2.3.250 Problems 24901 to 25000

Table 2.1073: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
24901	24825	\begin{align*} 2 x {y^{\prime }}^{2}+\left (2 x -y\right ) y^{\prime }+1-y&=0 \\ \end{align*}	✓	✓	✓	✗	38.083
24902	19373	\begin{align*} y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✗	38.088
24903	27224	\begin{align*} y^{\prime }&=\cos \left (x -y\right ) \\ \end{align*}	✓	✓	✓	✓	38.109
24904	3649	\begin{align*} y^{\prime }&=\frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{y x} \\ \end{align*}	✓	✓	✓	✗	38.110
24905	13241	\begin{align*} y^{\prime } x +a_{3} x y^{2}+a_{2} y+a_{1} x +a_{0}&=0 \\ \end{align*}	✓	✓	✓	✗	38.135
24906	15943	\begin{align*} y^{\prime }&=\left (y-3\right ) \left (\sin \left (y\right ) \sin \left (t \right )+\cos \left (t \right )+1\right ) \\ y \left (0\right ) &= 4 \\ \end{align*}	✗	✗	✗	✗	38.137
24907	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*}	✓	✓	✓	✗	38.158
24908	11349	\begin{align*} y^{\prime }-a \left (x^{n}-x \right ) y^{3}-y^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	38.175
24909	19950	\begin{align*} x +y y^{\prime }&=m \left (-y+y^{\prime } x \right ) \\ \end{align*}	✓	✓	✓	✗	38.178
24910	22398	\begin{align*} 2 x +3 y+4&=\left (4 x +6 y+1\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	38.184
24911	3556	\begin{align*} y^{\prime }&=\frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{y x} \\ \end{align*}	✓	✓	✓	✗	38.202
24912	8688	\begin{align*} y^{\prime }&=2 \sqrt {2 x +y+1} \\ \end{align*}	✓	✓	✓	✓	38.211
24913	16316	\begin{align*} 2 x y^{3}+4 x^{3}+3 x^{2} y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	38.211
24914	19721	\begin{align*} \frac {2 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	38.211
24915	7245	\begin{align*} 3 y^{2} y^{\prime } x +3 y^{3}&=1 \\ \end{align*}	✓	✓	✓	✓	38.214
24916	26884	\begin{align*} y^{\prime }+\frac {5 y}{9 x}&=3 x^{3}+x \\ y \left (-1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	38.293
24917	7490	\begin{align*} \left (y-4 x -1\right )^{2}-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	38.325
24918	23853	\begin{align*} y^{3}+y^{\prime } \sqrt {-x^{2}+1}&=0 \\ \end{align*}	✓	✓	✓	✓	38.325
24919	24269	\begin{align*} y^{\prime } x +x +y&=0 \\ \end{align*}	✓	✓	✓	✓	38.329
24920	16244	\begin{align*} y^{\prime }&=3 x y^{3} \\ \end{align*}	✓	✓	✓	✓	38.330
24921	6998	\begin{align*} \left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	38.339
24922	22034	\begin{align*} \sin \left (x \right ) y+y \cos \left (x \right ) x +\left (x \sin \left (x \right )+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	38.375
24923	25871	\begin{align*} y y^{\prime }+\cot \left (x \right ) y^{2}&=\csc \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	38.376
24924	15880	\begin{align*} w^{\prime }&=3 w^{3}-12 w^{2} \\ \end{align*}	✓	✓	✓	✓	38.394
24925	20510	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	38.405
24926	8742	\begin{align*} 2 y^{\prime } x +y&=y^{2} \sqrt {x -y^{2} x^{2}} \\ \end{align*}	✓	✓	✓	✗	38.443
24927	9137	\begin{align*} \frac {y^{\prime } x +y}{1-y^{2} x^{2}}+x&=0 \\ \end{align*}	✓	✓	✓	✓	38.452
24928	27403	\begin{align*} x y^{\prime } \left (y^{\prime }+2\right )&=y \\ \end{align*}	✓	✓	✓	✓	38.452
24929	1754	\begin{align*} \left (2 x +1\right ) y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (x +1\right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	38.481
24930	7408	\begin{align*} y^{\prime }&=\sqrt {1+\sin \left (x \right )}\, \left (1+y^{2}\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	38.511
24931	21596	\begin{align*} y^{\prime }&=\frac {2 x +y}{y} \\ \end{align*}	✓	✓	✓	✓	38.546
24932	26341	\begin{align*} 2 x y^{2}-3 y^{3}+\left (7-3 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	38.549
24933	25859	\begin{align*} x^{3}+y^{4} x +2 y^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	38.569
24934	5357	\begin{align*} {y^{\prime }}^{2}&=y+x^{2} \\ \end{align*}	✓	✓	✓	✗	38.590
24935	20713	\begin{align*} x^{2} \left ({y^{\prime }}^{2}-y^{2}\right )+y^{2}&=x^{4}+2 y y^{\prime } x \\ \end{align*}	✓	✓	✓	✗	38.608
24936	25490	\begin{align*} y^{\prime }&=a \left (t \right ) y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	38.616
