2.3.209 Problems 20801 to 20900

Table 2.991: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
20801	11343	\begin{align*} a x y^{3}+b y^{2}+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.070
20802	15293	\begin{align*} x^{\prime }&=-3 x+3 y+z+5 \sin \left (2 t \right ) \\ y^{\prime }&=x-5 y-3 z+5 \cos \left (2 t \right ) \\ z^{\prime }&=-3 x+7 y+3 z+23 \,{\mathrm e}^{t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 2 \\ z \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	5.070
20803	19914	\begin{align*} {\mathrm e}^{x} x^{4}-2 m x y^{2}+2 m \,x^{2} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.073
20804	2324	\begin{align*} \sqrt {t^{2}+1}\, y^{\prime }&=\frac {t y^{3}}{\sqrt {t^{2}+1}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.074
20805	11505	\begin{align*} y y^{\prime }+4 x \left (x +1\right )+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.074
20806	11972	\begin{align*} y^{\prime }&=\frac {y x -y-{\mathrm e}^{x +1} x^{3}+{\mathrm e}^{x +1} x y^{2}}{\left (x -1\right ) x} \\ \end{align*}	✓	✓	✓	✗	5.074
20807	21030	\begin{align*} x^{\prime }&=x^{2} \\ x \left (t_{0} \right ) &= a \\ \end{align*}	✓	✓	✓	✓	5.074
20808	12343	\begin{align*} y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+v \left (v +1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	5.078
20809	15520	\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (2\right ) &= -12 \\ \end{align*}	✓	✓	✓	✓	5.080
20810	5297	\begin{align*} y \left (2 y^{2}+1\right ) y^{\prime }&=x \left (2 x^{2}+1\right ) \\ \end{align*}	✓	✓	✓	✓	5.084
20811	14723	\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y&=2 x^{3} \\ y \left (2\right ) &= 0 \\ y^{\prime }\left (2\right ) &= -8 \\ \end{align*}	✓	✓	✓	✓	5.084
20812	17792	\begin{align*} x^{2} y^{\prime \prime }-7 x y^{\prime }+\left (-2 x^{2}+7\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	5.084
20813	11903	\begin{align*} y^{\prime }&=\frac {y^{2}+2 y x +x^{2}+{\mathrm e}^{2 F \left (-\left (x -y\right ) \left (x +y\right )\right )}}{y^{2}+2 y x +x^{2}-{\mathrm e}^{2 F \left (-\left (x -y\right ) \left (x +y\right )\right )}} \\ \end{align*}	✓	✓	✓	✗	5.089
20814	18361	\begin{align*} y^{\prime \prime }+\alpha y^{\prime }&=0 \\ y \left (0\right ) &= {\mathrm e}^{\alpha } \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.089
20815	21098	\begin{align*} x&=x^{\prime } t -{\mathrm e}^{x^{\prime }} \\ \end{align*}	✓	✓	✓	✓	5.090
20816	1003	\begin{align*} x_{1}^{\prime }&=9 x_{1}+13 x_{2}-13 x_{6} \\ x_{2}^{\prime }&=-14 x_{1}+19 x_{2}-10 x_{3}-20 x_{4}+10 x_{5}+4 x_{6} \\ x_{3}^{\prime }&=-30 x_{1}+12 x_{2}-7 x_{3}-30 x_{4}+12 x_{5}+18 x_{6} \\ x_{4}^{\prime }&=-12 x_{1}+10 x_{2}-10 x_{3}-9 x_{4}+10 x_{5}+2 x_{6} \\ x_{5}^{\prime }&=6 x_{1}+9 x_{2}+6 x_{4}+5 x_{5}-15 x_{6} \\ x_{6}^{\prime }&=-14 x_{1}+23 x_{2}-10 x_{3}-20 x_{4}+10 x_{5} \\ \end{align*}	✓	✓	✓	✓	5.092
20817	4428	\begin{align*} y \ln \left (x \right ) \ln \left (y\right )+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.092
20818	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*}	✗	✓	✓	✗	5.092
20819	20831	\begin{align*} x y^{\prime }-y^{2}+\left (2 x +1\right ) y&=x^{2}+2 x \\ \end{align*}	✓	✓	✓	✓	5.092
20820	22767	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.092
20821	4647	\begin{align*} y^{\prime }&=\left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y \\ \end{align*}	✓	✓	✓	✓	5.093
