2.3.201 Problems 20001 to 20100

Table 2.933: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
20001	14461	\begin{align*} \tan \left (\theta \right )+2 r \theta ^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.107
20002	7338	\begin{align*} 3 x^{3} y^{2} y^{\prime }-x^{2} y^{3}&=1 \\ \end{align*}	✓	✓	✓	✓	3.108
20003	7855	\begin{align*} 4 y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.108
20004	7922	\begin{align*} y+\left (y x +x -3 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.108
20005	8751	\begin{align*} 3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.108
20006	15522	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ y \left (0\right ) &= 0 \\ y \left (2\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	3.108
20007	18477	\begin{align*} y^{\prime }&=\sin \left (2 x \right )^{2} \cos \left (y\right )^{2} \\ \end{align*}	✓	✓	✓	✗	3.108
20008	14437	\begin{align*} y^{\prime }&=\frac {y^{2}}{x -2} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.109
20009	19687	\begin{align*} t^{2} x^{\prime \prime }-2 t x^{\prime }+2 x&=0 \\ \end{align*}	✓	✓	✓	✓	3.109
20010	19790	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=\csc \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.109
20011	141	\begin{align*} \cos \left (x \right )+\ln \left (y\right )+\left (\frac {x}{y}+{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.111
20012	15967	\begin{align*} y^{\prime }&=t^{2} y+1+y+t^{2} \\ \end{align*}	✓	✓	✓	✓	3.112
20013	21996	\begin{align*} \cos \left (x \right ) x +\left (1-6 y^{5}\right ) y^{\prime }&=0 \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.112
20014	1660	\begin{align*} y^{\prime }&=\frac {x y^{2}+2 y^{3}}{x^{3}+x^{2} y+x y^{2}} \\ \end{align*}	✓	✓	✓	✗	3.113
20015	5322	\begin{align*} \left (4 x -x y^{3}-2 y^{4}\right ) y^{\prime }&=\left (2+y^{3}\right ) y \\ \end{align*}	✓	✓	✓	✓	3.114
20016	16975	\begin{align*} y^{\prime }&=-\frac {x}{y} \\ \end{align*}	✓	✓	✓	✓	3.114
20017	19758	\begin{align*} 5 x^{\prime }+x&=\sin \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	3.115
20018	3384	\begin{align*} x^{2} y^{\prime \prime }+x \left (x -7\right ) y^{\prime }+\left (x +12\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	3.118
20019	14980	\begin{align*} -y-3 y^{\prime } x +\left (1-x \right ) x y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.122
20020	25734	\begin{align*} 2 y^{\prime \prime }-3 y^{2}&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.122
20021	11495	\begin{align*} \cos \left (x \right ) y^{\prime }+y+\left (1+\sin \left (x \right )\right ) \cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.123
20022	23884	\begin{align*} \frac {2 x}{y}+5 y^{2}-4 x +\left (3 y^{2}-\frac {x^{2}}{y^{2}}+10 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.123
20023	7010	\begin{align*} y^{\prime } x -y^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✓	3.124
20024	10112	\begin{align*} y^{\prime \prime }-y x -x^{6}-x^{3}+42&=0 \\ \end{align*}	✓	✓	✓	✓	3.125
20025	12480	\begin{align*} x^{2} y^{\prime \prime }+\left (-x^{4}+\left (2 n +2 a +1\right ) x^{2}+\left (-1\right )^{n} a -a^{2}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.125
20026	12996	\begin{align*} \left (1-2 y\right ) {y^{\prime }}^{2}+\left (1+y^{2}\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.125
20027	2342	\begin{align*} 2 t \cos \left (y\right )+3 t^{2} y+\left (t^{3}-t^{2} \sin \left (y\right )-y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	3.128
20028	7527	\begin{align*} \left (x^{2}-\frac {2}{y^{3}}\right ) y^{\prime }+2 y x -3 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.128
20029	11342	\begin{align*} y^{\prime }+3 a y^{3}+6 a x y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	3.128
20030	11547	\begin{align*} \left (x^{2} y-1\right ) y^{\prime }+x y^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✗	3.129
20031	4362	\begin{align*} \left (y^{3}+\frac {x}{y}\right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	3.130
20032	693	\begin{align*} x^{2} y^{\prime }&=1-x^{2}+y^{2}-y^{2} x^{2} \\ \end{align*}	✓	✓	✓	✓	3.131
