2.3.269 Problems 26801 to 26900

Table 2.1111: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
26801	6244	\begin{align*} \left (c \,x^{4}+b \,x^{2}+a \right ) y+x^{3} y^{\prime }+x^{4} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✗	✗	56.826
26802	23965	\begin{align*} 3 y^{2}-2 x^{2}&=2 x y y^{\prime } \\ \end{align*}	✓	✓	✓	✓	57.045
26803	6484	\begin{align*} 2 y y^{\prime \prime }&=-y^{2} \left (1+a y^{3}\right )+6 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	57.072
26804	196	\begin{align*} 2 x^{2} y-x^{3} y^{\prime }&=y^{3} \\ \end{align*}	✓	✓	✓	✓	57.162
26805	5165	\begin{align*} x \left (x -2 y\right ) y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	57.220
26806	22554	\begin{align*} x y^{\prime }-y&=x^{2} y y^{\prime } \\ \end{align*}	✓	✓	✓	✓	57.296
26807	24335	\begin{align*} y \left (x \tan \left (x \right )+\ln \left (y\right )\right )+\tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✗	✓	✓	✓	57.309
26808	4084	\begin{align*} 3 x -y-6+\left (x +y+2\right ) y^{\prime }&=0 \\ y \left (2\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	57.316
26809	6447	\begin{align*} y y^{\prime \prime }&=-2 y^{2}+2 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	57.330
26810	13444	\begin{align*} y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+\lambda \operatorname {arccot}\left (x \right )^{n} \left (x^{1+k} y-1\right ) \\ \end{align*}	✓	✓	✗	✗	57.400
26811	22969	\begin{align*} y^{\prime }&=\frac {x -y}{x +y} \\ \end{align*}	✓	✓	✓	✓	57.458
26812	5618	\begin{align*} {y^{\prime }}^{3}-x y^{\prime }+a y&=0 \\ \end{align*}	✓	✓	✗	✗	57.645
26813	12580	\begin{align*} x \left (x^{2}-1\right ) y^{\prime \prime }+\left (3 x^{2}-1\right ) y^{\prime }+y x&=0 \\ \end{align*}	✗	✓	✓	✗	57.651
26814	13446	\begin{align*} y^{\prime }&=\lambda \operatorname {arccot}\left (x \right )^{n} y^{2}-b \lambda \,x^{m} \operatorname {arccot}\left (x \right )^{n} y+b m \,x^{m -1} \\ \end{align*}	✓	✗	✗	✗	57.690
26815	4249	\begin{align*} \left (x +\frac {2}{y}\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	57.701
26816	4707	\begin{align*} y^{\prime }&=a +b y+\sqrt {A +B y} \\ \end{align*}	✓	✓	✓	✓	57.720
26817	7542	\begin{align*} x^{2}-3 y^{2}+2 x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	57.864
26818	6832	\begin{align*} x y^{\prime }-y-\sqrt {x^{2}+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	58.004
26819	13522	\begin{align*} y y^{\prime }-y&=\frac {A}{\sqrt {x}} \\ \end{align*}	✗	✓	✓	✗	58.050
26820	2908	\begin{align*} 3 x -y+2+\left (x +2 y+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✗	✓	✓	58.086
26821	27348	\begin{align*} y^{\prime }&=\sqrt {x +2 y}-x \\ \end{align*}	✓	✓	✓	✗	58.089
26822	19707	\begin{align*} v^{\prime \prime }&=\left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}} \\ \end{align*}	✗	✗	✗	✗	58.293
26823	6049	\begin{align*} -\left (a +x \tan \left (x \right )\right ) y+x \left (1-2 x \tan \left (x \right )\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	58.329
26824	24360	\begin{align*} x -1-\left (3 x -2 y-5\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	58.352
26825	6311	\begin{align*} a \,{\mathrm e}^{y}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	58.371
