2.3.259 Problems 25801 to 25900

Table 2.1067: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
25801	4774	\begin{align*} y^{\prime } x -y+y^{2}&=x^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✗	67.401
25802	19378	\begin{align*} y y^{\prime } x&=x^{2} y^{\prime }+y^{2} \\ \end{align*}	✓	✓	✓	✓	67.538
25803	4079	\begin{align*} 4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	67.642
25804	23904	\begin{align*} x^{3}+y^{2}+\left (y x -3 x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	67.807
25805	10077	\begin{align*} y^{\prime \prime }-y y^{\prime }&=2 x \\ \end{align*}	✗	✓	✓	✗	67.959
25806	2521	\begin{align*} y^{\prime }&=y^{2}+\cos \left (t \right )^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	68.021
25807	15648	\begin{align*} y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	68.125
25808	12483	\begin{align*} x^{2} y^{\prime \prime }+\left (2 x^{2} \cot \left (x \right )+x \right ) y^{\prime }+\left (x \cot \left (x \right )+a \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	68.140
25809	12006	\begin{align*} y^{\prime }&=-\frac {y^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x} \\ \end{align*}	✓	✓	✓	✓	68.265
25810	23888	\begin{align*} \frac {8 x^{4} y+12 x^{3} y^{2}+2}{2 x +3 y}+\frac {\left (2 x^{5}+3 x^{4} y+3\right ) y^{\prime }}{1+x^{2} y^{4}}&=0 \\ \end{align*}	✗	✗	✗	✗	68.326
25811	6308	\begin{align*} y^{\prime \prime }&=\operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{3} \\ \end{align*}	✓	✓	✓	✗	68.366
25812	7411	\begin{align*} y^{\prime }&=y^{{1}/{3}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	68.778
25813	19976	\begin{align*} x -y y^{\prime }&=a {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	68.927
25814	4707	\begin{align*} y^{\prime }&=a +b y+\sqrt {A +B y} \\ \end{align*}	✓	✓	✓	✓	68.941
25815	20323	\begin{align*} x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	68.975
25816	12862	\begin{align*} -y^{3}+y y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✗	✗	69.011
25817	14267	\begin{align*} x^{\prime }&=\frac {2 x}{3 t}+\frac {2 t}{x} \\ \end{align*}	✓	✓	✓	✓	69.075
25818	19238	\begin{align*} y^{\prime }&=\frac {y^{2}}{y x -x^{2}} \\ \end{align*}	✓	✓	✓	✓	69.079
25819	5151	\begin{align*} x \left (4 x -y\right ) y^{\prime }+4 x^{2}-6 y x -y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	69.145
25820	13844	\begin{align*} x^{3} y^{\prime \prime }+\left (a \,x^{2}+b \right ) y^{\prime }+c x y&=0 \\ \end{align*}	✗	✓	✓	✗	69.167
25821	13654	\begin{align*} y^{\prime }&=-\left (a x +b \,x^{m}\right ) y^{3}+y^{2} \\ \end{align*}	✗	✗	✗	✗	69.344
25822	23290	\begin{align*} \sin \left (x \right ) y^{\prime \prime }+y^{\prime } x +y&=2 \\ y \left (\frac {3 \pi }{4}\right ) &= 1 \\ y^{\prime }\left (\frac {3 \pi }{4}\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	69.351
25823	21388	\begin{align*} y^{\prime }&=\sqrt {1-\frac {y^{2}}{x^{2}}}+\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	69.369
25824	17249	\begin{align*} \frac {9 t}{5}+2 y+\left (2 t +2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	69.609
25825	5202	\begin{align*} 8 y y^{\prime } x^{3}+3 x^{4}-6 y^{2} x^{2}-y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	69.626
25826	13434	\begin{align*} y^{\prime } x&=\lambda \arccos \left (x \right )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \arccos \left (x \right )^{n} \\ \end{align*}	✓	✓	✓	✗	69.704