20033	739	\begin{align*} \left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	3.131
20034	4888	\begin{align*} x^{2} y^{\prime }+a y^{2}+b \,x^{2} y^{3}&=0 \\ \end{align*}	✗	✓	✓	✗	3.131
20035	14050	\begin{align*} 2 y^{\prime } x -y+\ln \left (y^{\prime }\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.132
20036	7845	\begin{align*} y^{\prime } x&=2 y \\ \end{align*}	✓	✓	✓	✓	3.133
20037	20310	\begin{align*} y^{\prime } y+b y^{2}&=a \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.133
20038	21011	\begin{align*} t x^{\prime }+x&=2 t^{2} \\ \end{align*}	✓	✓	✓	✓	3.133
20039	23859	\begin{align*} x y^{\prime } y+x^{6}-2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.133
20040	6979	\begin{align*} y^{\prime } x +x y^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✓	3.135
20041	8373	\begin{align*} \left (-2+2 y\right ) y^{\prime }&=3 x^{2}+4 x +2 \\ y \left (1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	3.135
20042	16955	\begin{align*} y^{\prime } y+y^{4}&=\sin \left (x \right ) \\ \end{align*}	✗	✓	✗	✗	3.135
20043	22431	\begin{align*} 3 x +2 y^{2}+2 x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	3.135
20044	10422	\begin{align*} 3 y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+\sin \left (y\right ) {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.136
20045	4672	\begin{align*} y^{\prime }&=a_{0} +a_{1} y+a_{2} y^{2} \\ \end{align*}	✓	✓	✓	✓	3.138
20046	7394	\begin{align*} x +x y^{2}+{\mathrm e}^{x^{2}} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.138
20047	12379	\begin{align*} y^{\prime \prime } x +\left (b -x \right ) y^{\prime }-a y&=0 \\ \end{align*}	✗	✓	✓	✗	3.138
20048	4859	\begin{align*} 2 \left (1-x \right ) y^{\prime }&=4 x \sqrt {1-x}+y \\ \end{align*}	✓	✓	✓	✓	3.142
20049	13995	\begin{align*} 4 y^{\prime } x +3 y+{\mathrm e}^{x} x^{4} y^{5}&=0 \\ \end{align*}	✓	✓	✓	✓	3.143
20050	14883	\begin{align*} x^{\prime }&=\left (1+x\right ) \left (2-x\right ) \sin \left (x\right ) \\ \end{align*}	✓	✓	✓	✓	3.146
20051	3605	\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*}	✓	✓	✓	✓	3.147
20052	18838	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&={\mathrm e}^{t} \cos \left (2 t \right )+{\mathrm e}^{2 t} \left (3 t +4\right ) \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	3.147
20053	20971	\begin{align*} y^{\prime }&=\frac {\cos \left (x \right )}{\cos \left (y\right )^{2}} \\ y \left (\pi \right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✓	3.147
20054	25676	\begin{align*} y^{\prime }&=-\frac {x}{y} \\ \end{align*}	✓	✓	✓	✓	3.147
20055	7395	\begin{align*} \frac {y^{\prime }}{y}+y \,{\mathrm e}^{\cos \left (x \right )} \sin \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.148
20056	18066	\begin{align*} 2 x^{5}+4 x^{3} y-2 x y^{2}+\left (y^{2}+2 x^{2} y-x^{4}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.148
20057	25752	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=\sec \left (\ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	3.148
20058	2862	\begin{align*} \cos \left (y\right ) \sin \left (x \right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.149
20059	4678	\begin{align*} y^{\prime }&=x \left (2+x^{2} y-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	3.150
20060	7847	\begin{align*} y&=y^{\prime } x +{y^{\prime }}^{4} \\ \end{align*}	✓	✓	✓	✗	3.150
20061	5621	\begin{align*} {y^{\prime }}^{3}-a x y^{\prime }+x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	3.151
20062	11582	\begin{align*} \left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }-3 x y^{2}+x&=0 \\ \end{align*}	✓	✓	✓	✗	3.152
20063	5922	\begin{align*} c y+\left (b x +a \right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✓	✓	✗	3.153
20064	17911	\begin{align*} x -y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.153
20065	19322	\begin{align*} y+\left (2 x -{\mathrm e}^{y} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.153
20066	13936	\begin{align*} y^{\prime \prime }-y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}+\frac {1}{4}-\frac {\lambda ^{2}}{4}\right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	3.154
