align*} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	1.925
12008	21185	\begin{align*} x^{\prime \prime \prime }-3 x^{\prime }+k x&=0 \\ x \left (0\right ) &= 1 \\ x \left (\infty \right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	1.925
12009	4934	\begin{align*} x \left (1-x \right ) y^{\prime }&=2 y x +2 \\ \end{align*}	✓	✓	✓	✓	1.926
12010	6378	\begin{align*} \left (-a \,x^{2}+2\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.926
12011	1556	\begin{align*} y^{\prime }+\tan \left (x \right ) y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.927
12012	5451	\begin{align*} x {y^{\prime }}^{2}+y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✗	1.927
12013	23483	\begin{align*} y^{\prime \prime }+y&=x +{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	1.927
12014	15241	\begin{align*} y^{\prime \prime }+4 \pi ^{2} y&=3 \delta \left (t -\frac {1}{3}\right )-\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.928
12015	21380	\begin{align*} 3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.928
12016	2808	\begin{align*} x^{\prime }&=x \left (1-x\right ) \\ \end{align*}	✓	✓	✓	✓	1.929
12017	3280	\begin{align*} 2 y y^{\prime \prime }&=y^{3}+2 {y^{\prime }}^{2} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.930
12018	14487	\begin{align*} y^{\prime } x +\frac {\left (2 x +1\right ) y}{x +1}&=x -1 \\ \end{align*}	✓	✓	✓	✓	1.930
12019	23338	\begin{align*} y^{\prime \prime }-9 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.930
12020	5591	\begin{align*} 3 y^{2} {y^{\prime }}^{2}-2 y y^{\prime } x -x^{2}+4 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.931
12021	12422	\begin{align*} x^{2} y^{\prime \prime }+\frac {y}{\ln \left (x \right )}-x \,{\mathrm e}^{x} \left (2+x \ln \left (x \right )\right )&=0 \\ \end{align*}	✗	✓	✓	✗	1.931
12022	14255	\begin{align*} x^{\prime }&=\left (a +\frac {b}{t}\right ) x \\ x \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.931
12023	14309	\begin{align*} x^{\prime \prime }+x&=t^{2} \\ \end{align*}	✓	✓	✓	✓	1.931
12024	2298	\begin{align*} y \cos \left (t \right )+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.932
12025	4283	\begin{align*} y^{\prime } x +y&=\cos \left (x \right ) x^{2} \\ \end{align*}	✓	✓	✓	✓	1.932
12026	24149	\begin{align*} v v^{\prime }&=g \\ v \left (x_{0} \right ) &= v_{0} \\ \end{align*}	✓	✗	✓	✓	1.932
12027	25039	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.932
12028	2328	\begin{align*} 3 y^{\prime } t&=y \cos \left (t \right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.933
12029	5967	\begin{align*} x^{k} \left (a +b \,x^{k}\right ) y+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	1.933
12030	8435	\begin{align*} y&=\left ({\mathrm e}^{y} y-2 x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	1.933
12031	25231	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.933
12032	522	\begin{align*} 16 x^{2} y^{\prime \prime }-\left (-144 x^{3}+5\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.934
12033	15383	\begin{align*} 6 x y^{2}+4 x^{3}+3 \left (2 x^{2} y+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.934
12034	16818	\begin{align*} y^{\prime \prime \prime }+9 y^{\prime }&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.935
12035	22997	\begin{align*} \cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y&=x \\ \end{align*}	✓	✓	✓	✓	1.935
12036	24872	\begin{align*} y^{2} y^{\prime \prime }+{y^{\prime }}^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	1.935
12037	1171	\begin{align*} y+\ln \left (t \right ) y^{\prime }&=\cot \left (t \right ) \\ \end{align*}	✓	✓	✓	✗	1.937
12038	12552	\begin{align*} \left (4 x +3\right ) y+16 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.937
