2.3.220 Problems 21901 to 22000

Table 2.971: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
21901	13950	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{x}+b \right ) y^{\prime }+\left (c \left (a -c \right ) {\mathrm e}^{2 x}+\left (a k +b c -2 c k +c \right ) {\mathrm e}^{x}+k \left (b -k \right )\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	5.122
21902	2503	\begin{align*} \left (t -\sqrt {t y}\right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	5.123
21903	7475	\begin{align*} \left (x -2 y\right ) y^{\prime }+2 x +y&=0 \\ \end{align*}	✓	✓	✓	✓	5.128
21904	7544	\begin{align*} y-2 x -1+\left (x +y-4\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.129
21905	19723	\begin{align*} y^{\prime }+y x&=x \\ \end{align*}	✓	✓	✓	✓	5.132
21906	18561	\begin{align*} y^{3}+y^{\prime }&=0 \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	5.133
21907	19728	\begin{align*} y^{\prime }+y \cos \left (x \right )&=\frac {\sin \left (2 x \right )}{2} \\ \end{align*}	✓	✓	✓	✓	5.134
21908	21802	\begin{align*} r^{\prime }&=r \tan \left (t \right ) \\ r \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.134
21909	20171	\begin{align*} y^{\prime \prime }&=a^{2}+k^{2} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	5.138
21910	24136	\begin{align*} y^{\prime } x +y+x y \left (1+y^{\prime }\right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.138
21911	20300	\begin{align*} y^{\prime }&=\left (4 x +y+1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	5.140
21912	9135	\begin{align*} \frac {y}{1-y^{2} x^{2}}+\frac {x y^{\prime }}{1-y^{2} x^{2}}&=1 \\ \end{align*}	✓	✓	✓	✓	5.141
21913	7228	\begin{align*} \left (y x +x \right ) y^{\prime }+y&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.144
21914	8475	\begin{align*} 2 x -1+\left (3 y+7\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.144
21915	8780	\begin{align*} y^{\prime } x -2 \sqrt {y x}&=y \\ \end{align*}	✓	✓	✓	✓	5.144
21916	19387	\begin{align*} y^{\prime } \ln \left (x -y\right )&=1+\ln \left (x -y\right ) \\ \end{align*}	✓	✓	✓	✓	5.146
21917	21256	\begin{align*} x^{\prime \prime }&=x^{3}-x \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	5.146
21918	22532	\begin{align*} x^{2}-y^{2}+2 x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	5.146
21919	23191	\begin{align*} x +y+\left (x -y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.148
21920	25722	\begin{align*} y^{\prime } y&=3 x \\ y \left (-2\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	5.149
21921	4992	\begin{align*} x^{4} y^{\prime }&=\left (x^{3}+y\right ) y \\ \end{align*}	✓	✓	✓	✓	5.155
21922	10285	\begin{align*} y^{\prime }&=\sin \left (x \right )+y^{2} \\ \end{align*}	✓	✓	✓	✗	5.155
21923	17326	\begin{align*} t^{2} y+\sin \left (t \right )+\left (\frac {t^{3}}{3}-\cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.155
21924	12382	\begin{align*} y^{\prime \prime } x +\left (a x +b +n \right ) y^{\prime }+n a y&=0 \\ \end{align*}	✗	✓	✓	✗	5.156
21925	730	\begin{align*} 2 x y^{\prime } y&=y^{2}+x^{2} \\ \end{align*}	✓	✓	✓	✓	5.165
21926	16476	\begin{align*} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\ y \left (\sqrt {\pi }\right ) &= 3 \\ y^{\prime }\left (\sqrt {\pi }\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	5.165
21927	19940	\begin{align*} y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}&=1 \\ \end{align*}	✓	✓	✓	✓	5.168
21928	21719	\begin{align*} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 4 t & 0\le t \le 1 \\ 4 & 1<t \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	5.168
21929	4260	\begin{align*} \left (3 x^{2}-y^{2}\right ) y^{\prime }-2 y x&=0 \\ \end{align*}	✓	✓	✓	✗	5.173
21930	6576	\begin{align*} 3 y y^{\prime } y^{\prime \prime }&=-1+{y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	5.175
21931	7416	\begin{align*} y^{\prime }&=x y^{3} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.177
21932	1197	\begin{align*} y^{\prime }&=\frac {-a x -b y}{b x +c y} \\ \end{align*}	✓	✓	✓	✓	5.178
21933	2537	\begin{align*} y^{\prime }&=y+{\mathrm e}^{-y}+2 t \\ y \left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	5.178