20067	21669	\begin{align*} x^{4} \left (x^{2}+1\right ) \left (x -1\right )^{2} y^{\prime \prime }+4 x^{3} \left (x -1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✗	3.154
20068	2479	\begin{align*} \sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.156
20069	12922	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✗	3.157
20070	2924	\begin{align*} \frac {2}{y}-\frac {y}{x^{2}}+\left (\frac {1}{x}-\frac {2 x}{y^{2}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.158
20071	5083	\begin{align*} \left (x -2 y+1\right ) y^{\prime }&=1+2 x -y \\ \end{align*}	✓	✓	✓	✓	3.158
20072	23858	\begin{align*} y^{2} \sec \left (x \right )^{2} y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	3.159
20073	12699	\begin{align*} y^{\prime \prime }&=-\frac {\left (4 v \left (v +1\right ) \sin \left (x \right )^{2}-\cos \left (x \right )^{2}+2-4 n^{2}\right ) y}{4 \sin \left (x \right )^{2}} \\ \end{align*}	✗	✓	✓	✗	3.161
20074	11697	\begin{align*} x {y^{\prime }}^{2}+x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.163
20075	5021	\begin{align*} y^{\prime } \sqrt {-x^{4}+1}&=\sqrt {1-y^{4}} \\ \end{align*}	✓	✓	✓	✓	3.164
20076	136	\begin{align*} 4 x -y+\left (6 y-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.165
20077	17246	\begin{align*} 2 t -y^{2} \sin \left (t y\right )+\left (\cos \left (t y\right )-t y \sin \left (t y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.165
20078	17205	\begin{align*} {\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	3.166
20079	20951	\begin{align*} y^{\prime }&=y \left (y-2\right ) \left (3+y\right ) \\ \end{align*}	✓	✓	✓	✓	3.166
20080	14041	\begin{align*} y^{\prime } x -y^{2} \ln \left (x \right )+y&=0 \\ \end{align*}	✓	✓	✓	✓	3.167
20081	15564	\begin{align*} y^{\prime }&=\frac {y}{x}+\tan \left (x \right ) \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.167
20082	7864	\begin{align*} 1+2 y-\left (4-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.168
20083	11763	\begin{align*} 9 y {y^{\prime }}^{2}+4 x^{3} y^{\prime }-4 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	3.168
20084	17884	\begin{align*} y^{\prime }&=a^{x +y} \\ \end{align*}	✓	✓	✓	✓	3.168
20085	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*}	✓	✓	✓	✗	3.169
20086	15137	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+4 x^{2} y&=1 \\ \end{align*}	✗	✓	✓	✗	3.171
20087	11759	\begin{align*} \left (x +y\right ) {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	3.173
20088	24267	\begin{align*} \left (t^{2}+1\right ) s^{\prime }+2 t \left (s t^{2}-3 \left (t^{2}+1\right )^{2}\right )&=0 \\ s \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.173
20089	15612	\begin{align*} y^{\prime }&=\frac {y}{-x^{2}+1}+\sqrt {x} \\ y \left (\frac {1}{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.176
20090	4395	\begin{align*} x y^{2} \left (y^{\prime } x +y\right )&=1 \\ \end{align*}	✓	✓	✓	✓	3.178
20091	6031	\begin{align*} \left (b \,x^{2}+a \right ) y+x^{2} y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	3.181
20092	7033	\begin{align*} \left (y x -1\right )^{2} x y^{\prime }+\left (y^{2} x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.181
20093	15490	\begin{align*} y^{\prime }-2 \sqrt {{| y|}}&=0 \\ \end{align*}	✓	✓	✓	✓	3.181
20094	3661	\begin{align*} 2 x \left (y^{\prime }+x^{2} y^{3}\right )+y&=0 \\ \end{align*}	✓	✓	✓	✓	3.182
20095	20153	\begin{align*} \left (x^{3}+x +1\right ) y^{\prime \prime \prime }+\left (3+6 x \right ) y^{\prime \prime }+6 y&=0 \\ \end{align*}	✗	✗	✗	✗	3.182
20096	23900	\begin{align*} 2 x +2 x y^{2}-y^{3}-y^{5}+\left (1-3 x y^{2}-3 y^{4} x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.182
20097	12606	\begin{align*} y^{\prime \prime }&=-\frac {\left (x^{2} a \left (-a +1\right )-b \left (x +b \right )\right ) y}{x^{4}} \\ \end{align*}	✗	✓	✓	✗	3.184
20098	19708	\begin{align*} v^{\prime }+u^{2} v&=\sin \left (u \right ) \\ \end{align*}	✓	✓	✓	✓	3.184
20099	3385	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x -4\right ) y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.185
20100	11435	\begin{align*} x^{2} y^{\prime }+x^{2}+y x +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.185