12039	21321	\begin{align*} x^{\prime \prime }+\lambda x-x^{3}&=0 \\ x \left (0\right ) &= 0 \\ x \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	1.937
12040	22007	\begin{align*} y^{\prime }&=\frac {x^{2} y-y}{1+y} \\ y \left (3\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.937
12041	4651	\begin{align*} y^{\prime }&=f \left (x \right )+g \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	1.938
12042	22801	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.938
12043	24991	\begin{align*} y^{\prime }-\frac {2 y}{1+t}&=\left (1+t \right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.938
12044	124	\begin{align*} y^{2} y^{\prime }+2 x y^{3}&=6 x \\ \end{align*}	✓	✓	✓	✓	1.939
12045	25703	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (-1\right ) &= 5 \\ y^{\prime }\left (-1\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	1.939
12046	25813	\begin{align*} y^{\prime }&=y^{2}-y-6 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	1.940
12047	2405	\begin{align*} 3 y^{\prime \prime }+4 y^{\prime }+y&=\sin \left (t \right ) {\mathrm e}^{-t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.941
12048	4077	\begin{align*} 2 x \tan \left (y\right )+\left (x -x^{2} \tan \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.941
12049	7122	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x&=1 \\ \end{align*}	✓	✓	✓	✓	1.941
12050	18946	\begin{align*} 2 y^{\prime \prime }+y^{\prime }+6 y&=\delta \left (t -\frac {\pi }{6}\right ) \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.941
12051	20321	\begin{align*} x^{2}-a y&=\left (a x -y^{2}\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	1.941
12052	22014	\begin{align*} y^{\prime }&=\frac {x +2 y}{x} \\ \end{align*}	✓	✓	✓	✓	1.941
12053	1221	\begin{align*} y^{\prime }&=3-6 x +y-2 y x \\ \end{align*}	✓	✓	✓	✓	1.942
12054	7015	\begin{align*} x^{3} y^{\prime }-y^{2}-x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.942
12055	23972	\begin{align*} y^{\prime }-y x&=-x^{5}+4 x^{3} \\ \end{align*}	✓	✓	✓	✓	1.942
12056	7976	\begin{align*} {y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.943
12057	16202	\begin{align*} y^{3}-25 y+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.943
12058	22468	\begin{align*} x -x^{2}-y^{2}+\left (y+x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.943
12059	16719	\begin{align*} x^{2} y^{\prime \prime }+\frac {5 y}{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.944
12060	20227	\begin{align*} y^{\prime }&={\mathrm e}^{x -y}+x^{2} {\mathrm e}^{-y} \\ \end{align*}	✓	✓	✓	✓	1.945
12061	22933	\begin{align*} z+x^{\prime }&=x \\ y^{\prime }-2 x&=y+3 t \\ z^{\prime }+4 y&=z-\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.946
12062	1552	\begin{align*} y^{\prime }+\frac {y}{x}&=\frac {7}{x^{2}}+3 \\ \end{align*}	✓	✓	✓	✓	1.947
12063	5175	\begin{align*} 3 x \left (x +2 y\right ) y^{\prime }+x^{3}+3 y \left (2 x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	1.947
12064	16078	\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&={\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.947
12065	2309	\begin{align*} y+y^{\prime }&=\frac {1}{t^{2}+1} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.948
12066	9645	\begin{align*} y^{\prime \prime }+y&=\delta \left (t -2 \pi \right )+\delta \left (t -4 \pi \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.948
12067	22171	\begin{align*} \left (x^{2}-4\right ) y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	1.949
12068	22974	\begin{align*} y^{\prime }&=\frac {x -y+2}{x +1} \\ \end{align*}	✓	✓	✓	✓	1.949
12069	24266	\begin{align*} y^{\prime }&=4 x -2 y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.949
12070	684	\begin{align*} y^{\prime }&=2 x \sec \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	1.950
