2.3.141 Problems 14001 to 14100

Table 2.813: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
14001	2580	\begin{align*} t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.949
14002	19222	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=x+{\mathrm e}^{t}+{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.949
14003	20650	\begin{align*} 2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=x^{3} \\ \end{align*}	✓	✓	✓	✗	0.949
14004	595	\begin{align*} x^{\prime }&=2 x-3 y+2 \sin \left (2 t \right ) \\ y^{\prime }&=x-2 y-\cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.950
14005	3348	\begin{align*} y^{\prime \prime }&=\sin \left (y x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*} Series expansion around \(x=\frac {\pi }{2}\).	✓	✓	✓	✗	0.950
14006	3560	\begin{align*} y^{\prime }&=-y^{2} \\ \end{align*}	✓	✓	✓	✓	0.950
14007	5883	\begin{align*} 4 y^{\prime \prime }&=\left (x^{2}+a \right ) y \\ \end{align*}	✗	✓	✓	✗	0.950
14008	9655	\begin{align*} x^{\prime }&=4 x-7 y \\ y^{\prime }&=5 x \\ \end{align*}	✓	✓	✓	✓	0.950
14009	15560	\begin{align*} y^{\prime }&=a y+b \\ y \left (c \right ) &= d \\ \end{align*}	✓	✓	✓	✓	0.950
14010	16479	\begin{align*} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.950
14011	17679	\begin{align*} 6 x^{2} y^{\prime \prime }+5 y^{\prime } x -y&=0 \\ y \left (1\right ) &= a \\ y^{\prime }\left (1\right ) &= b \\ \end{align*}	✓	✓	✓	✓	0.950
14012	17853	\begin{align*} y^{\prime }&=y-x \\ \end{align*}	✓	✓	✓	✓	0.950
14013	20462	\begin{align*} x {y^{\prime }}^{2}-\left (x -a \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.950
14014	2192	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+32 y^{\prime \prime }-64 y^{\prime }+64 y&={\mathrm e}^{2 x} \left (\cos \left (2 x \right )-\sin \left (2 x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.951
14015	5989	\begin{align*} -y+\left (x +a \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.951
14016	9859	\begin{align*} 2 x \left (x +1\right ) y^{\prime \prime }+3 \left (x +1\right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.951
14017	14702	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.951
14018	21052	\begin{align*} x^{\prime }&=\frac {x^{2}+x}{2 x+1} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.951
14019	21699	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{3} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.951
14020	25296	\begin{align*} y^{\prime }-3 y&=\left \{\begin {array}{cc} 0 & 0\le t <2 \\ 2 & 2\le t <3 \\ 0 & 3\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.951
14021	10043	\begin{align*} y^{\prime \prime }&=k \\ \end{align*}	✓	✓	✓	✓	0.952
14022	15849	\begin{align*} y^{\prime }&=2-y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.952
14023	20778	\begin{align*} y^{\prime \prime } x +y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.952
14024	5935	\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=\left (1-x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	0.954
14025	8032	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=2 \\ \end{align*}	✓	✓	✓	✗	0.954
14026	14661	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{x} x^{4}+x^{3} {\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.954
14027	15660	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.954
14028	20571	\begin{align*} y^{\prime \prime } y^{\prime \prime \prime }&=2 \\ \end{align*}	✓	✓	✓	✗	0.954
14029	23847	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.954
14030	5884	\begin{align*} \left (-x^{2}+4 a +2\right ) y+4 y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.955
14031	6812	\begin{align*} 3 y^{\prime \prime } y^{\prime \prime \prime \prime }&=5 {y^{\prime \prime \prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.955
14032	15411	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.955
14033	18778	\begin{align*} 4 y^{\prime \prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.955
14034	23226	\begin{align*} y^{\prime \prime }+y^{\prime }&=3 \\ \end{align*}	✓	✓	✓	✓	0.955
14035	9341	\begin{align*} y^{\prime \prime }+y^{\prime }&=\frac {x -1}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.956