24937	25000	\begin{align*} y^{\prime } t +3 y&=t^{2} \\ y \left (-1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	38.670
24938	3639	\begin{align*} y^{\prime } x&=\sqrt {16 x^{2}-y^{2}}+y \\ \end{align*}	✓	✓	✓	✓	38.692
24939	24384	\begin{align*} y^{3} \sec \left (x \right )^{2}-\left (1-2 \tan \left (x \right ) y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	38.697
24940	6857	\begin{align*} -y+y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	38.707
24941	15547	\begin{align*} y^{\prime }&=\frac {y x}{x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	38.707
24942	20247	\begin{align*} x^{2}-y^{2}+2 y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	38.718
24943	24159	\begin{align*} x \left (x^{2}+y^{2}\right )^{2} \left (-y^{\prime } x +y\right )+y^{6} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	38.738
24944	27084	\begin{align*} y^{\prime }&=\sin \left (x \right ) y-3 x^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	38.760
24945	15569	\begin{align*} y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\ y \left (6\right ) &= -9 \\ \end{align*}	✓	✓	✓	✓	38.769
24946	11744	\begin{align*} x \left (x^{2}-1\right ) {y^{\prime }}^{2}+2 \left (-x^{2}+1\right ) y y^{\prime }+x y^{2}-x&=0 \\ \end{align*}	✗	✓	✓	✗	38.771
24947	24332	\begin{align*} k \,{\mathrm e}^{2 v}-u -2 \,{\mathrm e}^{2 v} \left ({\mathrm e}^{2 v}+k u \right ) v^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	38.773
24948	12082	\begin{align*} y^{\prime }&=\frac {-b^{3}+6 b^{2} x -12 b \,x^{2}+8 x^{3}-4 b y^{2}+8 x y^{2}+8 y^{3}}{\left (2 x -b \right )^{3}} \\ \end{align*}	✓	✓	✓	✗	38.779
24949	9011	\begin{align*} y^{\prime }&=y^{2} \\ y \left (x_{0} \right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	38.795
24950	13641	\begin{align*} y^{\prime }&=-y^{3}+\frac {y^{2}}{\sqrt {a x +b}} \\ \end{align*}	✓	✓	✓	✗	38.799
24951	13405	\begin{align*} y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+a \,x^{1+k} \cot \left (x \right )^{m} y-a \cot \left (x \right )^{m} \\ \end{align*}	✓	✓	✗	✗	38.815
24952	12860	\begin{align*} y^{\prime \prime }+a y^{\prime }+b \,{\mathrm e}^{y}-2 a&=0 \\ \end{align*}	✗	✗	✗	✗	38.850
24953	20964	\begin{align*} y^{\prime }&=\frac {x +y+1}{2+x}-{\mathrm e}^{\frac {x +y+1}{2+x}} \\ \end{align*}	✓	✓	✓	✗	38.851
24954	25793	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{y} \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	38.883
24955	24190	\begin{align*} 1+y^{2}+\left (y+x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	38.888
24956	14519	\begin{align*} \left (3 y^{2} x^{2}-x \right ) y^{\prime }+2 x y^{3}-y&=0 \\ \end{align*}	✓	✓	✓	✗	38.904
24957	2514	\begin{align*} 2 t \cos \left (y\right )+3 t^{2} y+\left (2 y+2 t^{2}\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	38.915
24958	5166	\begin{align*} x \left (x +2 y\right ) y^{\prime }+y \left (2 x -y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	38.920
24959	22416	\begin{align*} {\mathrm e}^{-x} y-\sin \left (x \right )-\left ({\mathrm e}^{-x}+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	38.934
24960	15585	\begin{align*} y^{\prime }&=\frac {2 x}{y} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	38.944
24961	24329	\begin{align*} y^{\prime } x&=y-y^{3} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	38.951
24962	15362	\begin{align*} y+\frac {x}{y^{\prime }}&=\sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	38.959
24963	7031	\begin{align*} 2 y y^{\prime } x +3 x^{2}-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	38.968
24964	5167	\begin{align*} x \left (x -2 y\right ) y^{\prime }+y \left (2 x -y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	38.972
24965	24292	\begin{align*} a^{2} \left (y^{\prime }-1\right )&=x^{2} y^{\prime }+y^{2} \\ \end{align*}	✓	✓	✓	✓	38.973
24966	27527	\begin{align*} 2 x y^{\prime } y^{\prime \prime }&=-1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	38.983
24967	14040	\begin{align*} 1+{\mathrm e}^{\frac {y}{x}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	39.000
24968	27399	\begin{align*} y&=y^{\prime } x -y^{\prime }-2 \\ \end{align*}	✓	✓	✓	✓	39.016
24969	25707	\begin{align*} y^{\prime }&=y^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✓	39.030
