2.3.248 Problems 24701 to 24800

Table 2.1069: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
24701	22557	\begin{align*} \left (x +x \cos \left (y\right )\right ) y^{\prime }-\sin \left (y\right )-y&=0 \\ \end{align*}	✓	✓	✓	✓	15.060
24702	4320	\begin{align*} \left (3+2 x +4 y\right ) y^{\prime }&=x +2 y+1 \\ \end{align*}	✓	✓	✓	✓	15.072
24703	7523	\begin{align*} y^{\prime }&=\frac {3 x y}{2 x^{2}-y^{2}} \\ \end{align*}	✓	✓	✓	✗	15.072
24704	22429	\begin{align*} \frac {y}{\left (x +y\right )^{2}}-1+\left (1-\frac {x}{\left (x +y\right )^{2}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	15.090
24705	23219	\begin{align*} y^{\prime }&=\frac {y-x +1}{3 x -y-1} \\ \end{align*}	✓	✓	✓	✓	15.095
24706	8705	\begin{align*} x y^{\prime }-y&=y y^{\prime } \\ \end{align*}	✓	✓	✓	✓	15.125
24707	5923	\begin{align*} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	15.138
24708	21863	\begin{align*} 2 {y^{\prime }}^{2}+y y^{\prime }-y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	15.159
24709	18574	\begin{align*} {\mathrm e}^{x} \sin \left (y\right )-2 y \sin \left (x \right )+\left (2 \cos \left (x \right )+{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	15.168
24710	4080	\begin{align*} 5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	15.175
24711	11575	\begin{align*} x^{2}+2 y x -y^{2}+\left (y^{2}+2 y x -x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	15.177
24712	8703	\begin{align*} x +y-\left (x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	15.178
24713	21988	\begin{align*} y^{\prime }&=\frac {x^{2}}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	15.181
24714	17152	\begin{align*} y^{\prime }-\frac {4 t y}{4 t^{2}-9}&=t \\ \end{align*}	✓	✓	✓	✓	15.191
24715	11622	\begin{align*} a \,x^{2} y^{n} y^{\prime }-2 x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	15.194
24716	6342	\begin{align*} g \left (y\right )+f \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	15.211
24717	23179	\begin{align*} x +y+\left (x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	15.214
24718	12095	\begin{align*} y^{\prime }&=\frac {\left (-\sqrt {a}\, x^{3}+2 \sqrt {a \,x^{4}+8 y}+2 x^{2} \sqrt {a \,x^{4}+8 y}+2 x^{3} \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2} \\ \end{align*}	✗	✓	✓	✗	15.220
24719	6452	\begin{align*} y y^{\prime \prime }&=\operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{2}+\operatorname {a3} y^{3}+\operatorname {a4} y^{4}+a {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	15.223
24720	26081	\begin{align*} x y^{\prime }&={\mathrm e}^{\frac {y}{x}} x +y \\ y \left (1\right ) &= \ln \left (2\right ) \\ \end{align*}	✓	✓	✓	✗	15.232
24721	8785	\begin{align*} x +y-\left (x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	15.241
24722	5281	\begin{align*} \left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	15.275
24723	15452	\begin{align*} \left (x^{2}+1\right ) y^{\prime }-y x -\alpha &=0 \\ \end{align*}	✓	✓	✓	✓	15.287
24724	15455	\begin{align*} x y^{\prime }-y^{2} \ln \left (x \right )+y&=0 \\ \end{align*}	✓	✓	✓	✓	15.304
24725	21156	\begin{align*} x^{\prime \prime }+\frac {\left (t^{5}+1\right ) x}{t^{4}+5}&=0 \\ \end{align*}	✗	✗	✗	✗	15.306