25827	12004	\begin{align*} y^{\prime }&=-\frac {y^{3}}{\left (-1+2 y \ln \left (x \right )-y\right ) x} \\ \end{align*}	✓	✓	✓	✓	69.810
25828	22605	\begin{align*} y^{\prime }&=\sqrt {\frac {5 x -6 y}{5 x +6 y}} \\ \end{align*}	✓	✓	✓	✓	69.812
25829	25217	\begin{align*} y^{\prime \prime }+a_{1} \left (t \right ) y^{\prime }+a_{0} \left (t \right ) y&=f \left (t \right ) \\ \end{align*}	✗	✗	✗	✗	69.872
25830	6260	\begin{align*} \left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	69.928
25831	5528	\begin{align*} \left (-a^{2}+1\right ) x^{2} {y^{\prime }}^{2}-2 y y^{\prime } x -a^{2} x^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	70.048
25832	21549	\begin{align*} a_{0} \left (x \right ) y^{\prime \prime }+a_{1} \left (x \right ) y^{\prime }+a_{2} \left (x \right ) y&=f \left (x \right ) \\ \end{align*}	✗	✗	✗	✗	70.091
25833	21928	\begin{align*} x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	70.132
25834	6315	\begin{align*} y y^{\prime }+y^{\prime \prime }&=y^{3} \\ \end{align*}	✓	✓	✓	✗	70.173
25835	11660	\begin{align*} {y^{\prime }}^{2}+a y+b \,x^{2}&=0 \\ \end{align*}	✓	✗	✓	✗	70.189
25836	2912	\begin{align*} 2 x +y+\left (4 x -2 y+1\right ) y^{\prime }&=0 \\ y \left (\frac {1}{2}\right ) &= 0 \\ \end{align*}	✓	✗	✓	✗	70.502
25837	15357	\begin{align*} 3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	70.577
25838	1681	\begin{align*} 3 \cos \left (x \right ) y+4 x \,{\mathrm e}^{x}+2 x^{3} y+\left (3 \sin \left (x \right )+3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	70.634
25839	11561	\begin{align*} \left (-x +y\right ) \sqrt {x^{2}+1}\, y^{\prime }-a \sqrt {\left (1+y^{2}\right )^{3}}&=0 \\ \end{align*}	✓	✓	✓	✗	70.784
25840	17234	\begin{align*} \frac {1}{t^{2}+1}-y^{2}-2 t y y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	71.054
25841	5295	\begin{align*} \left (a -3 x^{2}-y^{2}\right ) y y^{\prime }+x \left (a -x^{2}+y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	71.147
25842	12017	\begin{align*} y^{\prime }&=\frac {\left (2 y \ln \left (x \right )-1\right )^{3}}{\left (-1+2 y \ln \left (x \right )-y\right ) x} \\ \end{align*}	✓	✓	✓	✗	71.191
25843	20672	\begin{align*} y^{\prime \prime } x +\left (x^{2}+1\right ) y^{\prime }+2 y x&=2 x \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✗	✓	✓	✗	71.210
25844	26382	\begin{align*} x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	71.253
25845	6224	\begin{align*} y+x \left (x +1\right ) y^{\prime }+x \left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✗	✗	71.316
25846	6258	\begin{align*} -\left (k^{2}-p \left (1+p \right ) \left (-x^{2}+1\right )\right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	71.458
25847	10407	\begin{align*} y {y^{\prime \prime }}^{4}+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	71.467
25848	19901	\begin{align*} y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	71.569
25849	15127	\begin{align*} y y^{\prime }+y^{\prime \prime }&=1 \\ \end{align*}	✗	✓	✓	✗	71.711
25850	19717	\begin{align*} 2 x^{2} y+y^{3}-x^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	71.808
25851	21593	\begin{align*} y^{\prime }&=\frac {x +y+1}{x +2 y+3} \\ \end{align*}	✓	✓	✓	✓	71.869
25852	19967	\begin{align*} x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	71.974