26826	26269	\begin{align*} 3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	58.395
26827	11788	\begin{align*} \left (a y^{2}+b x +c \right ) {y^{\prime }}^{2}-b y y^{\prime }+d y^{2}&=0 \\ \end{align*}	✗	✗	✓	✗	58.429
26828	19374	\begin{align*} y^{2}&=\left (x^{3}-y x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	58.503
26829	26674	\begin{align*} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-2 \left (1-x \right ) y&=2 x -2 \\ y \left (\infty \right ) &= 1 \\ \end{align*}	✗	✓	✓	✗	58.539
26830	13421	\begin{align*} y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+\lambda \arcsin \left (x \right )^{n} \left (x^{1+k} y-1\right ) \\ \end{align*}	✓	✓	✗	✗	58.553
26831	13503	\begin{align*} y y^{\prime }-y&=A \left ({\mathrm e}^{\frac {2 x}{A}}-1\right ) \\ \end{align*}	✗	✓	✗	✗	58.596
26832	13635	\begin{align*} x \left (2 a \,x^{n} y+b \right ) y^{\prime }&=-a \left (3 n +m \right ) x^{n} y^{2}-b \left (2 n +m \right ) y+A \,x^{m}+x \,x^{-n} \\ \end{align*}	✓	✓	✓	✗	58.695
26833	6857	\begin{align*} x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	58.749
26834	20480	\begin{align*} \left (x^{2} y^{\prime }+y^{2}\right ) \left (x y^{\prime }+y\right )&=\left (y^{\prime }+1\right )^{2} \\ \end{align*}	✗	✗	✗	✗	58.789
26835	5475	\begin{align*} {y^{\prime }}^{2} x -a y y^{\prime }+b&=0 \\ \end{align*}	✓	✓	✓	✗	58.826
26836	24302	\begin{align*} y^{2}-\left (y x +2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	58.904
26837	6532	\begin{align*} y^{2} y^{\prime \prime }&=a \\ \end{align*}	✓	✓	✓	✓	58.905
26838	19976	\begin{align*} x -y y^{\prime }&=a {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	58.990
26839	21326	\begin{align*} -x^{\prime \prime }+x&={\mathrm e}^{-x^{2}} \\ x \left (a \right ) &= 0 \\ x \left (b \right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	59.008
26840	6073	\begin{align*} -p \left (1+p \right ) y+2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	59.191
26841	12107	\begin{align*} y^{\prime }&=\frac {\left (\left (x^{2}+1\right )^{{3}/{2}} x^{2}+\left (x^{2}+1\right )^{{3}/{2}}+y^{2} \left (x^{2}+1\right )^{{3}/{2}}+x^{2} y^{3}+y^{3}\right ) x}{\left (x^{2}+1\right )^{3}} \\ \end{align*}	✓	✓	✓	✗	59.210
26842	8715	\begin{align*} \left (x y^{\prime }+y\right )^{2}&=y^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	59.291
26843	6906	\begin{align*} {\mathrm e}^{\frac {y}{x}} x +y&=x y^{\prime } \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	59.353
26844	12870	\begin{align*} y^{\prime \prime }+a y y^{\prime }+y^{3} b&=0 \\ \end{align*}	✓	✓	✓	✗	59.363
26845	11626	\begin{align*} \left (2 x^{{5}/{2}} y^{{3}/{2}}+x^{2} y-x \right ) y^{\prime }-x^{{3}/{2}} y^{{5}/{2}}+x y^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✗	59.385
26846	14475	\begin{align*} \left (4 x -y\right ) y^{\prime }+2 x -5 y&=0 \\ y \left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	59.433
26847	23877	\begin{align*} y^{\prime }&=\frac {2 x^{2}+2 y^{2}-3 y x}{y x} \\ \end{align*}	✓	✓	✓	✓	59.445
26848	15822	\begin{align*} S^{\prime }&=S^{3}-2 S^{2}+S \\ S \left (0\right ) &= {\frac {3}{2}} \\ \end{align*}	✓	✓	✗	✓	59.471
26849	3231	\begin{align*} x^{2} y^{\prime \prime }+4 x y^{\prime }+3 y&=\left (x -1\right ) \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	59.537