24726	16307	\begin{align*} x y^{\prime }-y&=\sqrt {y x +x^{2}} \\ \end{align*}	✓	✓	✓	✓	15.310
24727	20284	\begin{align*} 2 y^{\prime }-y \sec \left (x \right )&=y^{3} \tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	15.319
24728	13378	\begin{align*} y^{\prime }&=\alpha y^{2}+\beta +\gamma \cos \left (\lambda x \right ) \\ \end{align*}	✓	✓	✓	✗	15.321
24729	9657	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=x+2 z \\ z^{\prime }&=-x+z \\ \end{align*}	✓	✓	✓	✗	15.328
24730	21092	\begin{align*} x^{\prime }+2 x t&=-4 t x^{3} \\ \end{align*}	✓	✓	✓	✓	15.328
24731	2907	\begin{align*} 2 x +3 y-1+\left (2 x +3 y+2\right ) y^{\prime }&=0 \\ y \left (3\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	15.329
24732	11581	\begin{align*} \left (2 y-4 x +1\right )^{2} y^{\prime }-\left (y-2 x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	15.330
24733	25879	\begin{align*} 3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	15.349
24734	5274	\begin{align*} x \left (3 x -7 y^{2}\right ) y^{\prime }+\left (5 x -3 y^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	15.355
24735	23874	\begin{align*} y^{\prime }&=\frac {x^{3}+x^{2} y-y^{3}}{x^{3}-x y^{2}} \\ \end{align*}	✓	✓	✓	✗	15.356
24736	8709	\begin{align*} y^{\prime }&=\frac {2 x y}{3 x^{2}-y^{2}} \\ \end{align*}	✓	✓	✓	✗	15.361
24737	22592	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x -y}}{y} \\ \end{align*}	✓	✓	✓	✓	15.366
24738	13963	\begin{align*} 2 \left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime \prime }+a \lambda \,{\mathrm e}^{\lambda x} y^{\prime }+c y&=0 \\ \end{align*}	✓	✓	✓	✗	15.385
24739	23947	\begin{align*} \left (x +2 y+2\right ) y^{\prime }&=3 x -y-1 \\ \end{align*}	✓	✓	✓	✓	15.385
24740	15338	\begin{align*} \left (t^{2}+x t^{2}\right ) x^{\prime }+x^{2}+t x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	15.386
24741	12144	\begin{align*} y^{\prime }&=\frac {y \left ({\mathrm e}^{-\frac {x^{2}}{2}} x y+{\mathrm e}^{-\frac {x^{2}}{4}} x +2 y^{2} {\mathrm e}^{-\frac {3 x^{2}}{4}}\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2 y \,{\mathrm e}^{-\frac {x^{2}}{4}}+2} \\ \end{align*}	✓	✓	✓	✗	15.392
24742	4806	\begin{align*} x y^{\prime }&=y+\sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	15.394
24743	14036	\begin{align*} 2 x +3 y-1+\left (2 x +3 y-5\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	15.404
24744	5543	\begin{align*} y {y^{\prime }}^{2}&=a^{2} x \\ \end{align*}	✓	✓	✓	✓	15.418
24745	19407	\begin{align*} y^{\prime }&=\frac {-3 x -2 y-1}{2 x +3 y-1} \\ \end{align*}	✓	✓	✓	✓	15.418
24746	23212	\begin{align*} x -y+\left (2 x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	15.425
24747	23870	\begin{align*} y^{\prime }&=\frac {2 x y}{x^{2}-y^{2}} \\ \end{align*}	✓	✓	✓	✓	15.430
24748	1659	\begin{align*} y^{\prime }&=\frac {y}{y-2 x} \\ \end{align*}	✓	✓	✓	✓	15.434
24749	5178	\begin{align*} x \left (a +b y\right ) y^{\prime }&=c y \\ \end{align*}	✓	✓	✓	✓	15.437
24750	25873	\begin{align*} \left (x -2\right ) y^{\prime }+y&=5 \left (x -2\right )^{2} \sqrt {y} \\ \end{align*}	✓	✓	✓	✓	15.454