20822	22987	\begin{align*} y^{\prime }+y \tan \left (x \right )&=\sec \left (x \right ) \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	5.093
20823	11767	\begin{align*} \left (a y-x^{2}\right ) {y^{\prime }}^{2}+2 x y {y^{\prime }}^{2}-y^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	5.094
20824	5044	\begin{align*} y y^{\prime }&=a_{0} +a_{1} y+a_{2} y^{2} \\ \end{align*}	✓	✓	✓	✓	5.095
20825	5448	\begin{align*} {y^{\prime }}^{2} x&=\left (-x +a \right )^{2} \\ \end{align*}	✓	✓	✓	✓	5.095
20826	7404	\begin{align*} y^{\prime }&=x^{2} \left (y+1\right ) \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	5.095
20827	8373	\begin{align*} \left (-2+2 y\right ) y^{\prime }&=3 x^{2}+4 x +2 \\ y \left (1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	5.096
20828	17306	\begin{align*} y&=t \left (2-y^{\prime }\right )+2 {y^{\prime }}^{2}+1 \\ \end{align*}	✓	✓	✓	✗	5.098
20829	13286	\begin{align*} y^{\prime }&=y^{2}+a \,{\mathrm e}^{\lambda x} y-a \,{\mathrm e}^{\lambda x} b -b^{2} \\ \end{align*}	✓	✓	✓	✗	5.099
20830	1646	\begin{align*} x^{2} y^{\prime }&=x^{2}+y x +y^{2} \\ \end{align*}	✓	✓	✓	✓	5.100
20831	4844	\begin{align*} \left (x +a \right ) y^{\prime }&=2 \left (x +a \right )^{5}+3 y \\ \end{align*}	✓	✓	✓	✓	5.102
20832	5487	\begin{align*} 4 {y^{\prime }}^{2} x&=\left (a -3 x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	5.103
20833	14457	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+4 y x&=0 \\ \end{align*}	✓	✓	✓	✓	5.103
20834	20404	\begin{align*} {y^{\prime }}^{3}+y^{\prime }&={\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✗	5.104
20835	11480	\begin{align*} x^{4} \left (y^{\prime }+y^{2}\right )+a&=0 \\ \end{align*}	✓	✓	✓	✓	5.105
20836	2975	\begin{align*} y^{2}+1+\left (2 y x -y^{2}\right ) y^{\prime }&=0 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	5.106
20837	3527	\begin{align*} y^{\prime }&=1-\frac {\sin \left (x +y\right )}{\cos \left (x \right ) \sin \left (y\right )} \\ y \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✓	5.106
20838	4408	\begin{align*} y^{\prime }&=\frac {1}{y x +x^{3} y^{3}} \\ \end{align*}	✓	✓	✓	✓	5.107
20839	11979	\begin{align*} y^{\prime }&=\frac {y \ln \left (x -1\right )+{\mathrm e}^{x +1} x^{3}+7 \,{\mathrm e}^{x +1} x y^{2}}{\ln \left (x -1\right ) x} \\ \end{align*}	✓	✓	✓	✗	5.108
20840	4769	\begin{align*} x y^{\prime }&=x^{3}+\left (-2 x^{2}+1\right ) y \\ \end{align*}	✓	✓	✓	✓	5.111
20841	25849	\begin{align*} 3 y^{2}+y \sin \left (2 y x \right )+\left (6 y x +x \sin \left (2 y x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.111
20842	8461	\begin{align*} y^{\prime }+\left (\left \{\begin {array}{cc} 1 & 0\le x \le 2 \\ 5 & 2<x \end {array}\right .\right ) y&=0 \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✗	5.112
20843	15521	\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \\ y^{\prime }\left (1\right ) &= 3 \\ y^{\prime }\left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.112
20844	21071	\begin{align*} {\mathrm e}^{x}-\frac {y^{2}}{2}+\left ({\mathrm e}^{y}-y x \right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.114
20845	3969	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=2 \sin \left (t \right )+\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (1+\cos \left (t \right )\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	5.115