12071	10415	\begin{align*} y^{\prime \prime }+\left (\sin \left (x \right )+2 x \right ) y^{\prime }+\cos \left (y\right ) y {y^{\prime }}^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	1.950
12072	4734	\begin{align*} y^{\prime }&={\mathrm e}^{y}+x \\ \end{align*}	✓	✓	✓	✓	1.951
12073	9369	\begin{align*} y^{\prime }&=x -y \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.952
12074	15929	\begin{align*} y^{\prime }&=\frac {y}{t^{2}}+4 \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.952
12075	21158	\begin{align*} x^{\prime \prime }+2 t^{3} x&=0 \\ \end{align*}	✓	✓	✓	✗	1.952
12076	6178	\begin{align*} \left (4 x +3\right ) y+16 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.953
12077	6971	\begin{align*} \tan \left (\theta \right ) r^{\prime }-r&=\tan \left (\theta \right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.953
12078	10273	\begin{align*} c y^{\prime }&=a x +y \\ \end{align*}	✓	✓	✓	✓	1.953
12079	20224	\begin{align*} y^{\prime } x -y-\cos \left (\frac {1}{x}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.953
12080	24959	\begin{align*} y^{3} y^{\prime }&=t \\ \end{align*}	✓	✓	✓	✓	1.953
12081	1265	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= {\frac {5}{4}} \\ y^{\prime }\left (0\right ) &= -{\frac {3}{4}} \\ \end{align*}	✓	✓	✓	✓	1.954
12082	19790	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=\csc \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.954
12083	22467	\begin{align*} x^{2}+y^{2}+y+\left (x^{2}+y^{2}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.954
12084	22599	\begin{align*} y^{\prime }&={\mathrm e}^{x +3 y}+1 \\ \end{align*}	✓	✓	✓	✓	1.955
12085	24992	\begin{align*} y^{\prime }-\frac {2 y}{t}&=\frac {1+t}{t} \\ y \left (1\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	1.955
12086	3586	\begin{align*} y^{\prime \prime }&=\cos \left (x \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.956
12087	7127	\begin{align*} y^{\prime \prime }&=2 k y^{3} \\ \end{align*}	✓	✓	✓	✓	1.956
12088	7495	\begin{align*} \cos \left (x +y\right ) y^{\prime }&=\sin \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	1.957
12089	23763	\begin{align*} -\frac {u^{\prime \prime }}{2}&=x \\ u \left (0\right ) &= 0 \\ u \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.957
12090	25776	\begin{align*} y^{\prime }&=-y x +1 \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.957
12091	11813	\begin{align*} {y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5}&=0 \\ \end{align*}	✓	✓	✓	✗	1.959
12092	13929	\begin{align*} y^{\prime \prime }-\left (a \,{\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{\lambda x}+c \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	1.959
12093	24763	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right )^{3} \tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.959
12094	4257	\begin{align*} 1+y+\left (1-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.960
12095	8427	\begin{align*} y^{\prime }&=2 y+x^{2}+5 \\ \end{align*}	✓	✓	✓	✓	1.960
12096	14669	\begin{align*} y^{\prime \prime \prime \prime }+16 y&=x \,{\mathrm e}^{\sqrt {2}\, x} \sin \left (\sqrt {2}\, x \right )+{\mathrm e}^{-\sqrt {2}\, x} \cos \left (\sqrt {2}\, x \right ) \\ \end{align*}	✓	✓	✓	✓	1.960
12097	138	\begin{align*} 2 x y^{2}+3 x^{2}+\left (2 x^{2} y+4 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.961
12098	14840	\begin{align*} t^{2} x^{\prime \prime }+t x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	1.961
12099	15592	\begin{align*} y^{\prime }&=\frac {-y x +1}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	1.961
12100	7324	\begin{align*} x^{2} y^{\prime \prime }+y&=3 x^{2} \\ \end{align*}	✓	✓	✓	✓	1.962