2.3.170 Problems 16901 to 17000

Table 2.871: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
16901	24250	\begin{align*} x \left (x^{2}+1\right ) y^{\prime }+2 y&=\left (x^{2}+1\right )^{3} \\ \end{align*}	✓	✓	✓	✓	1.733
16902	2093	\begin{align*} 4 x^{2} y^{\prime \prime }+2 x \left (x^{2}+8\right ) y^{\prime }+\left (3 x^{2}+5\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.734
16903	5079	\begin{align*} 2 y^{\prime } y&=x y^{2}+x^{3} \\ \end{align*}	✓	✓	✓	✓	1.734
16904	5831	\begin{align*} c y+\left (b x +a \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	1.734
16905	11449	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x -2 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.734
16906	15383	\begin{align*} 6 x y^{2}+4 x^{3}+3 \left (2 x^{2} y+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.734
16907	22326	\begin{align*} y^{\prime }+\tan \left (x \right ) y&=0 \\ y \left (\pi \right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	1.734
16908	19467	\begin{align*} y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.735
16909	20426	\begin{align*} x^{2} {y^{\prime }}^{2}-2 x y^{\prime } y+2 y^{2}&=x^{2} \\ \end{align*}	✓	✓	✓	✓	1.735
16910	22050	\begin{align*} y+3 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.736
16911	1560	\begin{align*} x^{2} y^{\prime }+3 y x&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.737
16912	8453	\begin{align*} x \left (x +1\right ) y^{\prime }+y x&=1 \\ y \left ({\mathrm e}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.737
16913	9097	\begin{align*} \left (1+y\right ) y^{\prime }&=-x^{2}+1 \\ y \left (-1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	1.737
16914	8686	\begin{align*} y^{\prime }&=\cos \left (x -y-1\right ) \\ \end{align*}	✓	✓	✓	✓	1.739
16915	23453	\begin{align*} \left (1+a \cos \left (2 x \right )\right ) y^{\prime \prime }+\lambda y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.739
16916	1719	\begin{align*} y^{2}+\left (x y^{2}+6 y x +\frac {1}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.740
16917	2318	\begin{align*} y^{\prime }&=\left (t +1\right ) \left (1+y\right ) \\ \end{align*}	✓	✓	✓	✓	1.740
16918	17640	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +36 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	1.740
16919	24184	\begin{align*} 6 x +y^{2}+y \left (2 x -3 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.740
16920	24185	\begin{align*} 2 y x -3 x^{2}+\left (y+x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.740
16921	102	\begin{align*} 2 y^{\prime } x&=y+2 \cos \left (x \right ) x \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.741
16922	138	\begin{align*} 2 x y^{2}+3 x^{2}+\left (2 x^{2} y+4 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.741
16923	4338	\begin{align*} y^{2}+\left (y x +y^{2}-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.742
16924	6215	\begin{align*} -\left (x +1\right )^{3} y+y^{\prime } x +x^{2} \left (x +1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.742
16925	13245	\begin{align*} y^{\prime } x&=a \,x^{n} y^{2}+b y+c \,x^{m} \\ \end{align*}	✓	✓	✓	✗	1.742
16926	17786	\begin{align*} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=8 x \\ \end{align*}	✓	✓	✓	✓	1.742
16927	8427	\begin{align*} y^{\prime }&=2 y+x^{2}+5 \\ \end{align*}	✓	✓	✓	✓	1.743
16928	15531	\begin{align*} y^{\prime }&=-y x \\ \end{align*}	✓	✓	✓	✓	1.743
16929	15537	\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	1.743
16930	17194	\begin{align*} y+y^{\prime }&=\sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.743
16931	22950	\begin{align*} y^{\prime } \sin \left (y\right )&=\sec \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.743
16932	1221	\begin{align*} y^{\prime }&=3-6 x +y-2 y x \\ \end{align*}	✓	✓	✓	✓	1.744
16933	14457	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+4 y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.744
16934	21557	\begin{align*} y^{\prime \prime } x -\frac {\left (1-2 x \right ) y^{\prime }}{1-x}+\frac {\left (x^{2}-3 x +1\right ) y}{1-x}&=\left (1-x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	1.744