20846	6186	\begin{align*} \operatorname {a2} y+\operatorname {a1} \left (b x +a \right ) y^{\prime }+\left (b x +a \right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.115
20847	21383	\begin{align*} 3 x^{2}+4 y x +\left (2 x^{2}+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.115
20848	4306	\begin{align*} \cos \left (y\right )^{2}+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.117
20849	7400	\begin{align*} \frac {y^{\prime }}{\theta }&=\frac {y \sin \left (\theta \right )}{y^{2}+1} \\ y \left (\pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	5.118
20850	21977	\begin{align*} y^{\prime }&=\frac {y^{2}}{x} \\ \end{align*}	✓	✓	✓	✓	5.119
20851	17952	\begin{align*} \cos \left (x \right ) y^{\prime }-y \sin \left (x \right )&=-\sin \left (2 x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.121
20852	10019	\begin{align*} p^{\prime }&=a p-b p^{2} \\ p \left (\operatorname {t0} \right ) &= \operatorname {p0} \\ \end{align*}	✓	✓	✓	✓	5.122
20853	22994	\begin{align*} y^{\prime }&=\frac {y x +a^{2}}{a^{2}-x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.122
20854	22998	\begin{align*} v^{\prime }&=60 t -4 v \\ v \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.122
20855	5857	\begin{align*} \left (\cot \left (x \right )+\csc \left (x \right )\right ) y^{\prime }+y^{\prime \prime }&=1+a \csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	5.123
20856	26613	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{-2 x} \left (9 \sin \left (2 x \right )+8 \cos \left (2 x \right )\right ) \\ y \left (\infty \right ) &= 0 \\ \end{align*}	✗	✓	✗	✓	5.123
20857	14484	\begin{align*} y^{\prime }+4 y x&=8 x \\ \end{align*}	✓	✓	✓	✓	5.124
20858	19949	\begin{align*} x^{2}+y^{2}+1-2 x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.125
20859	2541	\begin{align*} y^{\prime }&=t y^{3}-y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.126
20860	24258	\begin{align*} \left (x +a \right ) y^{\prime }&=b x -n y \\ \end{align*}	✓	✓	✓	✓	5.126
20861	20524	\begin{align*} y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=2 x \\ \end{align*}	✓	✓	✓	✗	5.128
20862	21372	\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.128
20863	18946	\begin{align*} 2 y^{\prime \prime }+y^{\prime }+6 y&=\delta \left (t -\frac {\pi }{6}\right ) \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	5.132
20864	2486	\begin{align*} 4 y t +\left (t^{2}+1\right ) y^{\prime }&=t \\ y \left (1\right ) &= {\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	5.133
20865	11439	\begin{align*} x^{2} \left (y^{\prime }+y^{2}\right )+4 y x +2&=0 \\ \end{align*}	✓	✓	✓	✓	5.134
20866	23876	\begin{align*} y^{\prime }&=1+\frac {3 y}{x} \\ \end{align*}	✓	✓	✓	✓	5.134
20867	3464	\begin{align*} \left (y^{3}+x \right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✗	5.137
20868	16227	\begin{align*} y y^{\prime }&=3 \sqrt {x y^{2}+9 x} \\ y \left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✗	5.137
20869	6969	\begin{align*} y^{\prime }+y&=x y^{3} \\ \end{align*}	✓	✓	✓	✓	5.138
20870	11479	\begin{align*} \left (a \,x^{2}+b x +c \right ) \left (x y^{\prime }-y\right )-y^{2}+x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	5.138
20871	21765	\begin{align*} 1+{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.138
20872	9594	\begin{align*} \left (1-2 \sin \left (x \right )\right ) y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.139
20873	16340	\begin{align*} x y^{2}-6+x^{2} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.139
