2.3.211 Problems 21001 to 21100

Table 2.953: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
21001	17204	\begin{align*} \ln \left (t y\right )+\frac {t y^{\prime }}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	3.976
21002	3642	\begin{align*} y^{\prime } x +y \ln \left (x \right )&=y \ln \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	3.977
21003	7217	\begin{align*} y^{\prime } x&=y \\ y \left (2\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.977
21004	13727	\begin{align*} y^{\prime \prime } x +\left (1-3 n \right ) y^{\prime }-a^{2} n^{2} x^{2 n -1} y&=0 \\ \end{align*}	✗	✓	✓	✗	3.979
21005	22424	\begin{align*} \left (x^{2}+2 y \,{\mathrm e}^{2 x}\right ) y^{\prime }+2 y x +2 y^{2} {\mathrm e}^{2 x}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.979
21006	4680	\begin{align*} y^{\prime }&=a x y^{2} \\ \end{align*}	✓	✓	✓	✓	3.980
21007	8665	\begin{align*} y^{\prime } x +y&=y^{2} \\ y \left (1\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	3.980
21008	747	\begin{align*} x^{2} y^{\prime }+2 y x&=5 y^{3} \\ \end{align*}	✓	✓	✓	✓	3.984
21009	734	\begin{align*} \left (x +2 y\right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	3.987
21010	23257	\begin{align*} \left (1+a \cos \left (2 x \right )\right ) y^{\prime \prime }+\lambda y&=0 \\ \end{align*}	✗	✓	✗	✗	3.987
21011	2866	\begin{align*} 1+y^{2}&=\frac {y^{\prime }}{x^{3} \left (x -1\right )} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.991
21012	22010	\begin{align*} y^{\prime }&=\frac {2 x y}{x^{2}-y^{2}} \\ \end{align*}	✓	✓	✓	✓	3.991
21013	24958	\begin{align*} 1-y^{2}-t y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.992
21014	24032	\begin{align*} y^{\left (8\right )}+8 y^{\left (7\right )}+28 y^{\left (6\right )}+56 y^{\left (5\right )}+70 y^{\prime \prime \prime \prime }+56 y^{\prime \prime \prime }+28 y^{\prime \prime }+8 y^{\prime }&={\mathrm e}^{-x} x^{9} \\ \end{align*}	✓	✓	✓	✗	3.993
21015	4423	\begin{align*} y^{4}+y x +\left (x y^{3}-x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.994
21016	13725	\begin{align*} y^{\prime \prime } x +a y^{\prime }+\left (b x +c \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.994
21017	15852	\begin{align*} y^{\prime }&=y \left (y-1\right ) \left (y-3\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.994
21018	8168	\begin{align*} 2 y^{\prime }&=y^{3} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.996
21019	1204	\begin{align*} \frac {x}{\left (y^{2}+x^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (y^{2}+x^{2}\right )^{{3}/{2}}}&=0 \\ \end{align*}	✓	✓	✓	✓	3.998
21020	19492	\begin{align*} y^{\prime \prime } x +\left (x^{2}-1\right ) y^{\prime }+x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✗	3.998
21021	2332	\begin{align*} y^{\prime }&=\frac {t +y}{t -y} \\ \end{align*}	✓	✓	✓	✓	4.000
21022	11862	\begin{align*} y^{\prime }&=-\frac {a x}{2}+F \left (y+\frac {a \,x^{2}}{4}+\frac {b x}{2}\right ) \\ \end{align*}	✓	✓	✓	✗	4.000
21023	19199	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.002
21024	4690	\begin{align*} y^{\prime }+\left (a x +y\right ) y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	4.003
21025	5198	\begin{align*} \left (1-x^{3} y\right ) y^{\prime }&=y^{2} x^{2} \\ \end{align*}	✓	✓	✓	✗	4.005
21026	22515	\begin{align*} x^{2}+y^{2}+2 x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	4.006
