2.3.261 Problems 26001 to 26100

Table 2.1095: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
26001	21160	\begin{align*} x^{\prime \prime }+p \left (t \right ) x^{\prime }+q \left (t \right ) x&=0 \\ \end{align*}	✗	✗	✗	✗	30.873
26002	24364	\begin{align*} x +y-4-\left (3 x -y-4\right ) y^{\prime }&=0 \\ y \left (3\right ) &= 7 \\ \end{align*}	✓	✓	✓	✗	30.892
26003	15385	\begin{align*} \frac {1}{x^{2}}+\frac {3 y^{2}}{x^{4}}&=\frac {2 y y^{\prime }}{x^{3}} \\ \end{align*}	✓	✓	✓	✓	30.918
26004	13892	\begin{align*} \left (x^{2}+a \right )^{2} y^{\prime \prime }+b \,x^{n} \left (x^{2}+a \right ) y^{\prime }-m \left (b \,x^{n +1}+\left (m -1\right ) x^{2}+a \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	30.920
26005	6898	\begin{align*} x y^{\prime }-y-x \sin \left (\frac {y}{x}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	30.937
26006	25887	\begin{align*} x^{2}+2 y x -4 y^{2}-\left (x^{2}-8 y x -4 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	30.961
26007	18846	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=3 x^{2}+2 \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	30.970
26008	22438	\begin{align*} y^{\prime }&=\frac {y}{y^{3}-3 x} \\ \end{align*}	✓	✓	✓	✓	30.994
26009	2525	\begin{align*} y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\ y \left (1\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	30.997
26010	8674	\begin{align*} \frac {1}{\sqrt {-x^{2}+1}}+\frac {y^{\prime }}{\sqrt {1-y^{2}}}&=0 \\ \end{align*}	✓	✓	✓	✓	31.009
26011	12539	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (-x^{2}+2 \left (1-m +2 l \right ) x -m^{2}+1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	31.027
26012	5476	\begin{align*} {y^{\prime }}^{2} x +a y y^{\prime }+b x&=0 \\ \end{align*}	✓	✓	✓	✓	31.047
26013	4297	\begin{align*} \cos \left (y\right )-x \sin \left (y\right ) y^{\prime }&=\sec \left (x \right )^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	31.059
26014	6829	\begin{align*} \sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	31.083
26015	2925	\begin{align*} \frac {y x +1}{y}+\frac {\left (-x +2 y\right ) y^{\prime }}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	31.155
26016	22415	\begin{align*} r^{\prime }&=\frac {r \sin \left (t \right )}{2 r \cos \left (t \right )-1} \\ \end{align*}	✓	✓	✓	✓	31.167
26017	15256	\begin{align*} y^{\prime \prime }+3 y^{\prime }+\frac {y}{t}&=t \\ \end{align*}	✗	✓	✓	✗	31.183
26018	19296	\begin{align*} \sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	31.203
26019	13228	\begin{align*} y^{\prime }&=a y^{2}+b y+c x +k \\ \end{align*}	✓	✓	✓	✗	31.214
26020	20718	\begin{align*} {y^{\prime }}^{3}+m {y^{\prime }}^{2}&=a \left (y+m x \right ) \\ \end{align*}	✓	✓	✗	✗	31.217
26021	15632	\begin{align*} y^{\prime }&=3 x y^{{1}/{3}} \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	31.229
26022	13360	\begin{align*} x y^{\prime }&=\left (a y+b \ln \left (x \right )\right )^{2} \\ \end{align*}	✓	✓	✓	✓	31.234
26023	21818	\begin{align*} 2 \sin \left (y\right ) x +2 x +3 \cos \left (x \right ) y+\left (\cos \left (y\right ) x^{2}+3 \sin \left (x \right )\right ) y^{\prime }&=0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	31.246
26024	5176	\begin{align*} a x y y^{\prime }&=x^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✓	31.247