24751	2906	\begin{align*} x +y+4&=\left (2 x +2 y-1\right ) y^{\prime } \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	15.461
24752	1197	\begin{align*} y^{\prime }&=\frac {-a x -b y}{b x +c y} \\ \end{align*}	✓	✓	✓	✓	15.465
24753	23917	\begin{align*} y^{\prime }+\frac {2 y}{x}&=\frac {x^{2}}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	15.467
24754	11623	\begin{align*} y^{m} x^{n} \left (a x y^{\prime }+b y\right )+\alpha x y^{\prime }+\beta y&=0 \\ \end{align*}	✓	✓	✓	✗	15.475
24755	2333	\begin{align*} {\mathrm e}^{\frac {t}{y}} \left (y-t \right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	15.480
24756	13483	\begin{align*} y^{\prime }&=-f^{\prime }\left (x \right ) y^{2}+f \left (x \right ) g \left (x \right ) y-g \left (x \right ) \\ \end{align*}	✓	✓	✗	✗	15.482
24757	15172	\begin{align*} x y^{\prime \prime }+\left (6 x y^{2}+1\right ) y^{\prime }+2 y^{3}+1&=0 \\ \end{align*}	✗	✗	✗	✗	15.494
24758	18493	\begin{align*} y^{\prime }&=\left (1+y^{2}\right ) \tan \left (2 x \right ) \\ y \left (0\right ) &= -\sqrt {3} \\ \end{align*}	✓	✓	✗	✓	15.498
24759	17046	\begin{align*} y^{\prime }&=\sqrt {y^{2}-1} \\ y \left (4\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	15.518
24760	22016	\begin{align*} y^{\prime }&=\frac {y^{2}+2 x}{y x} \\ \end{align*}	✓	✓	✓	✓	15.525
24761	21842	\begin{align*} x y^{\prime }-y&=y^{3} \\ \end{align*}	✓	✓	✓	✓	15.526
24762	19335	\begin{align*} x y^{\prime }-y&=x^{2} y^{4} \left (x y^{\prime }+y\right ) \\ \end{align*}	✓	✓	✓	✗	15.527
24763	17215	\begin{align*} 3 t^{2}+3 y^{2}+6 t y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	15.535
24764	12236	\begin{align*} y^{\prime }&=\frac {y \left (-1-x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2}-x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} \ln \left (x \right )+x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} y+2 x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} y \ln \left (x \right )+x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} y \ln \left (x \right )^{2}\right )}{\left (1+\ln \left (x \right )\right ) x} \\ \end{align*}	✗	✓	✓	✓	15.538
24765	2904	\begin{align*} 6 x -3 y+6+\left (2 x -y+5\right ) y^{\prime }&=0 \\ y \left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	15.547
24766	19399	\begin{align*} y^{\prime }&=\frac {x +2 y+2}{y-2 x} \\ \end{align*}	✓	✓	✓	✓	15.552
24767	19329	\begin{align*} \left (x +y\right ) y^{\prime }&=-x +y \\ \end{align*}	✓	✓	✓	✓	15.554
24768	20261	\begin{align*} x^{2}+3 y^{2}-2 x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	15.559
24769	5287	\begin{align*} \left (1-y^{2} x^{4}\right ) y^{\prime }&=x^{3} y^{3} \\ \end{align*}	✓	✓	✓	✓	15.575
24770	11982	\begin{align*} y^{\prime }&=\frac {x \left (-2 x -2+3 x^{2} \sqrt {x^{2}+3 y}\right )}{3 x +3} \\ \end{align*}	✗	✓	✓	✗	15.580
24771	14221	\begin{align*} \left (2 u+1\right ) u^{\prime }-t -1&=0 \\ \end{align*}	✓	✓	✓	✓	15.597
24772	119	\begin{align*} x \left (x +y\right ) y^{\prime }+y \left (3 x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	15.601
24773	24157	\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*}	✓	✓	✓	✓	15.602