21934	5089	\begin{align*} \left (6 x -2 y\right ) y^{\prime }&=2+3 x -y \\ \end{align*}	✓	✓	✓	✓	5.178
21935	6912	\begin{align*} x +y-1+\left (2 x +2 y-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.178
21936	22300	\begin{align*} {y^{\prime }}^{3}&=y \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.178
21937	17339	\begin{align*} 2 x -y-2+\left (-x +2 y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.179
21938	22425	\begin{align*} y^{2}+2 x^{2}+x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	5.179
21939	15055	\begin{align*} 3 y^{2}-x +2 y \left (y^{2}-3 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.183
21940	15782	\begin{align*} y^{\prime }&=\frac {t}{y} \\ \end{align*}	✓	✓	✓	✓	5.184
21941	12148	\begin{align*} y^{\prime }&=2 x +1+y^{2}-2 x^{2} y+x^{4}+y^{3}-3 y^{2} x^{2}+3 x^{4} y-x^{6} \\ \end{align*}	✓	✓	✓	✗	5.191
21942	25770	\begin{align*} y^{\prime }&=x^{2}-y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.192
21943	16290	\begin{align*} y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	5.193
21944	3457	\begin{align*} \frac {y^{\prime }}{\tan \left (x \right )}-\frac {y}{x^{2}+1}&=0 \\ \end{align*}	✓	✓	✓	✓	5.194
21945	12147	\begin{align*} y^{\prime }&=-\frac {2 x}{3}+1+y^{2}+\frac {2 x^{2} y}{3}+\frac {x^{4}}{9}+y^{3}+y^{2} x^{2}+\frac {x^{4} y}{3}+\frac {x^{6}}{27} \\ \end{align*}	✓	✓	✓	✓	5.194
21946	7399	\begin{align*} x^{2} y^{\prime }&=\frac {4 x^{2}-x -2}{\left (x +1\right ) \left (1+y\right )} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.197
21947	799	\begin{align*} \left (2 x +1\right ) y^{\prime }+y&=\left (2 x +1\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✓	5.198
21948	5093	\begin{align*} \left (x \,{\mathrm e}^{-x}-2 y\right ) y^{\prime }&=2 \,{\mathrm e}^{-2 x} x -\left ({\mathrm e}^{-x}+x \,{\mathrm e}^{-x}-2 y\right ) y \\ \end{align*}	✓	✓	✓	✗	5.198
21949	10134	\begin{align*} w^{\prime }&=-\frac {1}{2}-\frac {\sqrt {1-12 w}}{2} \\ w \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	5.200
21950	19726	\begin{align*} p^{\prime }&=\frac {p+a \,t^{3}-2 p t^{2}}{t \left (-t^{2}+1\right )} \\ \end{align*}	✓	✓	✓	✓	5.207
21951	13649	\begin{align*} y^{\prime } x&=a \,x^{4} y^{3}+\left (b \,x^{2}-1\right ) y+c x \\ \end{align*}	✓	✓	✓	✗	5.215
21952	4401	\begin{align*} y^{\prime }&={\mathrm e}^{\frac {x y^{\prime }}{y}} \\ \end{align*}	✓	✓	✓	✗	5.217
21953	13224	\begin{align*} \left (a \,x^{2}+b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A&=0 \\ \end{align*}	✓	✓	✓	✗	5.218
21954	5118	\begin{align*} \left (a x +b y\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	5.223
21955	20573	\begin{align*} a y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✓	5.223
21956	22388	\begin{align*} y^{\prime }&=\frac {x}{2 y}+\frac {y}{2 x} \\ \end{align*}	✓	✓	✓	✓	5.223
21957	18593	\begin{align*} 3 y x +y^{2}+\left (x^{2}+y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.226
21958	11530	\begin{align*} x y^{\prime } y-y^{2}+a \,x^{3} \cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.227
21959	7860	\begin{align*} x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.228
21960	8437	\begin{align*} \cos \left (x \right )^{2} \sin \left (x \right ) y^{\prime }+\cos \left (x \right )^{3} y&=1 \\ \end{align*}	✓	✓	✓	✓	5.228
21961	8367	\begin{align*} x \sinh \left (y\right ) y^{\prime }&=\cosh \left (y\right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.230
21962	12176	\begin{align*} y^{\prime }&=\frac {x +1+y^{4}-2 y^{2} x^{2}+x^{4}+y^{6}-3 x^{2} y^{4}+3 x^{4} y^{2}-x^{6}}{y} \\ \end{align*}	✓	✓	✓	✗	5.230
21963	13560	\begin{align*} y^{\prime } y&=a \,{\mathrm e}^{\lambda x} y+1 \\ \end{align*}	✗	✓	✓	✗	5.230
21964	11725	\begin{align*} x^{2} {y^{\prime }}^{2}-2 x y^{\prime } y-x^{4}+\left (-x^{2}+1\right ) y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	5.233
21965	20682	\begin{align*} 1+y^{2}-x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	5.233
21966	18614	\begin{align*} y^{\prime }&=a y+b y^{3} \\ \end{align*}	✓	✓	✓	✓	5.234
21967	17904	\begin{align*} x^{3} y^{\prime }-\sin \left (y\right )&=1 \\ y \left (\infty \right ) &= 5 \pi \\ \end{align*}	✓	✗	✗	✗	5.235
21968	14036	\begin{align*} 2 x +3 y-1+\left (2 x +3 y-5\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.236
