2.3.180 Problems 17901 to 18000

Table 2.891: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
17901	24980	\begin{align*} \cos \left (t \right ) y^{\prime }+\sin \left (t \right ) y&=1 \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	2.076
17902	7731	\begin{align*} y^{\prime }+\tan \left (x \right ) y&=y^{3} \sec \left (x \right )^{4} \\ \end{align*}	✓	✓	✓	✓	2.077
17903	8472	\begin{align*} y^{\prime } x -4 y&=x^{6} {\mathrm e}^{x} \\ y \left (x_{0} \right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	2.077
17904	23252	\begin{align*} {\mathrm e}^{x} {y^{\prime }}^{2}+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.077
17905	24389	\begin{align*} \left (2 x -1\right ) y+2 \left (x^{2}+y^{2}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.077
17906	795	\begin{align*} 2 y+\left (x +1\right ) y^{\prime }&=3 x +3 \\ \end{align*}	✓	✓	✓	✓	2.078
17907	4969	\begin{align*} x^{3} y^{\prime }&=x^{4}+y^{2} \\ \end{align*}	✓	✓	✓	✓	2.078
17908	25750	\begin{align*} y^{\prime \prime }+y \sec \left (x \right )&=0 \\ \end{align*}	✗	✓	✗	✗	2.079
17909	1578	\begin{align*} y^{\prime }&=\frac {3 x^{2}+2 x +1}{y-2} \\ \end{align*}	✓	✓	✓	✓	2.080
17910	8868	\begin{align*} y^{\prime }-2 y&=x^{2}+x \\ \end{align*}	✓	✓	✓	✓	2.080
17911	7418	\begin{align*} x^{2} y^{\prime }+\sin \left (x \right )-y&=0 \\ \end{align*}	✓	✓	✓	✓	2.081
17912	4623	\begin{align*} y^{\prime }&={\mathrm e}^{\sin \left (x \right )}-y \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.082
17913	5132	\begin{align*} x y^{\prime } y&=\left (x^{2}+1\right ) \left (1-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	2.082
17914	15601	\begin{align*} y^{\prime }&=\cot \left (x \right ) y+\sin \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.082
17915	25398	\begin{align*} y^{\prime }&=a \left (t \right ) y \\ \end{align*}	✓	✓	✓	✓	2.082
17916	17167	\begin{align*} t y^{\prime }+y&=\cos \left (t \right ) \\ y \left (\frac {\pi }{2}\right ) &= \frac {4}{\pi } \\ \end{align*}	✓	✓	✓	✓	2.083
17917	22439	\begin{align*} i^{\prime }&=\frac {t -i t}{t^{2}+1} \\ i \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.084
17918	22949	\begin{align*} 1+y^{2}&=\left (x^{2}+1\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.084
17919	5245	\begin{align*} \left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }+x^{2}-3 x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.085
17920	2471	\begin{align*} y \cos \left (t \right )+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.086
17921	4209	\begin{align*} \sqrt {x^{2}+1}\, y^{\prime }-y&=2 \sqrt {x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	2.086
17922	7115	\begin{align*} y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}}&=x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.086
17923	13255	\begin{align*} x^{2} y^{\prime }&=a \,x^{2} y^{2}+b x y+c \,x^{2 n}+s \,x^{n} \\ \end{align*}	✓	✓	✓	✗	2.087
17924	22363	\begin{align*} y^{\prime }&=\frac {x y^{2}+x}{4 y} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.087
17925	2304	\begin{align*} \frac {t y}{t^{2}+1}+y^{\prime }&=1-\frac {t^{3} y}{t^{4}+1} \\ \end{align*}	✓	✓	✓	✗	2.088
17926	25053	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.088
17927	10437	\begin{align*} y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }+4 x^{2} y \,{\mathrm e}^{-2 x}&=4 \left (x^{3}+x^{2}\right ) {\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✗	2.089
17928	15336	\begin{align*} \left (1+u \right ) v+\left (1-v\right ) u v^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.089
17929	22332	\begin{align*} y^{\prime }&=y^{3} \\ \end{align*}	✓	✓	✓	✓	2.089
17930	17193	\begin{align*} y+y^{\prime }&=t \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.090
17931	19788	\begin{align*} v^{\prime \prime }+\frac {2 x v^{\prime }}{x^{2}+1}+\frac {v}{\left (x^{2}+1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	2.091
17932	20955	\begin{align*} y^{\prime }&=y-y^{2} \\ y \left (0\right ) &= {\frac {3}{2}} \\ \end{align*}	✓	✓	✓	✓	2.091
