2.3.191 Problems 19001 to 19100

Table 2.955: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
19001	906	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.632
19002	13010	\begin{align*} 2 x^{2} y \left (-1+y\right ) y^{\prime \prime }-x^{2} \left (3 y-1\right ) {y^{\prime }}^{2}+2 x y \left (-1+y\right ) y^{\prime }+\left (a y^{2}+b \right ) \left (-1+y\right )^{3}+c x y^{2} \left (-1+y\right )+d \,x^{2} y^{2} \left (y+1\right )&=0 \\ \end{align*}	✗	✗	✗	✗	3.632
19003	18566	\begin{align*} y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.632
19004	13481	\begin{align*} y^{\prime }&=y^{2}-f \left (x \right )^{2}+f^{\prime }\left (x \right ) \\ \end{align*}	✓	✓	✗	✗	3.633
19005	22565	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.633
19006	7922	\begin{align*} y+\left (y x +x -3 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.635
19007	27524	\begin{align*} x^{2}-1+\left (x^{2} y^{2}+x^{3}+x \right ) y^{\prime }&=0 \\ \end{align*}	✗	✓	✓	✓	3.635
19008	4196	\begin{align*} x y^{\prime }-y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	3.636
19009	14108	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=2 x \,{\mathrm e}^{2 x}-\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.637
19010	8658	\begin{align*} y^{\prime }&=\frac {x^{2}}{\left (x^{3}+1\right ) y} \\ \end{align*}	✓	✓	✓	✓	3.638
19011	17481	\begin{align*} y^{\prime \prime }+4 y&=1 \\ \end{align*}	✓	✓	✓	✓	3.638
19012	17951	\begin{align*} \sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=1 \\ \end{align*}	✓	✓	✓	✓	3.638
19013	10202	\begin{align*} x \left (x -1\right ) y^{\prime \prime }+3 x y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.639
19014	6421	\begin{align*} y y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	3.641
19015	7322	\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y&=2 x^{3} \\ \end{align*}	✓	✓	✓	✓	3.641
19016	13279	\begin{align*} \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }&=\alpha \,x^{k} y^{2}+\beta \,x^{s} y-\alpha \,\lambda ^{2} x^{k}+\beta \lambda \,x^{s} \\ \end{align*}	✓	✓	✓	✗	3.641
19017	141	\begin{align*} \cos \left (x \right )+\ln \left (y\right )+\left (\frac {x}{y}+{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.642
19018	17528	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }+4 y&=t \\ \end{align*}	✓	✓	✓	✓	3.643
19019	17973	\begin{align*} 3 x^{2}-2 x -y+\left (2 y-x +3 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.643
19020	2091	\begin{align*} x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.644
19021	2976	\begin{align*} y^{\prime }+y \cot \left (x \right )-\sec \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.644
19022	6764	\begin{align*} x^{2} y^{\prime \prime \prime \prime }&=2 y^{\prime \prime \prime } \\ \end{align*}	✓	✓	✓	✓	3.644
19023	18521	\begin{align*} y+2 y^{\prime }&=3 t^{2} \\ \end{align*}	✓	✓	✓	✓	3.644
19024	1121	\begin{align*} \left (t +1\right ) y+t y^{\prime }&=2 t \,{\mathrm e}^{-t} \\ y \left (1\right ) &= a \\ \end{align*}	✓	✓	✓	✓	3.645
19025	1722	\begin{align*} -y+\left (x^{4}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.645
19026	13894	\begin{align*} \left (x -a \right )^{2} \left (x -b \right )^{2} y^{\prime \prime }+\left (x -a \right ) \left (x -b \right ) \left (2 x +\lambda \right ) y^{\prime }+\mu y&=0 \\ \end{align*}	✓	✓	✓	✗	3.645
19027	16245	\begin{align*} y^{\prime }&=\frac {2+\sqrt {x}}{2+\sqrt {y}} \\ \end{align*}	✓	✓	✓	✗	3.645
19028	23252	\begin{align*} {\mathrm e}^{x} {y^{\prime }}^{2}+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.645
19029	1532	\begin{align*} y^{\prime }&=x \left (1+y^{2}\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.647
19030	6496	\begin{align*} {y^{\prime }}^{2} x +x y y^{\prime \prime }&=y y^{\prime } \\ \end{align*}	✓	✓	✓	✗	3.647
19031	7937	\begin{align*} x^{2} \cos \left (y\right ) y^{\prime }&=2 \sin \left (y\right ) x -1 \\ \end{align*}	✓	✓	✓	✗	3.647