21969	18377	\begin{align*} \ln \left (x \right ) y^{\prime \prime }-y \sin \left (x \right )&=0 \\ y \left ({\mathrm e}\right ) &= {\mathrm e}^{-1} \\ y^{\prime }\left ({\mathrm e}\right ) &= 0 \\ \end{align*} Series expansion around \(x={\mathrm e}\).	✓	✓	✓	✓	5.237
21970	6288	\begin{align*} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\left (a -x \right ) \left (b -x \right ) \left (c -x \right ) \left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (a -x \right )^{2} \left (b -x \right )^{2} \left (c -x \right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	5.242
21971	5133	\begin{align*} x y^{\prime } y+x^{2} \operatorname {arccot}\left (\frac {y}{x}\right )-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.243
21972	11383	\begin{align*} y^{\prime }-a \left (1+\tan \left (y\right )^{2}\right )+\tan \left (y\right ) \tan \left (x \right )&=0 \\ \end{align*}	✗	✗	✗	✗	5.245
21973	15848	\begin{align*} y^{\prime }&=\sqrt {y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	5.245
21974	21400	\begin{align*} y^{\prime }+\tan \left (\theta \right ) y&=\cos \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	5.246
21975	19379	\begin{align*} \left ({\mathrm e}^{x}-3 y^{2} x^{2}\right ) y^{\prime }+{\mathrm e}^{x} y&=2 x y^{3} \\ \end{align*}	✓	✓	✓	✗	5.247
21976	1160	\begin{align*} y^{\prime }&=\frac {4 y-3 x}{2 x -y} \\ \end{align*}	✓	✓	✓	✓	5.248
21977	4862	\begin{align*} 3 y^{\prime } x&=\left (2+x y^{3}\right ) y \\ \end{align*}	✓	✓	✓	✓	5.251
21978	24207	\begin{align*} y \left (2 y x +1\right )-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	5.251
21979	18604	\begin{align*} x y^{\prime } y&=y^{2}+x^{2} \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.253
21980	20303	\begin{align*} -y+y^{\prime } x&=\sqrt {y^{2}+x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.253
21981	23949	\begin{align*} {\mathrm e}^{x} \cos \left (y\right )+x -\left ({\mathrm e}^{x} \sin \left (y\right )+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.257
21982	17249	\begin{align*} \frac {9 t}{5}+2 y+\left (2 t +2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.261
21983	18603	\begin{align*} \left (y+{\mathrm e}^{\frac {x}{y}} x \right ) y^{\prime }&={\mathrm e}^{\frac {x}{y}} y \\ \end{align*}	✓	✓	✓	✓	5.261
21984	15049	\begin{align*} y^{\prime }&=\frac {3 x -4 y-2}{3 x -4 y-3} \\ \end{align*}	✓	✓	✓	✓	5.263
21985	11928	\begin{align*} y^{\prime }&=\left (-\ln \left (y\right )+x \right ) y \\ \end{align*}	✓	✓	✓	✓	5.266
21986	11427	\begin{align*} y^{\prime } x +a y-f \left (x \right ) g \left (x^{a} y\right )&=0 \\ \end{align*}	✗	✓	✓	✗	5.270
21987	2880	\begin{align*} x +y+\left (x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.273
21988	8662	\begin{align*} x y^{\prime } y&=\sqrt {1+y^{2}} \\ \end{align*}	✓	✓	✓	✓	5.273
21989	166	\begin{align*} y^{\prime }&=-\frac {y \left (2 x^{3}-y^{3}\right )}{x \left (2 y^{3}-x^{3}\right )} \\ \end{align*}	✓	✓	✓	✓	5.274
21990	22465	\begin{align*} x^{3}+y+\left (x^{2} y-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.274
21991	18057	\begin{align*} 1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.276
21992	3320	\begin{align*} 3 {y^{\prime }}^{4} x&=y {y^{\prime }}^{3}+1 \\ \end{align*}	✓	✓	✗	✗	5.277
21993	3681	\begin{align*} \frac {y^{\prime }}{y}-\frac {2 \ln \left (y\right )}{x}&=\frac {1-2 \ln \left (x \right )}{x} \\ y \left (1\right ) &= {\mathrm e} \\ \end{align*}	✓	✓	✓	✓	5.280
21994	14271	\begin{align*} x^{\prime }&=a x+b x^{3} \\ \end{align*}	✓	✓	✓	✓	5.280
21995	4320	\begin{align*} \left (3+2 x +4 y\right ) y^{\prime }&=x +2 y+1 \\ \end{align*}	✓	✓	✓	✓	5.283
21996	10008	\begin{align*} x^{2} y^{\prime }+y^{2}&=x y^{\prime } y \\ \end{align*}	✓	✓	✓	✓	5.283
21997	17064	\begin{align*} y^{\prime }&=t y^{2} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	5.286
21998	8710	\begin{align*} y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.289
21999	19769	\begin{align*} y^{\prime \prime }&=-m^{2} y \\ \end{align*}	✓	✓	✓	✓	5.289
22000	4318	\begin{align*} \left (1-{\mathrm e}^{-\frac {y}{x}}\right ) y^{\prime }+1-\frac {y}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	5.291