26025	23299	\begin{align*} \cos \left (x \right ) y^{\prime \prime }+y&=\sin \left (x \right ) \\ \end{align*}	✗	✓	✗	✗	31.252
26026	17111	\begin{align*} y^{\prime }&=\frac {\sqrt {t}}{y} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	31.276
26027	14529	\begin{align*} y x +x^{2} y^{\prime }&=x y^{3} \\ \end{align*}	✓	✓	✓	✓	31.299
26028	17233	\begin{align*} \cos \left (t \right )^{2}-\sin \left (t \right )^{2}+y+\left (\sec \left (y\right ) \tan \left (y\right )+t \right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	31.305
26029	4322	\begin{align*} y+2&=\left (2 x +y-4\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	31.347
26030	27453	\begin{align*} \sqrt {x}\, y^{\prime }&=\sqrt {-x +y}+\sqrt {x} \\ \end{align*}	✓	✓	✓	✓	31.358
26031	7008	\begin{align*} \left (x y \sqrt {x^{2}-y^{2}}+x \right ) y^{\prime }&=y-x^{2} \sqrt {x^{2}-y^{2}} \\ \end{align*}	✗	✓	✓	✗	31.371
26032	12862	\begin{align*} y y^{\prime }+y^{\prime \prime }-y^{3}&=0 \\ \end{align*}	✓	✓	✗	✗	31.380
26033	17244	\begin{align*} 5 t y^{2}+y+\left (2 t^{3}-t \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	31.412
26034	15479	\begin{align*} x^{\prime \prime }+x^{\prime }+x-x^{3}&=0 \\ \end{align*}	✗	✗	✗	✗	31.415
26035	11349	\begin{align*} y^{\prime }-a \left (x^{n}-x \right ) y^{3}-y^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	31.420
26036	13241	\begin{align*} x y^{\prime }+a_{3} x y^{2}+a_{2} y+a_{1} x +a_{0}&=0 \\ \end{align*}	✓	✓	✓	✗	31.449
26037	22038	\begin{align*} y^{\prime }&=\frac {3 y x^{2}}{x^{3}+2 y^{4}} \\ \end{align*}	✓	✓	✓	✓	31.456
26038	11653	\begin{align*} y^{\prime } \cos \left (a y\right )-b \left (1-c \cos \left (a y\right )\right ) \sqrt {\cos \left (a y\right )^{2}-1+c \cos \left (a y\right )}&=0 \\ \end{align*}	✓	✓	✓	✗	31.483
26039	15062	\begin{align*} \left (y^{2}-x^{2}\right ) y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	31.506
26040	24402	\begin{align*} 2 x -3 y+1-\left (3 x +2 y-4\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	31.533
26041	25714	\begin{align*} \left (-x +y\right ) y^{\prime }&=x +y \\ \end{align*}	✓	✓	✓	✓	31.602
26042	22423	\begin{align*} y^{\prime }&=\frac {2 \sin \left (2 x \right )-\tan \left (y\right )}{x \sec \left (y\right )^{2}} \\ y \left (\pi \right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✗	31.608
26043	27508	\begin{align*} \left (y-2 x y^{\prime }\right )^{2}&=4 y {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	31.641
26044	2914	\begin{align*} 3 x +y+\left (x +3 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	31.681
26045	11796	\begin{align*} x^{2} \left (x^{2} y^{4}-1\right ) {y^{\prime }}^{2}+2 x^{3} y^{3} \left (y^{2}-x^{2}\right ) y^{\prime }-y^{2} \left (y^{2} x^{4}-1\right )&=0 \\ \end{align*}	✗	✗	✗	✗	31.692
26046	24333	\begin{align*} y^{\prime } \tan \left (x \right ) \sin \left (2 y\right )&=\sin \left (x \right )^{2}+\cos \left (y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	31.713
26047	4250	\begin{align*} \sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	31.826
26048	7503	\begin{align*} y^{\prime }&=\frac {x^{2}-y^{2}}{3 x y} \\ \end{align*}	✓	✓	✓	✓	31.846
26049	14063	\begin{align*} {\mathrm e}^{2 y} {y^{\prime }}^{3}+\left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x}&=0 \\ \end{align*}	✓	✓	✗	✗	31.868
26050	25054	\begin{align*} y^{\prime }&=\cos \left (t +y\right ) \\ y \left (t_{0} \right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	31.868