16935	25035	\begin{align*} t^{2}-y-t y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.744
16936	14905	\begin{align*} x^{\prime }+\left (a +\frac {1}{t}\right ) x&=b \\ x \left (1\right ) &= x_{0} \\ \end{align*}	✓	✓	✓	✗	1.745
16937	12309	\begin{align*} y^{\prime \prime }-y^{\prime }+y \,{\mathrm e}^{2 x}&=0 \\ \end{align*}	✓	✓	✓	✗	1.746
16938	14201	\begin{align*} x^{\prime }&=x \left (1-\frac {x}{4}\right ) \\ \end{align*}	✓	✓	✓	✓	1.746
16939	208	\begin{align*} y^{\prime }&=\sqrt {x +y} \\ \end{align*}	✓	✓	✓	✓	1.747
16940	5138	\begin{align*} x \left (1-y\right ) y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.747
16941	7320	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -16 y&=8 x^{4} \\ \end{align*}	✓	✓	✓	✓	1.747
16942	18587	\begin{align*} y^{\prime }&=-1+{\mathrm e}^{2 x}+y \\ \end{align*}	✓	✓	✓	✓	1.747
16943	1556	\begin{align*} y^{\prime }+\tan \left (x \right ) y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.748
16944	17538	\begin{align*} t^{2} \left (\ln \left (t \right )-1\right ) y^{\prime \prime }-t y^{\prime }+y&=-\frac {3 \left (1+\ln \left (t \right )\right )}{4 \sqrt {t}} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.748
16945	19018	\begin{align*} x_{1}^{\prime }&=3 x_{2}-2 x_{4} \\ x_{2}^{\prime }&=-\frac {x_{1}}{2}+x_{2}-3 x_{3}-\frac {5 x_{4}}{2} \\ x_{3}^{\prime }&=3 x_{2}-5 x_{3}-3 x_{4} \\ x_{4}^{\prime }&=x_{1}+3 x_{2}-3 x_{4} \\ \end{align*}	✓	✓	✓	✓	1.748
16946	20408	\begin{align*} x&=y^{\prime } y-{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.748
16947	76	\begin{align*} y^{\prime }-2 y x&={\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	1.749
16948	1539	\begin{align*} y^{\prime } x +y \ln \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.750
16949	5903	\begin{align*} -y+\left (a +1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✓	✓	✗	1.750
16950	9483	\begin{align*} x^{\prime }&=-2 x+y-t +3 \\ y^{\prime }&=x+4 y+t -2 \\ \end{align*}	✓	✓	✓	✓	1.750
16951	14504	\begin{align*} x^{\prime }-x&=\sin \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.750
16952	21664	\begin{align*} \cos \left (x \right ) u^{\prime \prime }+\sin \left (x \right ) u^{\prime }+\left (\cos \left (x \right )+\sin \left (x \right )\right ) u&=0 \\ u \left (\frac {\pi }{4}\right ) &= 2 \\ u^{\prime }\left (\frac {\pi }{4}\right ) &= 0 \\ \end{align*} Series expansion around \(x=\frac {\pi }{4}\).	✓	✓	✓	✗	1.750
16953	18250	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{x} \left (1-2 \sin \left (x \right )^{2}\right )+10 x +1 \\ \end{align*}	✓	✓	✓	✓	1.751
16954	18515	\begin{align*} 2 y+t y^{\prime }&=\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.751
16955	3669	\begin{align*} y^{\prime }+\frac {2 x y}{x^{2}+1}&=x y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.752
16956	4096	\begin{align*} y^{\prime }&=\frac {y-2 x}{x} \\ \end{align*}	✓	✓	✓	✓	1.752
16957	13892	\begin{align*} \left (x^{2}+a \right )^{2} y^{\prime \prime }+b \,x^{n} \left (x^{2}+a \right ) y^{\prime }-m \left (b \,x^{n +1}+\left (m -1\right ) x^{2}+a \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	1.752
16958	22368	\begin{align*} y^{\prime }&=8 y x +3 y \\ \end{align*}	✓	✓	✓	✓	1.752
16959	23977	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.752
16960	4106	\begin{align*} y^{\prime }-3 y&={\mathrm e}^{3 x}+{\mathrm e}^{-3 x} \\ y \left (5\right ) &= 5 \\ \end{align*}	✓	✓	✓	✗	1.753
16961	4204	\begin{align*} y^{\prime }+y \cos \left (x \right )&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.753
16962	4769	\begin{align*} y^{\prime } x&=x^{3}+\left (-2 x^{2}+1\right ) y \\ \end{align*}	✓	✓	✓	✓	1.753
16963	8661	\begin{align*} y^{\prime }&=\frac {x^{2}}{1+y^{2}} \\ \end{align*}	✓	✓	✓	✓	1.753
16964	12387	\begin{align*} y^{\prime \prime } x -\left (x^{2}-x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.753
16965	18570	\begin{align*} 2+3 x^{2}-2 y x +\left (3-x^{2}+6 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.753