26850	21076	\begin{align*} x^{2}+y^{2}+\left (a x y+y^{4}\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	59.565
26851	5691	\begin{align*} a \left (1+{y^{\prime }}^{3}\right )^{{1}/{3}}+x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	59.640
26852	17903	\begin{align*} x^{2} y^{\prime }+\cos \left (2 y\right )&=1 \\ y \left (\infty \right ) &= \frac {10 \pi }{3} \\ \end{align*}	✗	✓	✗	✗	59.645
26853	5232	\begin{align*} \left (x +y\right )^{2} y^{\prime }&=\left (x +y+2\right )^{2} \\ \end{align*}	✓	✓	✓	✓	59.697
26854	21106	\begin{align*} x^{\prime \prime }+p \left (t \right ) x^{\prime }+q \left (t \right ) x&=0 \\ \end{align*}	✗	✗	✗	✗	59.761
26855	17102	\begin{align*} y^{\prime }&=y^{3}-1 \\ \end{align*}	✓	✓	✓	✓	59.776
26856	6909	\begin{align*} x +2 y-4-\left (2 x -4 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	59.892
26857	24270	\begin{align*} y^{2}-x \left (2 x +3 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	59.910
26858	24324	\begin{align*} 6 y^{2}-x \left (2 x^{3}+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	59.968
26859	13268	\begin{align*} x^{3} y^{\prime }&=x^{3} a y^{2}+\left (b \,x^{2}+c \right ) y+s x \\ \end{align*}	✓	✓	✓	✗	59.970
26860	16303	\begin{align*} \left (2 y x +2 x^{2}\right ) y^{\prime }&=x^{2}+2 y x +2 y^{2} \\ \end{align*}	✓	✓	✓	✗	59.980
26861	2903	\begin{align*} 3 x -y+1+\left (x -3 y-5\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	59.984
26862	7547	\begin{align*} \sqrt {\frac {y}{x}}+\cos \left (x \right )+\left (\sqrt {\frac {x}{y}}+\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✓	✗	59.987
26863	15153	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✗	✓	✗	✗	60.009
26864	5877	\begin{align*} \left (\operatorname {a0} +4 \operatorname {a1} \cosh \left (x \right )^{2}-\operatorname {a2} \operatorname {sech}\left (x \right )^{2}\right ) y+\tanh \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✗	✗	60.065
26865	2330	\begin{align*} 2 t y y^{\prime }&=3 y^{2}-t^{2} \\ \end{align*}	✓	✓	✓	✓	60.100
26866	24156	\begin{align*} 5 v-u +\left (3 v-7 u \right ) v^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	60.165
26867	6370	\begin{align*} 2 y^{\prime \prime }&=y \left (a -y^{2}\right ) \\ \end{align*}	✓	✓	✓	✗	60.175
26868	14247	\begin{align*} {x^{\prime }}^{2}+x t&=\sqrt {t +1} \\ \end{align*}	✗	✗	✗	✗	60.183
26869	13506	\begin{align*} y y^{\prime }-y&=\frac {4}{9} x +2 A \,x^{2}+2 A^{2} x^{3} \\ \end{align*}	✗	✓	✓	✗	60.192
26870	25833	\begin{align*} y y^{\prime }+x&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	60.362
26871	25005	\begin{align*} y^{\prime }&=\frac {y^{2}-4 y t +6 t^{2}}{t^{2}} \\ y \left (2\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	60.368
26872	26897	\begin{align*} y x +x^{2} y^{\prime }&=-\frac {1}{y^{{3}/{2}}} \\ \end{align*}	✓	✓	✓	✓	60.450
26873	6996	\begin{align*} x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	60.513
26874	17010	\begin{align*} 4 x \left (x^{2}+y^{2}\right )-5 y+4 y \left (x^{2}+y^{2}-5 x \right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	60.570
26875	19870	\begin{align*} y^{\prime \prime }&=\frac {1}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	60.573