14036	9913	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.956
14037	14720	\begin{align*} x^{2} y^{\prime \prime }-2 y&=4 x -8 \\ y \left (1\right ) &= 4 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.956
14038	14851	\begin{align*} 2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }+\frac {\lambda y}{x^{2}+1}&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.956
14039	6122	\begin{align*} 2 y-4 \left (1-x \right ) y^{\prime }+\left (1-x \right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.957
14040	14064	\begin{align*} x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✗	0.957
14041	21635	\begin{align*} \left (x -1\right ) y^{\prime \prime }+y^{\prime } x +\frac {y}{x}&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	0.957
14042	17181	\begin{align*} y^{\prime }-5 y&=t \\ \end{align*}	✓	✓	✓	✓	0.958
14043	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*}	✓	✓	✓	✗	0.958
14044	23783	\begin{align*} x^{\prime }&=a x+b y \\ y^{\prime }&=c x+d y \\ \end{align*}	✓	✓	✓	✓	0.958
14045	9807	\begin{align*} x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+4&=0 \\ \end{align*}	✓	✓	✓	✗	0.959
14046	9874	\begin{align*} 2 x^{2} y^{\prime \prime }+x \left (4 x -1\right ) y^{\prime }+2 \left (3 x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.959
14047	9914	\begin{align*} \left (1-x \right ) x y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.959
14048	15896	\begin{align*} y^{\prime }&=y^{2}-y \\ \end{align*}	✓	✓	✓	✓	0.959
14049	18998	\begin{align*} x_{1}^{\prime }&=x_{1}+5 x_{2}+3 x_{3}-5 x_{4} \\ x_{2}^{\prime }&=2 x_{1}+3 x_{2}+2 x_{3}-4 x_{4} \\ x_{3}^{\prime }&=-x_{2}-2 x_{3}+x_{4} \\ x_{4}^{\prime }&=2 x_{1}+4 x_{2}+2 x_{3}-5 x_{4} \\ \end{align*}	✓	✓	✓	✓	0.959
14050	25233	\begin{align*} t^{2} y^{\prime \prime }+2 t y^{\prime }-2 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.959
14051	25416	\begin{align*} y^{\prime }+2 y&=\operatorname {Heaviside}\left (t -4\right )-\operatorname {Heaviside}\left (t -6\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.959
14052	7540	\begin{align*} 2 y+y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	0.960
14053	7944	\begin{align*} 4 x -2 y^{\prime } y+x {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.960
14054	12385	\begin{align*} y^{\prime \prime } x -2 \left (a x +b \right ) y^{\prime }+\left (a^{2} x +2 a b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.960
14055	14846	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.960
14056	18246	\begin{align*} y^{\prime \prime }+y&=\cos \left (2 x \right )^{2}+\sin \left (\frac {x}{2}\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.960
14057	20436	\begin{align*} x^{2} \left (y-y^{\prime } x \right )&=y {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.960
14058	25809	\begin{align*} y^{\prime }&=y \left (2-y\right ) \left (4-y\right ) \\ \end{align*}	✓	✓	✓	✓	0.960
14059	3847	\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2}+3 x_{3}+4 x_{4} \\ x_{2}^{\prime }&=4 x_{1}+3 x_{2}+2 x_{3}+x_{4} \\ x_{3}^{\prime }&=4 x_{1}+5 x_{2}+6 x_{3}+7 x_{4} \\ x_{4}^{\prime }&=7 x_{1}+6 x_{2}+5 x_{3}+4 x_{4} \\ \end{align*}	✓	✓	✓	✓	0.961
14060	9907	\begin{align*} x^{2} y^{\prime \prime }+2 x \left (x -2\right ) y^{\prime }+2 \left (2-3 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.961
14061	12151	\begin{align*} y^{\prime }&=\frac {2 x y^{2}+4 y \ln \left (2 x +1\right ) x +2 \ln \left (2 x +1\right )^{2} x +y^{2}-2+\ln \left (2 x +1\right )^{2}+2 y \ln \left (2 x +1\right )}{2 x +1} \\ \end{align*}	✓	✓	✓	✓	0.961
14062	14324	\begin{align*} t x^{\prime \prime }+4 x^{\prime }+\frac {2 x}{t}&=0 \\ \end{align*}	✓	✓	✓	✓	0.961
14063	23371	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.961
14064	2292	\begin{align*} y_{1}^{\prime }&=-3 y_{1}+y_{2}-3 y_{3} \\ y_{2}^{\prime }&=4 y_{1}-y_{2}+2 y_{3} \\ y_{3}^{\prime }&=4 y_{1}-2 y_{2}+3 y_{3} \\ \end{align*}	✓	✓	✓	✓	0.962
14065	2830	\begin{align*} x_{1}^{\prime }&=2 x_{2} \\ x_{2}^{\prime }&=-2 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.962
14066	7428	\begin{align*} t +y+1-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.962