16966	22028	\begin{align*} y+2 x y^{3}+\left (1+3 y^{2} x^{2}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.753
16967	3773	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.754
16968	14153	\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*}	✓	✓	✓	✗	1.754
16969	9817	\begin{align*} x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✗	1.755
16970	19426	\begin{align*} y^{\prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.755
16971	1195	\begin{align*} 2+3 x^{2}-2 y x +\left (3-x^{2}+6 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.756
16972	6986	\begin{align*} y^{\prime }&=x^{3}+\frac {2 y}{x}-\frac {y^{2}}{x} \\ \end{align*}	✓	✓	✓	✓	1.756
16973	9779	\begin{align*} y^{\prime \prime }&=-{\mathrm e}^{-2 y} \\ y \left (3\right ) &= 0 \\ y^{\prime }\left (3\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.756
16974	12401	\begin{align*} 4 y^{\prime \prime } x +2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.756
16975	20002	\begin{align*} \left (y^{\prime } y+n x \right )^{2}&=\left (y^{2}+n \,x^{2}\right ) \left (1+{y^{\prime }}^{2}\right ) \\ \end{align*}	✓	✓	✗	✓	1.756
16976	8465	\begin{align*} x^{2} y^{\prime }-y&=x^{3} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.757
16977	11390	\begin{align*} y^{\prime } x +y-x \sin \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.757
16978	13392	\begin{align*} y^{\prime }&=a y^{2}+2 a b \tan \left (x \right ) y+b \left (a b -1\right ) \tan \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.759
16979	14145	\begin{align*} -8 x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+y^{\prime \prime } x&=4 x^{3} {\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✗	1.759
16980	14961	\begin{align*} x^{\prime \prime }-4 x^{\prime }&=\tan \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.759
16981	15394	\begin{align*} y&=y^{\prime } x +y^{\prime } \\ \end{align*}	✓	✓	✓	✓	1.759
16982	3530	\begin{align*} x^{2} y^{\prime }-4 y x&=x^{7} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.760
16983	4941	\begin{align*} \left (x -2\right ) \left (x -3\right ) y^{\prime }+x^{2}-8 y+3 y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.760
16984	16037	\begin{align*} x^{\prime }&=\frac {y}{10} \\ y^{\prime }&=\frac {z}{5} \\ z^{\prime }&=\frac {2 x}{5} \\ \end{align*}	✓	✓	✓	✓	1.760
16985	5453	\begin{align*} x {y^{\prime }}^{2}-2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	1.761
16986	15837	\begin{align*} v^{\prime }&=2 V \left (t \right )-2 v \\ \end{align*}	✓	✓	✓	✓	1.761
16987	19501	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=12 x -10 \\ \end{align*}	✓	✓	✓	✓	1.761
16988	19080	\begin{align*} y^{\prime }&=2 y x -x^{3}+x \\ \end{align*}	✓	✓	✓	✓	1.762
16989	10143	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\ y^{\prime }\left (1\right ) &= 0 \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.763
16990	21972	\begin{align*} y^{\prime }&=y \sin \left (x \right )+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	1.763
16991	5137	\begin{align*} x \left (1-y\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.764
16992	15506	\begin{align*} y^{\prime }-2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.764
16993	23931	\begin{align*} y^{\prime \prime }+k^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.764
16994	4342	\begin{align*} 2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.765
16995	5217	\begin{align*} \left (1-x^{2}+y^{2}\right ) y^{\prime }&=1+x^{2}-y^{2} \\ \end{align*}	✓	✓	✓	✓	1.765
16996	8545	\begin{align*} y^{\prime \prime } x +3 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.765
16997	14140	\begin{align*} y^{\prime \prime } x +2 y^{\prime }-y x&=2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	1.765
16998	5036	\begin{align*} y^{\prime } y+x \,{\mathrm e}^{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	1.766
16999	8677	\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \\ \end{align*}	✓	✓	✓	✓	1.766
17000	8742	\begin{align*} 2 y^{\prime } x +y&=y^{2} \sqrt {x -y^{2} x^{2}} \\ \end{align*}	✓	✓	✓	✗	1.766