25853	13425	\begin{align*} y^{\prime }&=\lambda \arcsin \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\ \end{align*}	✗	✓	✓	✗	72.161
25854	15976	\begin{align*} p^{\prime }&=3 p-2 q-7 r \\ q^{\prime }&=-2 p+6 r \\ r^{\prime }&=\frac {73 q}{100}+2 r \\ \end{align*}	✓	✓	✓	✓	72.198
25855	13562	\begin{align*} y y^{\prime }&=a y \cosh \left (x \right )+1 \\ \end{align*}	✗	✗	✗	✗	72.296
25856	17051	\begin{align*} y^{\prime }&=\sqrt {25-y^{2}} \\ y \left (3\right ) &= -6 \\ \end{align*}	✓	✓	✓	✗	72.371
25857	8695	\begin{align*} x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	72.383
25858	3289	\begin{align*} x y {y^{\prime }}^{2}+\left (y x -1\right ) y^{\prime }&=y \\ \end{align*}	✗	✗	✗	✗	72.435
25859	11989	\begin{align*} y^{\prime }&=-\frac {\left (-\ln \left (-1+y\right )+\ln \left (1+y\right )+2 \ln \left (x \right )\right ) x \left (1+y\right )^{2}}{8} \\ \end{align*}	✗	✓	✓	✗	72.442
25860	13565	\begin{align*} y y^{\prime }&=\left (a x +3 b \right ) y+c \,x^{3}-a b \,x^{2}-2 b^{2} x \\ \end{align*}	✗	✓	✗	✗	72.455
25861	24365	\begin{align*} x^{2}+y^{2}+1+x \left (x -2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	72.535
25862	17909	\begin{align*} x^{2} y^{\prime }+\sin \left (2 y\right )&=1 \\ y \left (\infty \right ) &= \frac {11 \pi }{4} \\ \end{align*}	✗	✓	✗	✓	72.735
25863	12067	\begin{align*} y^{\prime }&=-\frac {\ln \left (x \right )-\sinh \left (x \right ) x^{2}-2 \sinh \left (x \right ) x y-\sinh \left (x \right )-\sinh \left (x \right ) y^{2}}{\ln \left (x \right )} \\ \end{align*}	✓	✓	✓	✗	72.777
25864	23965	\begin{align*} 3 y^{2}-2 x^{2}&=2 y y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	72.783
25865	15822	\begin{align*} S^{\prime }&=S^{3}-2 S^{2}+S \\ S \left (0\right ) &= {\frac {3}{2}} \\ \end{align*}	✓	✓	✗	✓	72.946
25866	12870	\begin{align*} y^{\prime \prime }+a y y^{\prime }+y^{3} b&=0 \\ \end{align*}	✓	✓	✓	✗	73.191
25867	14868	\begin{align*} x^{\prime \prime }+\left (5 x^{4}-6 x^{2}\right ) x^{\prime }+x^{3}&=0 \\ \end{align*}	✗	✗	✗	✗	73.322
25868	23297	\begin{align*} 2 y^{\prime \prime } x -7 \cos \left (x \right ) y^{\prime }+y&={\mathrm e}^{-x} \\ \end{align*}	✗	✗	✗	✗	73.355
25869	1203	\begin{align*} x \ln \left (x \right )+y x +\left (y \ln \left (x \right )+y x \right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	73.412
25870	6174	\begin{align*} \left (k^{2} x +b \right ) y+2 \left (a x +1\right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✗	✗	73.486
25871	12930	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}-\left (a y-1\right ) y^{\prime }+2 y^{2} a^{2}-2 b^{2} y^{3}+a y&=0 \\ \end{align*}	✗	✗	✓	✗	73.522
25872	19122	\begin{align*} y&=x {y^{\prime }}^{2}+{y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	73.565
25873	26269	\begin{align*} 3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	73.662
25874	18339	\begin{align*} 2 x^{2} \left (2-\ln \left (x \right )\right ) y^{\prime \prime }+x \left (4-\ln \left (x \right )\right ) y^{\prime }-y&=\frac {\left (2-\ln \left (x \right )\right )^{2}}{\sqrt {x}} \\ y \left (\infty \right ) &= 0 \\ \end{align*}	✗	✓	✗	✗	73.719
25875	13554	\begin{align*} y y^{\prime }&=\left (a x +b \right ) y+1 \\ \end{align*}	✗	✓	✓	✗	73.809
25876	12961	\begin{align*} 2 y y^{\prime \prime }-6 {y^{\prime }}^{2}+y^{2} \left (1+a y^{3}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	73.912