14067	20862	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.962
14068	25052	\begin{align*} y^{\prime }&=a y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.962
14069	9369	\begin{align*} y^{\prime }&=x -y \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.963
14070	23326	\begin{align*} y^{\prime \prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.963
14071	23502	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x -4 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.963
14072	74	\begin{align*} y^{\prime }-2 y&=3 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.964
14073	3287	\begin{align*} x \left (-1+{y^{\prime }}^{2}\right )&=2 y^{\prime } y \\ \end{align*}	✓	✓	✓	✓	0.964
14074	5950	\begin{align*} c y^{\prime }+\left (b x +a \right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.964
14075	6973	\begin{align*} 2 y+y^{\prime }&=\frac {3 \,{\mathrm e}^{-2 x}}{4} \\ \end{align*}	✓	✓	✓	✓	0.964
14076	7789	\begin{align*} y^{\prime \prime }&=9 x^{2}+2 x -1 \\ \end{align*}	✓	✓	✓	✓	0.964
14077	9557	\begin{align*} y^{\prime \prime } x +\left (x -6\right ) y^{\prime }-3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.964
14078	19046	\begin{align*} x_{1}^{\prime }&=-4 x_{1}+x_{2}+3 x_{3}+3 t \\ x_{2}^{\prime }&=-2 x_{2} \\ x_{3}^{\prime }&=-2 x_{1}+x_{2}+x_{3}+3 \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.964
14079	20618	\begin{align*} y^{\prime \prime }-2 b x y^{\prime }+b^{2} x^{2} y&=x \\ \end{align*}	✓	✓	✓	✗	0.964
14080	22211	\begin{align*} -a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.964
14081	25225	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.964
14082	9256	\begin{align*} 4 y+y^{\prime \prime }&=4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \\ \end{align*}	✓	✓	✓	✓	0.965
14083	18197	\begin{align*} y^{\prime \prime }+3 y^{\prime }&=3 x \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.965
14084	19609	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (4 x +4\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.965
14085	19698	\begin{align*} x^{\prime \prime }+2 x^{\prime }+4 x&={\mathrm e}^{t} \cos \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.965
14086	3875	\begin{align*} x_{1}^{\prime }&=2 x_{1}+4 x_{2}+8 \sin \left (2 t \right ) \\ x_{2}^{\prime }&=-2 x_{1}-2 x_{2}+8 \cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.966
14087	18999	\begin{align*} x_{1}^{\prime }&=-5 x_{1}+x_{2}-4 x_{3}-x_{4} \\ x_{2}^{\prime }&=-3 x_{2} \\ x_{3}^{\prime }&=x_{1}-x_{2}+x_{4} \\ x_{4}^{\prime }&=2 x_{1}-x_{2}+2 x_{3}-2 x_{4} \\ \end{align*}	✓	✓	✓	✓	0.966
14088	2839	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.967
14089	5489	\begin{align*} 4 x {y^{\prime }}^{2}-3 y^{\prime } y+3&=0 \\ \end{align*}	✓	✓	✓	✗	0.967
14090	9916	\begin{align*} y^{\prime \prime } x +\left (3 x +4\right ) y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.967
14091	10364	\begin{align*} a {y^{\prime \prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.967
14092	13948	\begin{align*} y^{\prime \prime }+\left (2 a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+a \left (b +\lambda \right ) {\mathrm e}^{\lambda x}+c \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.967
14093	13956	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+c \right ) y^{\prime }+\left (a \lambda \,{\mathrm e}^{\lambda x}+{\mathrm e}^{\mu x} b \mu \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.967
14094	14847	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (L \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.967
14095	18291	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.967
14096	19457	\begin{align*} 3 y-\left (x +3\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.967
14097	17176	\begin{align*} y+y^{\prime }&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	0.968
14098	22654	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.968
14099	23154	\begin{align*} y^{\prime } x +\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.968
14100	85	\begin{align*} y^{\prime }+y&={\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.969