19032	6531	\begin{align*} 4 f \left (x \right ) y y^{\prime \prime }&=4 f \left (x \right )^{2} y+3 f \left (x \right ) g \left (x \right ) y^{2}-f \left (x \right ) y^{4}+2 y^{3} f^{\prime }\left (x \right )+\left (-6 f \left (x \right ) y^{2}+2 f^{\prime }\left (x \right )\right ) y^{\prime }+3 f \left (x \right ) {y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	3.648
19033	13824	\begin{align*} \left (x^{2}+a \right ) y^{\prime \prime }+2 b x y^{\prime }+2 \left (b -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	3.648
19034	16236	\begin{align*} y^{\prime }&=3 y^{2}-\sin \left (x \right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	3.648
19035	8450	\begin{align*} x y^{\prime }+y&=1+4 x \\ y \left (1\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	3.649
19036	26899	\begin{align*} y^{\prime }&=\frac {y^{2}}{x^{2}}-\frac {y}{x}+1 \\ \end{align*}	✓	✓	✓	✓	3.650
19037	5493	\begin{align*} 16 {y^{\prime }}^{2} x +8 y y^{\prime }+y^{6}&=0 \\ \end{align*}	✓	✓	✓	✓	3.651
19038	21968	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (\frac {\pi }{8}\right ) &= 0 \\ y \left (\frac {\pi }{6}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.651
19039	2471	\begin{align*} \cos \left (t \right ) y+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.652
19040	4054	\begin{align*} x^{2} y^{\prime \prime }+2 x \left (x +2\right ) y^{\prime }+2 \left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.652
19041	11431	\begin{align*} 3 x y^{\prime }-3 x y^{4} \ln \left (x \right )-y&=0 \\ \end{align*}	✓	✓	✓	✓	3.652
19042	15166	\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=2 x \\ \end{align*}	✓	✓	✓	✗	3.652
19043	27395	\begin{align*} y \left (y-2 x y^{\prime }\right )^{3}&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✗	✗	3.653
19044	2359	\begin{align*} y^{\prime }&=t \left (1+y\right ) \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.654
19045	11881	\begin{align*} y^{\prime }&=\frac {y+F \left (\frac {y}{x}\right )}{x -1} \\ \end{align*}	✓	✓	✓	✗	3.654
19046	24129	\begin{align*} y x -\left (x +2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.654
19047	21345	\begin{align*} y^{\prime }&=\frac {a x +b}{y^{n}+d} \\ \end{align*}	✓	✓	✓	✓	3.655
19048	21994	\begin{align*} y^{\prime }&=\frac {x +1}{1+y^{4}} \\ \end{align*}	✓	✓	✓	✓	3.655
19049	1590	\begin{align*} y^{\prime }+\frac {\left (y+1\right ) \left (-1+y\right ) \left (-2+y\right )}{x +1}&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.658
19050	2321	\begin{align*} \cos \left (y\right ) \sin \left (t \right ) y^{\prime }&=\cos \left (t \right ) \sin \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	3.658
19051	5614	\begin{align*} {y^{\prime }}^{3}+y^{\prime }+a -b x&=0 \\ \end{align*}	✓	✓	✓	✓	3.658
19052	7530	\begin{align*} t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}}&=0 \\ \end{align*}	✓	✓	✓	✗	3.658
19053	23849	\begin{align*} 2 x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	3.658
19054	21481	\begin{align*} y^{\prime \prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.659
19055	5843	\begin{align*} 2 y-\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.660
19056	20228	\begin{align*} x^{2} y^{\prime }+y&=1 \\ \end{align*}	✓	✓	✓	✓	3.660
19057	4728	\begin{align*} y^{\prime }&=\sec \left (x \right )^{2} \sec \left (y\right )^{3} \\ \end{align*}	✓	✓	✓	✗	3.661
19058	10214	\begin{align*} \left (x^{2}-x \right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.661
19059	2667	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	3.662
19060	23891	\begin{align*} 2 x^{2} y-y^{2}+6 x^{3} y^{3}+\left (2 y^{2} x^{4}-x^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.662
19061	678	\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.664
19062	1550	\begin{align*} y^{\prime }+2 y x&=x \,{\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.664
19063	6016	\begin{align*} 16 y-7 x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.664
19064	21320	\begin{align*} x^{\prime \prime }+6 x^{5}&=0 \\ x \left (0\right ) &= 0 \\ x \left (b \right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	3.664
19065	24143	\begin{align*} y \ln \left (x \right ) \ln \left (y\right )+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.664
