2.3.160 Problems 15901 to 16000

Table 2.893: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
15901	19381	\begin{align*} x^{2}+y&=x y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.108
15902	7573	\begin{align*} 2 y^{\prime \prime }+18 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.109
15903	11325	\begin{align*} y^{\prime }+a y^{2}-b&=0 \\ \end{align*}	✓	✓	✓	✓	2.109
15904	19085	\begin{align*} \left (x^{2} y^{3}+y x \right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	2.109
15905	19119	\begin{align*} y&=2 x y^{\prime }+\frac {x^{2}}{2}+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✗	✓	2.109
15906	22351	\begin{align*} y^{\prime }&=2 x \\ \end{align*}	✓	✓	✓	✓	2.109
15907	23058	\begin{align*} \cot \left (\theta \right ) r^{\prime }&=r+b \\ \end{align*}	✓	✓	✓	✓	2.109
15908	25201	\begin{align*} \left (t -1\right ) y^{\prime \prime }-t y^{\prime }+y&=2 t \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.109
15909	17663	\begin{align*} 4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=\arctan \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	2.110
15910	23137	\begin{align*} x y^{\prime }+y&=3 \\ \end{align*}	✓	✓	✓	✓	2.110
15911	25191	\begin{align*} t^{2} y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y&={\mathrm e}^{-t} t^{2} \\ \end{align*}	✓	✓	✓	✗	2.110
15912	32	\begin{align*} y^{\prime }&=\sqrt {x -y} \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.111
15913	6085	\begin{align*} \left (1-a \right ) a y-2 a x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.112
15914	15901	\begin{align*} y^{\prime }&=-3 y+4 \cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	2.112
15915	19684	\begin{align*} t^{2} x^{\prime \prime }-6 x^{\prime } t +12 x&=0 \\ \end{align*}	✓	✓	✓	✓	2.112
15916	2686	\begin{align*} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <4 \\ 0 & 4<t \end {array}\right . \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.113
15917	6014	\begin{align*} \left (x^{2}+6\right ) y+4 x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.113
15918	17171	\begin{align*} x^{\prime }&=x+t +1 \\ x \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.113
15919	27211	\begin{align*} x^{2}+y^{2} y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	2.113
15920	16474	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }-y&=0 \\ y \left (1\right ) &= 8 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.114
15921	7009	\begin{align*} y^{\prime }+a y&=b \sin \left (k x \right ) \\ \end{align*}	✓	✓	✓	✓	2.115
15922	22930	\begin{align*} x^{\prime }-5 x+y^{\prime }+2 z&=24 \,{\mathrm e}^{-t} \\ x^{\prime }-x-y&=0 \\ 5 y^{\prime }-11 y+2 z^{\prime }-2 z&=0 \\ \end{align*}	✓	✓	✓	✓	2.115
15923	3980	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=\delta \left (t -2\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.118
15924	9098	\begin{align*} \frac {y^{\prime \prime }}{y^{\prime }}&=x^{2} \\ \end{align*}	✓	✓	✓	✓	2.118
15925	19929	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	2.118
15926	25657	\begin{align*} 2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.119
15927	2769	\begin{align*} x_{1}^{\prime }&=-x_{1}-x_{2}+1 \\ x_{2}^{\prime }&=-4 x_{2}-x_{3}+t \\ x_{3}^{\prime }&=5 x_{2}+{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	2.120
15928	22852	\begin{align*} x \left (1-x \right ) y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.120
15929	1408	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+2 x_{3} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ x_{3}^{\prime }&=-2 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	2.121
15930	25202	\begin{align*} \left (t -1\right ) y^{\prime \prime }-t y^{\prime }+y&=2 t \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.121
15931	5995	\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.122
15932	15160	\begin{align*} y^{\prime \prime }+2 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.122
15933	9771	\begin{align*} x y^{\prime \prime }+y^{\prime }+x&=0 \\ y \left (2\right ) &= -1 \\ y^{\prime }\left (2\right ) &= -{\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	2.123