26876	25050	\begin{align*} y^{\prime }&=\frac {t -y}{t +y} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	60.576
26877	27478	\begin{align*} {y^{\prime }}^{3}+\left (-2 y^{\prime }+{y^{\prime }}^{2}\right ) x&=3 y^{\prime }-y \\ \end{align*}	✓	✓	✓	✗	60.621
26878	21368	\begin{align*} x^{2}-2 y^{2}+x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	60.649
26879	6065	\begin{align*} \left (b \,x^{2}+a \right ) y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	60.717
26880	20004	\begin{align*} \left (x y^{\prime }-y\right ) \left (y y^{\prime }+x \right )&=h^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✗	60.777
26881	6172	\begin{align*} \left (c \,x^{2}+b x +a \right ) y+2 \left (1-2 x \right ) y^{\prime }+4 x \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✗	✗	60.780
26882	25214	\begin{align*} y^{\prime \prime }+\sqrt {t}\, y^{\prime }-\sqrt {-3+t}\, y&=0 \\ y \left (10\right ) &= y_{1} \\ y^{\prime }\left (10\right ) &= y_{1} \\ \end{align*}	✗	✗	✗	✗	60.806
26883	21040	\begin{align*} x^{\prime }&=2+\sin \left (x\right ) \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	60.825
26884	14010	\begin{align*} y^{2}-x^{2}+2 m x y+\left (m y^{2}-m \,x^{2}-2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	60.839
26885	21822	\begin{align*} \left (x^{2}+y^{2}\right ) \left (x y^{\prime }+y\right )&=x y \left (x y^{\prime }-y\right ) \\ \end{align*}	✓	✓	✓	✓	60.937
26886	25185	\begin{align*} y^{\prime \prime }+\sqrt {t}\, y^{\prime }+y&=\sqrt {t} \\ \end{align*}	✗	✗	✗	✗	61.001
26887	788	\begin{align*} 2 x^{2} y-x^{3} y^{\prime }&=y^{3} \\ \end{align*}	✓	✓	✓	✓	61.032
26888	25788	\begin{align*} y y^{\prime }&=-x \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	61.079
26889	13740	\begin{align*} x y^{\prime \prime }+\left (a b \,x^{2}+b -5\right ) y^{\prime }+2 a^{2} \left (b -2\right ) x^{3} y&=0 \\ \end{align*}	✗	✓	✓	✗	61.140
26890	19818	\begin{align*} \left (5 x -2 y+7\right ) y^{\prime }&=x -3 y+2 \\ \end{align*}	✓	✓	✓	✗	61.193
26891	13557	\begin{align*} y y^{\prime }&=\frac {y}{\sqrt {a x +b}}+1 \\ \end{align*}	✓	✓	✓	✓	61.210
26892	10077	\begin{align*} y^{\prime \prime }-y y^{\prime }&=2 x \\ \end{align*}	✗	✓	✓	✗	61.333
26893	23224	\begin{align*} y^{\prime }&=\frac {\sqrt {2}\, \sqrt {\frac {x +y}{x}}}{2} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	61.371
26894	1165	\begin{align*} y^{\prime }&=\frac {3 y^{2}-x^{2}}{2 y x} \\ \end{align*}	✓	✓	✓	✓	61.401
26895	5684	\begin{align*} 2 \left (y+1\right )^{{3}/{2}}+3 x y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	61.622
26896	11644	\begin{align*} \cos \left (y\right ) y^{\prime }+x \sin \left (y\right ) \cos \left (y\right )^{2}-\sin \left (y\right )^{3}&=0 \\ \end{align*}	✗	✓	✓	✓	61.663
26897	19903	\begin{align*} \left (3 x +4 y\right ) y^{\prime }+y-2 x&=0 \\ \end{align*}	✓	✓	✓	✗	61.677
26898	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*}	✓	✓	✓	✗	61.855
26899	3053	\begin{align*} y^{2}+\left (x^{3}-2 y x \right ) y^{\prime }&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	61.862
26900	13828	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\left (2 a \,x^{2}+b \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	61.907