26051	22288	\begin{align*} y^{\prime \prime }+y&=x \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	31.884
26052	15480	\begin{align*} x^{\prime \prime }+x^{\prime }+x+x^{3}&=0 \\ \end{align*}	✗	✗	✗	✗	31.896
26053	27391	\begin{align*} 2 x y^{\prime }-y&=y^{\prime } \ln \left (y y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✗	31.902
26054	18305	\begin{align*} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y&=2 \ln \left (x \right )^{2}+12 x \\ \end{align*}	✓	✓	✓	✓	31.922
26055	24347	\begin{align*} 2 x -y+\left (-6+4 x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	31.938
26056	5922	\begin{align*} c y+\left (b x +a \right ) y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	31.944
26057	22416	\begin{align*} {\mathrm e}^{-x} y-\sin \left (x \right )-\left ({\mathrm e}^{-x}+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	31.992
26058	2953	\begin{align*} x^{2} y^{2}-y+\left (2 x^{3} y+x \right ) y^{\prime }&=0 \\ y \left (2\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	31.999
26059	21810	\begin{align*} x^{2}+2 y x -2 y^{2}+\left (y^{2}+2 y x -2 x^{2}\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	32.008
26060	6889	\begin{align*} x -y y^{\prime }&=a {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	32.021
26061	27467	\begin{align*} y y^{\prime }&=4 x +3 y-2 \\ \end{align*}	✓	✓	✓	✓	32.055
26062	13484	\begin{align*} y^{\prime }&=g \left (x \right ) \left (y-f \left (x \right )\right )^{2}+f^{\prime }\left (x \right ) \\ \end{align*}	✓	✓	✓	✗	32.072
26063	11350	\begin{align*} y^{\prime }-\left (a \,x^{n}+b x \right ) y^{3}-c y^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	32.123
26064	3461	\begin{align*} \left (\cos \left (x \right )^{2}+y \sin \left (2 x \right )\right ) y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	32.144
26065	6538	\begin{align*} y^{\prime } \left (1+{y^{\prime }}^{2}\right )+\left (1+y^{2}\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	32.185
26066	13384	\begin{align*} y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+a \,x^{1+k} \cos \left (x \right )^{m} y-a \cos \left (x \right )^{m} \\ \end{align*}	✓	✓	✓	✗	32.185
26067	19233	\begin{align*} x y^{\prime }+y&=y^{\prime } \sqrt {1-x^{2} y^{2}} \\ \end{align*}	✓	✓	✓	✗	32.204
26068	14552	\begin{align*} 6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime }&=0 \\ y \left (\frac {1}{2}\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	32.226
26069	23218	\begin{align*} y^{\prime }&=\frac {x -y+5}{2 x -y-3} \\ \end{align*}	✓	✓	✓	✗	32.261
26070	9126	\begin{align*} \sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	32.289
26071	19922	\begin{align*} y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	32.306
26072	25032	\begin{align*} 3 y-5 t +2 y y^{\prime }-t y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	32.379
26073	17282	\begin{align*} t \left (\ln \left (t \right )-\ln \left (y\right )\right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	32.511
26074	25877	\begin{align*} y^{\prime }&=\frac {2 x y}{x^{2}-y^{2}} \\ \end{align*}	✓	✓	✓	✓	32.523
26075	11531	\begin{align*} x y y^{\prime }-y^{2}+y x +x^{3}-2 x^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	32.525
26076	18599	\begin{align*} x y y^{\prime }&=\left (x +y\right )^{2} \\ \end{align*}	✓	✓	✓	✗	32.530