21027	23892	\begin{align*} x^{4}-3 y+3 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.007
21028	11857	\begin{align*} a \,x^{n} f \left (y^{\prime }\right )+y^{\prime } x -y&=0 \\ \end{align*}	✗	✓	✓	✗	4.008
21029	4303	\begin{align*} \sqrt {x^{2}+1}\, y^{\prime }+\sqrt {1+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	4.009
21030	23150	\begin{align*} y^{\prime }&=\frac {\left (a -x \right ) y}{d \,x^{2}+c x +b} \\ \end{align*}	✓	✓	✓	✓	4.010
21031	18579	\begin{align*} \frac {x}{\left (y^{2}+x^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (y^{2}+x^{2}\right )^{{3}/{2}}}&=0 \\ \end{align*}	✓	✓	✓	✓	4.012
21032	15763	\begin{align*} y_{1}^{\prime }&=y_{2} \\ y_{2}^{\prime }&=-3 y_{1}+2 y_{3} \\ y_{3}^{\prime }&=y_{4} \\ y_{4}^{\prime }&=2 y_{1}-5 y_{3} \\ \end{align*}	✓	✓	✓	✓	4.013
21033	12873	\begin{align*} b \sin \left (y\right )+a {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.017
21034	9989	\begin{align*} y^{\prime }&=\frac {\sec \left (x \right ) \left (\sin \left (y\right )+y\right )}{x} \\ \end{align*}	✓	✓	✓	✓	4.019
21035	4798	\begin{align*} y^{\prime } x +y&=a \left (x^{2}+1\right ) y^{3} \\ \end{align*}	✓	✓	✓	✓	4.020
21036	1573	\begin{align*} y^{\prime } x -2 y&=-1 \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✗	4.023
21037	8799	\begin{align*} p \,x^{2} u^{\prime \prime }+q x u^{\prime }+r u&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.026
21038	5170	\begin{align*} 2 x \left (2 x^{2}+y\right ) y^{\prime }+\left (12 x^{2}+y\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	4.029
21039	7024	\begin{align*} \left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.029
21040	2337	\begin{align*} 2 t \sin \left (y\right )+{\mathrm e}^{t} y^{3}+\left (\cos \left (y\right ) t^{2}+3 \,{\mathrm e}^{t} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.030
21041	11676	\begin{align*} {y^{\prime }}^{2}-2 x^{2} y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✗	4.034
21042	13907	\begin{align*} x^{n} y^{\prime \prime }+\left (a \,x^{n}-x^{n -1}+a b x +b \right ) y^{\prime }+a^{2} b x y&=0 \\ \end{align*}	✗	✗	✗	✗	4.035
21043	21427	\begin{align*} \frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	4.036
21044	1727	\begin{align*} 3 x^{2} y^{3}-y^{2}+y+\left (-y x +2 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.039
21045	5022	\begin{align*} y^{\prime } \sqrt {x^{4}+x^{2}+1}&=\sqrt {1+y^{2}+y^{4}} \\ \end{align*}	✓	✓	✓	✓	4.039
21046	11592	\begin{align*} 3 y^{2} y^{\prime } x +y^{3}-2 x&=0 \\ \end{align*}	✓	✓	✓	✓	4.039
21047	15536	\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}	✓	✓	✓	✓	4.040
21048	17230	\begin{align*} {\mathrm e}^{y}-2 t y+\left (t \,{\mathrm e}^{y}-t^{2}\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✗	✗	✗	4.040
21049	17842	\begin{align*} y^{\prime }&=\sqrt {1-y^{2}} \\ \end{align*}	✓	✓	✓	✓	4.041
21050	13312	\begin{align*} y^{\prime }&=a \,x^{n} {\mathrm e}^{2 \lambda x} y^{2}+\left (b \,x^{n} {\mathrm e}^{\lambda x}-\lambda \right ) y+c \,x^{n} \\ \end{align*}	✓	✓	✓	✗	4.042
21051	5049	\begin{align*} y^{\prime } y+x +f \left (y^{2}+x^{2}\right ) g \left (x \right )&=0 \\ \end{align*}	✗	✓	✓	✗	4.043
21052	7017	\begin{align*} y^{\prime } x -y-x \sin \left (\frac {y}{x}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.043