19066	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.	✓	✓	✓	✗	3.664
19067	5211	\begin{align*} \left (x -y^{2}\right ) y^{\prime }&=x^{2}-y \\ \end{align*}	✓	✓	✓	✗	3.665
19068	5302	\begin{align*} \left (x^{3}+a y^{3}\right ) y^{\prime }&=x^{2} y \\ \end{align*}	✓	✓	✓	✓	3.665
19069	12607	\begin{align*} y^{\prime \prime }&=-\frac {\left ({\mathrm e}^{\frac {2}{x}}-v^{2}\right ) y}{x^{4}} \\ \end{align*}	✗	✓	✓	✗	3.665
19070	15749	\begin{align*} y_{1}^{\prime }&=y_{2}-2 y_{1}+\sin \left (2 x \right ) \\ y_{2}^{\prime }&=-3 y_{1}+y_{2}-2 \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	3.666
19071	19792	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+x^{2} y&=x^{3}-x^{2} \arctan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.666
19072	20466	\begin{align*} y^{2} \left (-x y^{\prime }+y\right )&=x^{4} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	3.666
19073	7877	\begin{align*} \cos \left (y\right )+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✓	3.668
19074	17890	\begin{align*} y^{\prime }&=a x +b y+c \\ \end{align*}	✓	✓	✓	✓	3.668
19075	1567	\begin{align*} x y^{\prime }+2 y&=8 x^{2} \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.669
19076	14143	\begin{align*} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.669
19077	20679	\begin{align*} x^{3}+x y^{2}+a^{2} y+\left (y^{3}+x^{2} y-a^{2} x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.669
19078	21123	\begin{align*} x^{\prime \prime }+\lambda ^{2} x&=0 \\ x \left (0\right ) &= 0 \\ x \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.669
19079	11980	\begin{align*} y^{\prime }&=\left (1+y^{2} {\mathrm e}^{-\frac {4 x}{3}}+y^{3} {\mathrm e}^{-2 x}\right ) {\mathrm e}^{\frac {2 x}{3}} \\ \end{align*}	✓	✓	✓	✗	3.670
19080	26858	\begin{align*} x y^{\prime }&=x -y \\ \end{align*}	✓	✓	✓	✓	3.671
19081	26213	\begin{align*} y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	3.672
19082	9195	\begin{align*} \sec \left (x \right ) y^{\prime }&=\sec \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	3.674
19083	18292	\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.675
19084	4719	\begin{align*} y^{\prime }+\tan \left (x \right ) \sec \left (x \right ) \cos \left (y\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.676
19085	6254	\begin{align*} y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.676
19086	22337	\begin{align*} 1+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.677
19087	4059	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.678
19088	4339	\begin{align*} 3 x^{2}+3 y^{2}+x \left (x^{2}+3 y^{2}+6 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.678
19089	9743	\begin{align*} x^{8} {y^{\prime }}^{2}+3 x y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.678
19090	12642	\begin{align*} y^{\prime \prime }&=\frac {12 y}{\left (x +1\right )^{2} \left (x^{2}+2 x +3\right )} \\ \end{align*}	✓	✓	✓	✗	3.678
19091	23167	\begin{align*} y^{\prime }-2 y x&=4 x \sqrt {y} \\ \end{align*}	✓	✓	✓	✓	3.678
19092	25796	\begin{align*} y^{\prime }&=y-\cos \left (\frac {\pi x}{2}\right ) \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.678
19093	7480	\begin{align*} 3 x^{2}+y+\left (x^{2} y-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.679
19094	26356	\begin{align*} y&=y^{\prime } \ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	3.679
19095	27320	\begin{align*} -x y^{\prime }+y&=2 x^{3} \tan \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✗	3.680
19096	11469	\begin{align*} x^{3} y^{\prime }-y^{2}-x^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	3.681
19097	27503	\begin{align*} 2 x -\ln \left (y+1\right )-\frac {\left (x +y\right ) y^{\prime }}{y+1}&=0 \\ \end{align*}	✓	✓	✓	✗	3.683
19098	131	\begin{align*} 3 x y^{2} y^{\prime }&=3 x^{4}+y^{3} \\ \end{align*}	✓	✓	✓	✓	3.685
19099	1137	\begin{align*} y^{\prime }&=\left (1-2 x \right ) y^{2} \\ y \left (0\right ) &= -{\frac {1}{6}} \\ \end{align*}	✓	✓	✓	✓	3.685
19100	8782	\begin{align*} {\mathrm e}^{x}+y+\left (x -2 \sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.685