15934	17657	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.123
15935	21173	\begin{align*} t^{2} x^{\prime \prime }+3 x^{\prime } t -3 x&=t^{2} \\ \end{align*}	✓	✓	✓	✓	2.123
15936	20956	\begin{align*} y^{\prime }&=y-y^{2} \\ y \left (0\right ) &= -{\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	2.124
15937	26235	\begin{align*} -x y^{\prime }+y&=a \left (1+x^{2} y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	2.124
15938	6281	\begin{align*} y+\left (b x +a \right )^{4} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.125
15939	16478	\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.125
15940	1212	\begin{align*} 1+\left (-\sin \left (y\right )+\frac {x}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.126
15941	6128	\begin{align*} -\left (2 x +3\right ) y+\left (x^{2}+x +1\right ) y^{\prime }+\left (x^{2}+3 x +4\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.126
15942	22477	\begin{align*} y^{\prime \prime }&=2 x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	2.126
15943	9579	\begin{align*} 9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (x^{6}-36\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.127
15944	10147	\begin{align*} x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y&=1 \\ \end{align*}	✓	✓	✓	✓	2.127
15945	3781	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }+25 y&=0 \\ y \left (1\right ) &= \frac {3 \sqrt {3}}{2} \\ y^{\prime }\left (1\right ) &= {\frac {15}{2}} \\ \end{align*}	✓	✓	✓	✓	2.128
15946	9724	\begin{align*} \left (x^{2}+y^{2}\right )^{2} {y^{\prime }}^{2}&=4 x^{2} y^{2} \\ \end{align*}	✓	✓	✓	✗	2.128
15947	12295	\begin{align*} y^{\prime \prime }-\left (a^{2} x^{2 n}-1\right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	2.128
15948	15927	\begin{align*} y^{\prime }&=\sin \left (t \right ) y+4 \\ \end{align*}	✓	✓	✓	✓	2.128
15949	24916	\begin{align*} y^{\prime }&=-y+3 t \\ \end{align*}	✓	✓	✓	✓	2.128
15950	1215	\begin{align*} \frac {4 x^{3}}{y^{2}}+\frac {3}{y}+\left (\frac {3 x}{y^{2}}+4 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.129
15951	5865	\begin{align*} a \cot \left (x \right )^{2} y+\tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.129
15952	21037	\begin{align*} x^{\prime }&=\arctan \left (x\right ) \\ \end{align*}	✓	✓	✓	✓	2.130
15953	23403	\begin{align*} 5 y^{\prime \prime }+\frac {3 y^{\prime }}{x -3}+\frac {3 y}{\left (x -3\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	2.130
15954	26896	\begin{align*} y^{\prime }-\frac {y}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	2.130
15955	1195	\begin{align*} 2+3 x^{2}-2 y x +\left (3-x^{2}+6 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.131
15956	6586	\begin{align*} a x -2 y^{\prime } y^{\prime \prime }+x {y^{\prime \prime }}^{2}&=0 \\ \end{align*}	✓	✓	✗	✗	2.131
15957	9911	\begin{align*} x \left (x +1\right ) y^{\prime \prime }+\left (5+x \right ) y^{\prime }-4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.131
15958	15848	\begin{align*} y^{\prime }&=\sqrt {y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.131
15959	21497	\begin{align*} y^{\prime \prime }+16 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	2.132
15960	22225	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+\left (-n^{2}+x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.132
15961	12686	\begin{align*} y^{\prime \prime }&=-\frac {a y}{\sin \left (x \right )^{2}} \\ \end{align*}	✗	✓	✓	✗	2.133
15962	14086	\begin{align*} y \left (3-4 y\right )^{2} {y^{\prime }}^{2}&=4-4 y \\ \end{align*}	✓	✓	✓	✓	2.133
15963	5806	\begin{align*} y b^{2}+2 a y^{\prime }+y^{\prime \prime }&=c \sin \left (k x \right ) \\ \end{align*}	✓	✓	✓	✓	2.134
15964	18249	\begin{align*} y^{\prime \prime }-3 y^{\prime }&=1+{\mathrm e}^{x}+\cos \left (x \right )+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.134
15965	18942	\begin{align*} y^{\prime \prime }+4 y&=\delta \left (t -4 \pi \right ) \\ y \left (0\right ) &= {\frac {1}{2}} \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.134