17933	21776	\begin{align*} \left ({y^{\prime }}^{2}-y^{2}\right ) {\mathrm e}^{y^{\prime }}-x {y^{\prime }}^{2}+x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.091
17934	1218	\begin{align*} y^{\prime }&=\frac {x^{3}-2 y}{x} \\ \end{align*}	✓	✓	✓	✓	2.092
17935	18091	\begin{align*} y^{\prime \prime }&=x \,{\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.092
17936	25775	\begin{align*} y^{\prime }&=-y x +1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.092
17937	691	\begin{align*} \left (x^{2}+1\right ) \tan \left (y\right ) y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	2.095
17938	797	\begin{align*} 3 y+y^{4} x^{3}+3 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.095
17939	1798	\begin{align*} x^{2} \left (y^{\prime }+y^{2}\right )-x \left (2+x \right ) y+x +2&=0 \\ \end{align*}	✓	✓	✓	✓	2.095
17940	8388	\begin{align*} y^{\prime }&=y-y^{3} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✓	2.095
17941	14665	\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+4 y^{\prime \prime }+3 y^{\prime }+y&=x^{2} {\mathrm e}^{-x}+3 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	2.095
17942	16334	\begin{align*} 4 y^{2}-y^{2} x^{2}+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.095
17943	22758	\begin{align*} t^{2} i^{\prime \prime }+2 i^{\prime } t +i&=t \ln \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.096
17944	7793	\begin{align*} y^{\prime }-5 y&={\mathrm e}^{x} x^{2}-x \,{\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	2.097
17945	15907	\begin{align*} y+y^{\prime }&=\cos \left (2 t \right ) \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	2.097
17946	24110	\begin{align*} y^{\prime \prime } x +2 y^{\prime }-3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.097
17947	8306	\begin{align*} y^{\prime }&=x \\ y \left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	2.098
17948	10281	\begin{align*} c y^{\prime }&=\frac {a x +b y^{2}}{y} \\ \end{align*}	✓	✓	✓	✓	2.098
17949	14584	\begin{align*} y^{\prime \prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.098
17950	24961	\begin{align*} y^{\prime }&=t y^{2} \\ \end{align*}	✓	✓	✓	✓	2.098
17951	19231	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.099
17952	1542	\begin{align*} y^{\prime }+\frac {\left (x +1\right ) y}{x}&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.100
17953	5498	\begin{align*} x^{2} {y^{\prime }}^{2}+y^{2}-y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	2.100
17954	24216	\begin{align*} y \left (x^{2}+y^{2}-1\right )+x \left (1+x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.100
17955	24784	\begin{align*} \left (4 x -y\right ) {y^{\prime }}^{2}+6 \left (x -y\right ) y^{\prime }+2 x -5 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.100
17956	14966	\begin{align*} t^{2} x^{\prime \prime }+t x^{\prime }-x&=0 \\ x \left (1\right ) &= 1 \\ x^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.102
17957	17983	\begin{align*} 2 x^{2} y+2 y+5+\left (2 x^{3}+2 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.102
17958	24472	\begin{align*} y^{\prime \prime }-9 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.102
17959	1672	\begin{align*} y^{\prime }&=y^{2} {\mathrm e}^{-x}+4 y+2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.103
17960	4007	\begin{align*} \left (x -2\right )^{2} y^{\prime \prime }+\left (x -2\right ) {\mathrm e}^{x} y^{\prime }+\frac {4 y}{x}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.103
17961	6144	\begin{align*} 8 y+\left (1-2 x \right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.103
17962	14486	\begin{align*} \left (u^{2}+1\right ) v^{\prime }+4 u v&=3 u \\ \end{align*}	✓	✓	✓	✓	2.103
17963	15611	\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (-1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.103
17964	4762	\begin{align*} y^{\prime } x&=1+x +a y \\ \end{align*}	✓	✓	✓	✓	2.104
17965	1564	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=\cos \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.105