24774	24298	\begin{align*} \sqrt {1-y^{2}}-y^{\prime } \sqrt {-x^{2}+1}&=0 \\ y \left (0\right ) &= \frac {\sqrt {3}}{2} \\ \end{align*}	✓	✓	✓	✗	15.612
24775	4352	\begin{align*} 2 x^{2} y^{4}-y+\left (4 x^{3} y^{3}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	15.619
24776	18554	\begin{align*} y^{\prime }&=\left (t^{2}+y^{2}\right )^{{3}/{2}} \\ \end{align*}	✗	✗	✗	✗	15.624
24777	5327	\begin{align*} \left (x^{2}-y^{5}\right ) y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✗	15.627
24778	5207	\begin{align*} \left (y+1\right ) y^{\prime } \sqrt {x^{2}+1}&=y^{3} \\ \end{align*}	✓	✓	✓	✓	15.631
24779	21090	\begin{align*} x^{\prime }&=-\frac {x+t +1}{x-t +1} \\ \end{align*}	✓	✓	✓	✓	15.634
24780	21394	\begin{align*} x y y^{\prime }+x^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	15.643
24781	13110	\begin{align*} x^{\prime }&=6 x-72 y+44 z \\ y^{\prime }&=4 x-4 y+26 z \\ z^{\prime }&=6 x-63 y+38 z \\ \end{align*}	✓	✓	✓	✗	15.649
24782	14246	\begin{align*} x x^{\prime }&=1-x t \\ \end{align*}	✗	✓	✓	✗	15.672
24783	6827	\begin{align*} 1+y^{2}-\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	15.675
24784	24277	\begin{align*} y \left (x +3 y\right )+x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	15.683
24785	2858	\begin{align*} \tan \left (x \right ) \sin \left (x \right )^{2}+\cos \left (x \right )^{2} \cot \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	15.701
24786	743	\begin{align*} x \left (x +y\right ) y^{\prime }+y \left (3 x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	15.720
24787	22586	\begin{align*} y^{\prime } \sqrt {x^{3}+1}&=x^{2} y+x^{2} \\ \end{align*}	✓	✓	✓	✓	15.723
24788	17069	\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	15.724
24789	14496	\begin{align*} x y^{\prime }+y&=-2 x^{6} y^{4} \\ \end{align*}	✓	✓	✓	✓	15.737
24790	23878	\begin{align*} y^{\prime }&=\frac {2 y^{3}+2 x^{2} y}{x^{3}+2 x y^{2}} \\ \end{align*}	✓	✓	✓	✗	15.737
24791	13367	\begin{align*} y^{\prime }&=\alpha y^{2}+\beta +\gamma \sin \left (\lambda x \right ) \\ \end{align*}	✓	✓	✓	✗	15.743
24792	9155	\begin{align*} x^{3}+y^{3}-x y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	15.747
24793	19310	\begin{align*} 1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	15.747
24794	13487	\begin{align*} y^{\prime }&=f^{\prime }\left (x \right ) y^{2}+a \,{\mathrm e}^{\lambda x} f \left (x \right ) y+a \,{\mathrm e}^{\lambda x} \\ \end{align*}	✓	✓	✓	✗	15.751
24795	22319	\begin{align*} y^{\prime }&=\frac {-x +3}{y+5} \\ \end{align*}	✓	✓	✓	✓	15.756
24796	4432	\begin{align*} 2 y^{\prime }+x&=4 \sqrt {y} \\ \end{align*}	✓	✓	✓	✗	15.757
24797	4948	\begin{align*} \left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (y-a \right ) \left (y-b \right )&=0 \\ \end{align*}	✓	✓	✓	✓	15.760
24798	4407	\begin{align*} 2 y-x \left (\ln \left (x^{2} y\right )-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	15.763
24799	13644	\begin{align*} y^{\prime }&=a x y^{3}+2 a b \,x^{2} y^{2}-b -2 a \,b^{3} x^{4} \\ \end{align*}	✗	✗	✗	✗	15.780
24800	4746	\begin{align*} 2 y^{\prime }+a x&=-\sqrt {a^{2} x^{2}-4 b \,x^{2}-4 c y} \\ \end{align*}	✓	✓	✓	✗	15.806