20874	21976	\begin{align*} y^{\prime }&=\frac {x +y}{x} \\ \end{align*}	✓	✓	✓	✓	5.139
20875	11859	\begin{align*} f \left (x -\frac {3 {y^{\prime }}^{2}}{2}\right )+{y^{\prime }}^{3}-y&=0 \\ \end{align*}	✗	✓	✓	✗	5.140
20876	5746	\begin{align*} y^{\prime \prime }&=\left (x^{2}+a \right ) y \\ \end{align*}	✗	✓	✓	✗	5.141
20877	6275	\begin{align*} -y-2 \left (-x +a \right )^{3} y^{\prime }+\left (-x +a \right )^{4} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.142
20878	11885	\begin{align*} y^{\prime }&=\frac {y^{2} \left (2+F \left (\frac {x^{2}-y}{y x^{2}}\right ) x^{2}\right )}{x^{3}} \\ \end{align*}	✗	✓	✓	✗	5.142
20879	17936	\begin{align*} y^{\prime }-y \tan \left (x \right )&=\frac {1}{\cos \left (x \right )^{3}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.142
20880	4700	\begin{align*} y^{\prime }+\left (\tan \left (x \right )+y^{2} \sec \left (x \right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	5.144
20881	4918	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=1-y \left (2 x -y\right ) \\ \end{align*}	✓	✓	✓	✓	5.144
20882	13320	\begin{align*} y^{\prime }&=y^{2}-a^{2}+a \lambda \sinh \left (\lambda x \right )-a^{2} \sinh \left (\lambda x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	5.145
20883	25430	\begin{align*} y^{\prime }-a \left (t \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	5.145
20884	25821	\begin{align*} y^{\prime }&={\mathrm e}^{3 x +2 y} \\ \end{align*}	✓	✓	✓	✓	5.145
20885	3043	\begin{align*} x y^{\prime }-2 y-2 x^{4} y^{3}&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.147
20886	4835	\begin{align*} \left (x +1\right ) y^{\prime }&=\left (x +1\right )^{4}+2 y \\ \end{align*}	✓	✓	✓	✓	5.148
20887	24867	\begin{align*} {y^{\prime }}^{2}+y y^{\prime }-x -1&=0 \\ \end{align*}	✓	✓	✓	✗	5.148
20888	25500	\begin{align*} y^{\prime }&=\left (y+4\right ) \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	5.148
20889	4441	\begin{align*} 2 x y^{4} {\mathrm e}^{y}+2 x y^{3}+y+\left (x^{2} y^{4} {\mathrm e}^{y}-x^{2} y^{2}-3 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.149
20890	7706	\begin{align*} x y^{\prime }+3 y&=x^{2} y^{2} \\ \end{align*}	✓	✓	✓	✓	5.151
20891	15015	\begin{align*} \tan \left (y\right )-\cot \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.151
20892	25090	\begin{align*} t y^{\prime }+y&=\ln \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	5.153
20893	1604	\begin{align*} y^{\prime }+y&=\frac {2 x \,{\mathrm e}^{-x}}{1+y \,{\mathrm e}^{x}} \\ \end{align*}	✓	✓	✓	✗	5.154
20894	13003	\begin{align*} 3 \left (1-y\right ) y y^{\prime \prime }-2 \left (-2 y+1\right ) {y^{\prime }}^{2}-h \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	5.155
20895	53	\begin{align*} y^{3} y^{\prime }&=\left (1+y^{4}\right ) \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.158
20896	5439	\begin{align*} 3 {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	5.159
20897	8383	\begin{align*} 2 x \sin \left (y\right )^{2}-\left (x^{2}+10\right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.159
20898	4618	\begin{align*} y^{\prime }&=a \,x^{n} y \\ \end{align*}	✓	✓	✓	✓	5.161
20899	8433	\begin{align*} x y^{\prime }+\left (x +1\right ) y&=\sin \left (2 x \right ) {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	5.161
20900	8777	\begin{align*} y^{\prime }&=x^{2} \left (1+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	5.161