17966	2322	\begin{align*} t^{2} \left (1+y^{2}\right )+2 y y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.105
17967	5874	\begin{align*} b y+a \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	2.105
17968	7878	\begin{align*} y^{2}+y x -y^{\prime } x&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.105
17969	10055	\begin{align*} a y^{2} y^{\prime \prime }+b y^{2}&=c \\ \end{align*}	✓	✓	✓	✓	2.105
17970	19505	\begin{align*} y^{\prime \prime }+k^{2} y&=\sin \left (b x \right ) \\ \end{align*}	✓	✓	✓	✓	2.105
17971	22360	\begin{align*} y^{\prime }&=-\frac {y}{x} \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.105
17972	4353	\begin{align*} x^{2}+y^{3}+y+\left (x^{3}+y^{2}-x \right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	2.107
17973	24375	\begin{align*} 3 y^{2}+3 x^{2}+x \left (x^{2}+3 y^{2}+6 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.107
17974	205	\begin{align*} 3 y+y^{4} x^{3}+3 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.108
17975	1710	\begin{align*} y+\left (2 x +\frac {1}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.108
17976	14886	\begin{align*} x^{\prime }&=t^{3} \left (1-x\right ) \\ x \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.108
17977	17283	\begin{align*} y^{\prime }+2 y&=t^{2} \sqrt {y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.108
17978	673	\begin{align*} y^{\prime } y&=x -1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.109
17979	6010	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=\ln \left (x +1\right ) \\ \end{align*}	✓	✓	✓	✓	2.109
17980	14133	\begin{align*} y x -x^{2} y^{\prime }+y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✗	2.109
17981	11473	\begin{align*} x \left (x^{2}+1\right ) y^{\prime }+x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	2.110
17982	1099	\begin{align*} -2 y+y^{\prime }&={\mathrm e}^{2 t} t^{2} \\ \end{align*}	✓	✓	✓	✓	2.111
17983	4982	\begin{align*} x \left (-x^{2}+1\right ) y^{\prime }&=a \,x^{3}+\left (-2 x^{2}+1\right ) y \\ \end{align*}	✓	✓	✓	✓	2.111
17984	5965	\begin{align*} \left (c \,x^{2}+b x +a \right ) y+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	2.111
17985	9411	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.111
17986	11433	\begin{align*} x^{2} y^{\prime }-y+x^{2} {\mathrm e}^{x -\frac {1}{x}}&=0 \\ \end{align*}	✓	✓	✓	✓	2.111
17987	16308	\begin{align*} y^{\prime }+3 y&=\frac {28 \,{\mathrm e}^{2 x}}{y^{3}} \\ \end{align*}	✓	✓	✓	✓	2.111
17988	1713	\begin{align*} 3 x^{2} y+2 x^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.112
17989	4625	\begin{align*} y^{\prime }&=\cot \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	2.112
17990	21670	\begin{align*} y^{\prime \prime }+p \left (x \right ) y^{\prime }+q \left (x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	2.112
17991	4326	\begin{align*} 2 x^{2}-x y^{2}-2 y+3-\left (x^{2} y+2 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.113
17992	9925	\begin{align*} 2 y^{\prime \prime } x +6 y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.113
17993	11376	\begin{align*} y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x}&=0 \\ \end{align*}	✓	✓	✓	✓	2.113
17994	14893	\begin{align*} i^{\prime }&=p \left (t \right ) i \\ \end{align*}	✓	✓	✓	✓	2.113
17995	24231	\begin{align*} y \left (3 x^{3}-x +y\right )+x^{2} \left (-x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.113
17996	25502	\begin{align*} y^{\prime }&=-4 t y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.113
17997	4411	\begin{align*} y x +2 x^{3} y+x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.114
17998	2996	\begin{align*} \left (x \tan \left (y\right )^{2}+x \right ) y^{\prime }&=2 x^{2}+\tan \left (y\right ) \\ \end{align*}	✓	✓	✓	✗	2.115
17999	17074	\begin{align*} y^{\prime }&=\frac {1+y}{t +1} \\ \end{align*}	✓	✓	✓	✓	2.115
18000	4294	\begin{align*} x^{2} y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	2.116