26077	3012	\begin{align*} y \sin \left (x \right )-2 \cos \left (y\right )+\tan \left (x \right )-\left (\cos \left (x \right )-2 \sin \left (y\right ) x +\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	32.535
26078	14713	\begin{align*} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y&=4 \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	32.541
26079	11673	\begin{align*} {y^{\prime }}^{2}+a x y^{\prime }-b \,x^{2}-c&=0 \\ \end{align*}	✓	✓	✓	✓	32.555
26080	8726	\begin{align*} y^{\prime }&=\frac {x +3 y-5}{x -y-1} \\ \end{align*}	✓	✓	✓	✓	32.562
26081	18609	\begin{align*} t^{2} y^{\prime }+2 y t -y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	32.563
26082	4923	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+x \sin \left (y\right ) \cos \left (y\right )&=x \left (x^{2}+1\right ) \cos \left (y\right )^{2} \\ \end{align*}	✗	✓	✓	✗	32.566
26083	5420	\begin{align*} {y^{\prime }}^{2}+\left (a +6 y\right ) y^{\prime }+y \left (3 a +b +9 y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	32.575
26084	23242	\begin{align*} y^{\prime \prime }+\cos \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	32.626
26085	15631	\begin{align*} y^{\prime }&=3 x y^{{1}/{3}} \\ y \left (-1\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✗	32.628
26086	12864	\begin{align*} y^{\prime \prime }+\left (3 a +y\right ) y^{\prime }-y^{3}+a y^{2}+2 a^{2} y&=0 \\ \end{align*}	✗	✓	✓	✗	32.642
26087	21005	\begin{align*} x^{\prime }+\frac {\left (2 t^{3}+\sin \left (t \right )+5\right ) x}{t^{12}+5}&=0 \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	32.652
26088	18572	\begin{align*} y^{\prime }&=-\frac {4 x +2 y}{2 x +3 y} \\ \end{align*}	✓	✓	✓	✓	32.685
26089	15057	\begin{align*} y^{\prime }&=\frac {-3+x +y}{y-x +1} \\ \end{align*}	✓	✓	✓	✓	32.722
26090	13350	\begin{align*} x y^{\prime }&=a \,x^{n} y^{2}+b -a \,b^{2} x^{n} \ln \left (x \right )^{2} \\ \end{align*}	✓	✗	✗	✗	32.735
26091	6988	\begin{align*} y^{\prime }&=\frac {1}{x^{2}}-\frac {y}{x}-y^{2} \\ \end{align*}	✓	✓	✓	✓	32.737
26092	9151	\begin{align*} x -y-\left (x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	32.744
26093	20191	\begin{align*} y^{\prime \prime }-2 b y^{\prime }+b^{2} x^{2} y&=0 \\ \end{align*}	✗	✓	✓	✗	32.770
26094	18604	\begin{align*} x y y^{\prime }&=x^{2}+y^{2} \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	32.776
26095	2923	\begin{align*} x y^{2}+2 y+\left (2 y^{3}-x^{2} y+2 x \right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	32.862
26096	2927	\begin{align*} y^{2} \csc \left (x \right )^{2}+6 y x -2&=\left (2 y \cot \left (x \right )-3 x^{2}\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	32.872
26097	11989	\begin{align*} y^{\prime }&=-\frac {\left (-\ln \left (-1+y\right )+\ln \left (y+1\right )+2 \ln \left (x \right )\right ) x \left (y+1\right )^{2}}{8} \\ \end{align*}	✗	✓	✓	✗	32.878
26098	2887	\begin{align*} y^{\prime }&=\frac {x +y}{x -y} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	32.881
26099	9140	\begin{align*} {\mathrm e}^{y^{2}}-\csc \left (y\right ) \csc \left (x \right )^{2}+\left (2 x y \,{\mathrm e}^{y^{2}}-\csc \left (y\right ) \cot \left (y\right ) \cot \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	32.902
26100	8752	\begin{align*} 2 x +4 y+\left (2 x -2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	32.962