25877	20012	\begin{align*} {\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{3}&=0 \\ \end{align*}	✓	✓	✗	✗	74.072
25878	4277	\begin{align*} y^{2}&=\left (x^{3}-y x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	74.210
25879	20511	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +5 y&=x^{2} \sin \left (\ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	74.234
25880	11443	\begin{align*} x^{2} \left (y^{\prime }+a y^{2}\right )+b \,x^{\alpha }+c&=0 \\ \end{align*}	✓	✓	✓	✗	74.462
25881	20121	\begin{align*} y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }&=x y^{2} \\ \end{align*}	✗	✗	✗	✗	74.581
25882	11917	\begin{align*} y^{\prime }&=\frac {1+2 x^{5} \sqrt {4 x^{2} y+1}}{2 x^{3}} \\ \end{align*}	✗	✓	✓	✗	74.612
25883	5429	\begin{align*} {y^{\prime }}^{2}-2 x^{3} y^{2} y^{\prime }-4 x^{2} y^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	74.622
25884	24305	\begin{align*} y \left (y^{2}-3 x^{2}\right )+x^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	74.696
25885	5682	\begin{align*} 2 \sqrt {a y^{\prime }}+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	74.889
25886	12008	\begin{align*} y^{\prime }&=-\frac {a b y-b c +b^{2} x +b a \sqrt {x}-a^{2}}{a \left (a y-c +b x +a \sqrt {x}\right )} \\ \end{align*}	✓	✓	✓	✗	74.901
25887	4961	\begin{align*} a \,x^{2} y^{\prime }&=x^{2}+a x y+b^{2} y^{2} \\ \end{align*}	✓	✓	✓	✗	74.907
25888	11560	\begin{align*} 2 x \left (x^{3} y+1\right ) y^{\prime }+\left (3 x^{3} y-1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	74.921
25889	11990	\begin{align*} y^{\prime }&=\frac {\left (-\ln \left (-1+y\right )+\ln \left (1+y\right )+2 \ln \left (x \right )\right )^{2} x \left (1+y\right )^{2}}{16} \\ \end{align*}	✗	✓	✓	✗	74.926
25890	6484	\begin{align*} 2 y y^{\prime \prime }&=-y^{2} \left (1+a y^{3}\right )+6 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	74.941
25891	9736	\begin{align*} {y^{\prime }}^{3}+x {y^{\prime }}^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✗	74.983
25892	13922	\begin{align*} \left (x^{n} a +b \,x^{m}+c \right ) y^{\prime \prime }+\left (\lambda ^{2}-x^{2}\right ) y^{\prime }+\left (x +\lambda \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	74.984
25893	13316	\begin{align*} y^{\prime }&=y^{2}+2 a \lambda x \,{\mathrm e}^{\lambda \,x^{2}}-a^{2} {\mathrm e}^{2 \lambda \,x^{2}} \\ \end{align*}	✓	✗	✗	✗	75.076
25894	4744	\begin{align*} 2 y^{\prime }&=2 \sin \left (y\right )^{2} \tan \left (y\right )-x \sin \left (2 y\right ) \\ \end{align*}	✗	✗	✓	✗	75.232
25895	13803	\begin{align*} x^{2} y^{\prime \prime }+x \left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (A \,x^{3}+B \,x^{2}+C x +d \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	75.254
25896	11681	\begin{align*} {y^{\prime }}^{2}+a y y^{\prime }-b x -c&=0 \\ \end{align*}	✓	✓	✓	✗	75.281
25897	11924	\begin{align*} y^{\prime }&=\frac {1+2 \sqrt {4 x^{2} y+1}\, x^{4}}{2 x^{3}} \\ \end{align*}	✗	✓	✓	✗	75.387
25898	6083	\begin{align*} p \left (1+2 k +p \right ) y-2 \left (1+k \right ) x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	75.407
25899	25886	\begin{align*} x^{2}-y^{2}-\frac {2 y^{3} y^{\prime }}{x}&=0 \\ \end{align*}	✓	✓	✓	✗	75.407
25900	3650	\begin{align*} y^{\prime }&=\frac {-2 x +4 y}{x +y} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	75.410