21053	19107	\begin{align*} \left (x^{2}-x^{3}+3 x y^{2}+2 y^{3}\right ) y^{\prime }+2 x^{3}+3 x^{2} y+y^{2}-y^{3}&=0 \\ \end{align*}	✗	✓	✓	✗	4.044
21054	8210	\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (2\right ) &= {\frac {1}{3}} \\ \end{align*}	✓	✓	✓	✓	4.046
21055	11423	\begin{align*} y^{\prime } x +x -y+x \cos \left (\frac {y}{x}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.047
21056	15362	\begin{align*} y+\frac {x}{y^{\prime }}&=\sqrt {y^{2}+x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.050
21057	11458	\begin{align*} \left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.052
21058	11335	\begin{align*} y^{\prime }-\frac {y^{2} f^{\prime }\left (x \right )}{g \left (x \right )}+\frac {g^{\prime }\left (x \right )}{f \left (x \right )}&=0 \\ \end{align*}	✗	✓	✓	✗	4.053
21059	15828	\begin{align*} y^{\prime }&=t y+t y^{2} \\ \end{align*}	✓	✓	✓	✓	4.054
21060	6943	\begin{align*} y \left (2 x^{2} y^{3}+3\right )+x \left (x^{2} y^{3}-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.055
21061	18508	\begin{align*} y^{\prime }&=\frac {t y \left (4-y\right )}{t +1} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✓	4.056
21062	24342	\begin{align*} y^{4}-2 y x +3 x^{2} y^{\prime }&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.057
21063	4336	\begin{align*} y+x \left (y^{2}+\ln \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.058
21064	18507	\begin{align*} y^{\prime }&=\frac {t \left (4-y\right ) y}{3} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✗	✗	4.058
21065	8690	\begin{align*} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.062
21066	11373	\begin{align*} y^{\prime }-\operatorname {R1} \left (x , \sqrt {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}\right ) \operatorname {R2} \left (y, \sqrt {b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.062
21067	15959	\begin{align*} y^{\prime }&=2 t y+3 t \,{\mathrm e}^{t^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.062
21068	24906	\begin{align*} 3 y y^{\prime } y^{\prime \prime }&=-1+{y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	4.062
21069	11466	\begin{align*} 3 x^{2} y^{\prime }-7 y^{2}-3 y x -x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.063
21070	22384	\begin{align*} y^{\prime }&=\frac {y+\cos \left (\frac {y}{x}\right )^{2}}{x} \\ y \left (1\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✗	4.063
21071	23217	\begin{align*} y^{\prime }&=\frac {5 x -y-2}{x +y+4} \\ \end{align*}	✓	✓	✓	✓	4.063
21072	14913	\begin{align*} \left (\frac {1}{y}-a \right ) y^{\prime }+\frac {2}{x}-b&=0 \\ \end{align*}	✓	✓	✓	✓	4.066
21073	18287	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=2 \,{\mathrm e}^{x} \left (\sin \left (x \right )+7 \cos \left (x \right )\right ) \\ y \left (-\infty \right ) &= 0 \\ \end{align*}	✗	✓	✗	✓	4.066
21074	22530	\begin{align*} y^{\prime }&=\frac {x +2 y}{y-2 x} \\ \end{align*}	✓	✓	✓	✓	4.066
21075	4964	\begin{align*} \left (b \,x^{2}+a \right ) y^{\prime }&=c x y \ln \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	4.068
21076	7524	\begin{align*} y^{\prime }&=x^{3} \left (y-x \right )^{2}+\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	4.069
21077	8670	\begin{align*} {\mathrm e}^{x}-\left ({\mathrm e}^{x}+1\right ) y y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.069