15966	8456	\begin{align*} 2 y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le x \le 3 \\ 0 & 3<x \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.135
15967	26721	\begin{align*} x y^{\prime \prime }+\frac {y^{\prime }}{2}+\frac {y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	2.135
15968	7538	\begin{align*} y^{\prime }&=2-\sqrt {2 x -y+3} \\ \end{align*}	✓	✓	✓	✓	2.136
15969	26151	\begin{align*} x y^{\prime }&=y+x \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.137
15970	26286	\begin{align*} \left (x^{3}+1\right ) x y^{\prime }+\left (2 x^{3}-1\right ) y&=\frac {x^{3}-2}{x} \\ \end{align*}	✓	✓	✓	✓	2.137
15971	14696	\begin{align*} \sin \left (x \right )^{2} y^{\prime \prime }-2 \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+\left (\cos \left (x \right )^{2}+1\right ) y&=\sin \left (x \right )^{3} \\ \end{align*}	✓	✓	✓	✗	2.138
15972	2067	\begin{align*} x y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.139
15973	5445	\begin{align*} 5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.139
15974	16332	\begin{align*} x y^{\prime }&=2 y-6 x^{3} \\ \end{align*}	✓	✓	✓	✓	2.139
15975	6284	\begin{align*} \left (-2 x^{3}+1\right ) y-x \left (-2 x^{3}+1\right ) y^{\prime }+x^{5} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.141
15976	21007	\begin{align*} x^{\prime }&=k x \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.141
15977	11356	\begin{align*} y^{\prime }-f \left (x \right ) y^{n}-g \left (x \right ) y-h \left (x \right )&=0 \\ \end{align*}	✗	✗	✗	✗	2.143
15978	19285	\begin{align*} y^{\prime }&=\left (x +y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.143
15979	21918	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-2 y^{\prime }+y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= -3 \\ y^{\prime \prime \prime }\left (0\right ) &= -5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.143
15980	25224	\begin{align*} 9 t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.143
15981	7159	\begin{align*} \frac {x}{y+1}&=\frac {y y^{\prime }}{x +1} \\ \end{align*}	✓	✓	✓	✗	2.145
15982	17193	\begin{align*} y+y^{\prime }&=t \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.145
15983	17764	\begin{align*} y^{\prime \prime }+16 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -8 \\ \end{align*}	✓	✓	✓	✓	2.145
15984	22459	\begin{align*} x y^{\prime \prime }-3 y^{\prime }&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	2.145
15985	24856	\begin{align*} 16 {y^{\prime }}^{2} x +8 y y^{\prime }+y^{6}&=0 \\ \end{align*}	✓	✓	✗	✗	2.145
15986	20869	\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=2 x^{3} \\ \end{align*}	✓	✓	✓	✓	2.146
15987	17020	\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.147
15988	5733	\begin{align*} 4 y+y^{\prime \prime }&=x \sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.148
15989	7426	\begin{align*} r^{\prime }+r \tan \left (\theta \right )&=\sec \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	2.148
15990	17782	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.148
15991	25231	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.148
15992	6422	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.149
15993	11336	\begin{align*} y^{\prime }+f \left (x \right ) y^{2}+g \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.149
15994	25200	\begin{align*} \left (t -1\right ) y^{\prime \prime }-t y^{\prime }+y&=2 t \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.149
15995	3003	\begin{align*} \left (1-x \right ) y^{\prime }-y-1&=0 \\ \end{align*}	✓	✓	✓	✓	2.150
15996	11707	\begin{align*} {y^{\prime }}^{2} x -y y^{\prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✗	2.150
15997	6119	\begin{align*} x \left (7+6 x \right ) y+x \left (1-x \right ) y^{\prime }+\left (-x^{2}-x +2\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.151
15998	7016	\begin{align*} x y^{\prime }+a y+b \,x^{n}&=0 \\ \end{align*}	✓	✓	✓	✓	2.151
15999	7388	\begin{align*} x^{\prime }&=\frac {t \,{\mathrm e}^{-t -2 x}}{x} \\ \end{align*}	✓	✓	✓	✓	2.152
16000	27269	\begin{align*} x y^{\prime }+\left (x +1\right ) y&=3 x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	2.153