24970	15098	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=2 \cos \left (\ln \left (x +1\right )\right ) \\ \end{align*}	✓	✓	✓	✗	39.063
24971	21285	\begin{align*} x^{\prime }-x&=\operatorname {Heaviside}\left (t -a \right ) \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	39.106
24972	12851	\begin{align*} a \sin \left (y\right )+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	39.181
24973	11686	\begin{align*} {y^{\prime }}^{2}-2 x^{3} y^{2} y^{\prime }-4 x^{2} y^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	39.184
24974	11793	\begin{align*} \left (y^{4}-a^{2} x^{2}\right ) {y^{\prime }}^{2}+2 a^{2} x y y^{\prime }+y^{2} \left (y^{2}-a^{2}\right )&=0 \\ \end{align*}	✗	✗	✗	✗	39.216
24975	27481	\begin{align*} y&=y^{\prime } \sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✓	39.221
24976	14444	\begin{align*} y \sec \left (x \right )^{2}+\sec \left (x \right ) \tan \left (x \right )+\left (\tan \left (x \right )+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	39.247
24977	21370	\begin{align*} y+y^{\prime } x +\frac {y^{3} \left (-y^{\prime } x +y\right )}{x}&=0 \\ \end{align*}	✓	✓	✓	✗	39.296
24978	27286	\begin{align*} x&=\left (x^{2}-2 y+1\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	39.312
24979	8290	\begin{align*} y^{\prime }&=x^{2}-y^{2} \\ y \left (3\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	39.319
24980	5977	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	39.356
24981	26220	\begin{align*} \left (1+y^{2}\right ) {\mathrm e}^{2 x}-\left (1+y^{2}\right ) {\mathrm e}^{y} y^{\prime }-\left (1+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	39.365
24982	27739	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +\left (x +1\right )^{2} y&=0 \\ \end{align*}	✗	✓	✓	✗	39.368
24983	11350	\begin{align*} y^{\prime }-\left (a \,x^{n}+b x \right ) y^{3}-c y^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	39.437
24984	21086	\begin{align*} x^{\prime }&=\frac {3 x^{2}-2 t^{2}}{t x} \\ \end{align*}	✓	✓	✓	✓	39.451
24985	27459	\begin{align*} x^{2} {y^{\prime }}^{2}-2 y y^{\prime } x&=x^{2}+3 y^{2} \\ \end{align*}	✓	✓	✓	✓	39.454
24986	2934	\begin{align*} \frac {x^{2}-y^{2}}{x \left (2 x^{2}+y^{2}\right )}+\frac {\left (x^{2}+2 y^{2}\right ) y^{\prime }}{y \left (2 x^{2}+y^{2}\right )}&=0 \\ \end{align*}	✓	✓	✓	✗	39.461
24987	6832	\begin{align*} y^{\prime } x -y-\sqrt {x^{2}+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	39.575
24988	19282	\begin{align*} y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✗	39.579
24989	12652	\begin{align*} y^{\prime \prime }&=-\frac {\left (3 x -1\right ) y^{\prime }}{2 x \left (-1+x \right )}-\frac {\left (-v \left (v +1\right ) \left (-1+x \right )^{2}-4 n^{2} x \right ) y}{4 x^{2} \left (-1+x \right )^{2}} \\ \end{align*}	✗	✓	✓	✗	39.595
24990	17250	\begin{align*} 2 t +\frac {19 y}{10}+\left (\frac {19 t}{10}+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	39.595
24991	6082	\begin{align*} p \left (2 k +p \right ) y-\left (1+2 k \right ) x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	39.606
24992	5307	\begin{align*} x \left (x^{3}+3 x^{2} y+y^{3}\right ) y^{\prime }&=\left (3 x^{2}+y^{2}\right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	39.671
24993	5115	\begin{align*} \left (140+7 x -16 y\right ) y^{\prime }+25+8 x +y&=0 \\ \end{align*}	✓	✓	✓	✓	39.708
24994	7252	\begin{align*} y^{2}-y x +\left (y x +x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	39.708
24995	26140	\begin{align*} y^{\prime \prime }+\left (1+\frac {1}{x^{2}+1}\right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	39.716
24996	5263	\begin{align*} x \left (x^{2}+2 y^{2}\right ) y^{\prime }&=\left (2 x^{2}+3 y^{2}\right ) y \\ \end{align*}	✓	✓	✓	✓	39.740
24997	5691	\begin{align*} a \left (1+{y^{\prime }}^{3}\right )^{{1}/{3}}+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	39.740
24998	12928	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}+a y y^{\prime }+b y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	39.888
24999	9122	\begin{align*} y^{\prime } x +2&=x^{3} \left (-1+y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	39.901
25000	11650	\begin{align*} x y^{\prime } \ln \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) \left (1-x \cos \left (y\right )\right )&=0 \\ \end{align*}	✗	✓	✓	✓	39.910