21078	2863	\begin{align*} x^{2} y^{\prime }+y^{2}&=0 \\ y \left (3\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.070
21079	17223	\begin{align*} \frac {2 t^{2} y \cos \left (t^{2}\right )-\sin \left (t^{2}\right ) y}{t^{2}}+\frac {\left (2 t y+\sin \left (t^{2}\right )\right ) y^{\prime }}{t}&=0 \\ \end{align*}	✓	✓	✓	✗	4.071
21080	9197	\begin{align*} y^{\prime }&=\frac {x +2 y}{2 x -y} \\ \end{align*}	✓	✓	✓	✓	4.072
21081	11638	\begin{align*} x \left (2 x^{2} y \ln \left (y\right )+1\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.072
21082	4424	\begin{align*} x^{2}+3 \ln \left (y\right )-\frac {x y^{\prime }}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	4.073
21083	11403	\begin{align*} y^{\prime } x +x y^{2}-\left (2 x^{2}+1\right ) y-x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	4.073
21084	21030	\begin{align*} x^{\prime }&=x^{2} \\ x \left (t_{0} \right ) &= a \\ \end{align*}	✓	✓	✓	✓	4.073
21085	24292	\begin{align*} a^{2} \left (y^{\prime }-1\right )&=x^{2} y^{\prime }+y^{2} \\ \end{align*}	✓	✓	✓	✓	4.073
21086	10151	\begin{align*} x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y x&=x \\ \end{align*}	✓	✓	✓	✓	4.074
21087	11330	\begin{align*} y^{\prime }+x y^{2}-x^{3} y-2 x&=0 \\ \end{align*}	✓	✓	✓	✓	4.074
21088	12440	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y-x^{5} \ln \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.075
21089	8243	\begin{align*} y^{\prime } y&=3 x \\ y \left (-2\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	4.076
21090	7506	\begin{align*} y^{\prime }&=\left (x +y+2\right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.077
21091	23899	\begin{align*} 3 x^{2} y \ln \left (y\right )+\left (2 x^{3}+2 y^{3}+3 y^{3} \ln \left (y\right )^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.078
21092	725	\begin{align*} y^{\prime }&=2 y x +3 x^{2} {\mathrm e}^{x^{2}} \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	4.079
21093	4315	\begin{align*} x \cos \left (\frac {y}{x}\right )^{2}-y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	4.079
21094	13944	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime }+c \left (a \,{\mathrm e}^{\lambda x}+b -c \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	4.079
21095	6895	\begin{align*} 2 y x +\left (y^{2}+x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.080
21096	24392	\begin{align*} 6 y x -3 y^{2}+2 y+2 \left (x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.080
21097	22404	\begin{align*} y^{\prime }&=\frac {3 x^{5}+3 y^{2} x^{2}}{2 x^{3} y-2 y^{3}} \\ \end{align*}	✓	✓	✓	✓	4.083
21098	5131	\begin{align*} x y^{\prime } y&=a \,x^{n}+b y^{2} \\ \end{align*}	✓	✓	✓	✗	4.084
21099	13938	\begin{align*} y^{\prime \prime }+\left (a +b \right ) {\mathrm e}^{\lambda x} y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (b \,{\mathrm e}^{\lambda x}+\lambda \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	4.084
21100	1002	\begin{align*} x_{1}^{\prime }&=139 x_{1}-14 x_{2}-52 x_{3}-14 x_{4}+28 x_{5} \\ x_{2}^{\prime }&=-22 x_{1}+5 x_{2}+7 x_{3}+8 x_{4}-7 x_{5} \\ x_{3}^{\prime }&=370 x_{1}-38 x_{2}-139 x_{3}-38 x_{4}+76 x_{5} \\ x_{4}^{\prime }&=152 x_{1}-16 x_{2}-59 x_{3}-13 x_{4}+35 x_{5} \\ x_{5}^{\prime }&=95 x_{1}-10 x_{2}-38 x_{3}-7 x_{4}+23 x_{5} \\ \end{align*}	✓	✓	✓	✓	4.085