2.3.230 Problems 22901 to 23000

Table 2.1033: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
22901	20300	\begin{align*} y^{\prime }&=\left (4 x +y+1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	18.138
22902	14455	\begin{align*} y^{2}+2 y x -x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	18.141
22903	13322	\begin{align*} y^{\prime }&=y^{2}+a x \sinh \left (b x \right )^{m} y+a \sinh \left (b x \right )^{m} \\ \end{align*}	✓	✓	✓	✗	18.145
22904	13650	\begin{align*} y^{\prime } x&=a y^{3}+3 a b \,x^{n} y^{2}-b n \,x^{n}-2 a \,b^{3} x^{3 n} \\ \end{align*}	✓	✓	✓	✗	18.158
22905	13411	\begin{align*} y^{\prime }&=\lambda \sin \left (\lambda x \right ) y^{2}+a \,x^{n} \cos \left (\lambda x \right ) y-a \,x^{n} \\ \end{align*}	✓	✓	✗	✗	18.159
22906	16380	\begin{align*} x \left (1-2 y\right )+\left (-x^{2}+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	18.163
22907	7483	\begin{align*} y^{2}+2 y x -x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	18.173
22908	8304	\begin{align*} y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\ y \left (0\right ) &= -{\frac {5}{2}} \\ \end{align*}	✓	✓	✓	✓	18.174
22909	13276	\begin{align*} x^{2} \left (a \,x^{n}-1\right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (p \,x^{n}+q \right ) x y+r \,x^{n}+s&=0 \\ \end{align*}	✓	✓	✓	✗	18.176
22910	12200	\begin{align*} y^{\prime }&=\frac {2 y^{6} \left (1+4 x y^{2}+y^{2}\right )}{y^{3}+4 x y^{5}+y^{5}+2+24 x y^{2}+96 x^{2} y^{4}+128 x^{3} y^{6}} \\ \end{align*}	✓	✗	✓	✗	18.177
22911	23953	\begin{align*} \left (x +\frac {x}{x^{2}+y^{2}}\right ) y^{\prime }+y-\frac {y}{x^{2}+y^{2}}&=0 \\ y \left (1\right ) &= \sqrt {3} \\ \end{align*}	✓	✓	✓	✗	18.177
22912	24948	\begin{align*} y^{\prime }&=2 y \left (5-y\right ) \\ \end{align*}	✓	✓	✓	✓	18.177
22913	11884	\begin{align*} y^{\prime }&=\frac {F \left (-\left (x -y\right ) \left (x +y\right )\right ) x}{y} \\ \end{align*}	✗	✓	✓	✗	18.187
22914	19714	\begin{align*} x^{\prime }&=k \left (A -n x\right ) \left (M -m x\right ) \\ \end{align*}	✓	✓	✓	✓	18.188
22915	9930	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	18.197
22916	2933	\begin{align*} \frac {x^{2}+3 y^{2}}{x \left (3 x^{2}+4 y^{2}\right )}+\frac {\left (2 x^{2}+y^{2}\right ) y^{\prime }}{y \left (3 x^{2}+4 y^{2}\right )}&=0 \\ \end{align*}	✓	✓	✓	✓	18.202
22917	24077	\begin{align*} x^{2} y^{\prime \prime }+a x y^{\prime }+b y&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	18.206
22918	27009	\begin{align*} x^{2} y^{\prime \prime }+25 y^{\prime } x +144 y&=0 \\ y \left (1\right ) &= -4 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	18.207
22919	5125	\begin{align*} y y^{\prime } x +x^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	18.209
22920	6965	\begin{align*} y^{\prime } x +y&=y^{2} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	18.213
22921	20284	\begin{align*} 2 y^{\prime }-y \sec \left (x \right )&=y^{3} \tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	18.213
22922	5081	\begin{align*} \left (x +2 y\right ) y^{\prime }+2 x -y&=0 \\ \end{align*}	✓	✓	✓	✓	18.214
22923	5059	\begin{align*} \left (x -y\right ) y^{\prime }&=\left ({\mathrm e}^{-\frac {x}{y}}+1\right ) y \\ \end{align*}	✓	✓	✓	✓	18.215
22924	15533	\begin{align*} y^{\prime }&=y^{2}-x^{2} \\ \end{align*}	✓	✓	✓	✗	18.217
22925	11656	\begin{align*} \left (-y+y^{\prime } x \right ) \cos \left (\frac {y}{x}\right )^{2}+x&=0 \\ \end{align*}	✓	✓	✓	✗	18.218
22926	24267	\begin{align*} \left (t^{2}+1\right ) s^{\prime }+2 t \left (s t^{2}-3 \left (t^{2}+1\right )^{2}\right )&=0 \\ s \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	18.219
22927	6873	\begin{align*} \frac {\sqrt {f \,x^{4}+c \,x^{3}+c \,x^{2}+b x +a}\, y^{\prime }}{\sqrt {a +b y+c y^{2}+c y^{3}+f y^{4}}}&=-1 \\ \end{align*}	✓	✓	✓	✓	18.221
22928	25235	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +4 y&=0 \\ y \left (1\right ) &= -3 \\ y^{\prime }\left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	18.221
22929	11874	\begin{align*} y^{\prime }&=\frac {F \left (\frac {a y^{2}+b \,x^{2}}{a}\right ) x}{\sqrt {a}\, y} \\ \end{align*}	✓	✓	✓	✗	18.224
22930	24217	\begin{align*} x^{3}+x y^{2}-y+\left (x^{2} y+y^{3}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	18.226
22931	21975	\begin{align*} y^{\prime }&=x +y^{2} \\ \end{align*}	✓	✓	✓	✗	18.230
22932	14433	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= -1 \\ \end{align*}	✓	✗	✗	✗	18.233
22933	6980	\begin{align*} y^{\prime } x -y \left (2 y \ln \left (x \right )-1\right )&=0 \\ \end{align*}	✓	✓	✓	✓	18.243
22934	7929	\begin{align*} 2 x^{\prime }-\frac {x}{y}+x^{3} \cos \left (y \right )&=0 \\ \end{align*}	✓	✓	✓	✓	18.243
22935	1885	\begin{align*} \left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	18.249
22936	3655	\begin{align*} y^{\prime }&=\frac {x +\frac {y}{2}}{\frac {x}{2}-y} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	18.250
22937	25813	\begin{align*} y^{\prime }&=y^{2}-y-6 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	18.251
22938	26877	\begin{align*} 2 y+y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	18.253
22939	23056	\begin{align*} \frac {r^{\prime }}{r}&=\tan \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	18.263
22940	23161	\begin{align*} y^{\prime } x +y&=x^{5} \\ \end{align*}	✓	✓	✓	✓	18.279
22941	22361	\begin{align*} 3 x \left (1+y^{2}\right )+y \left (x^{2}+2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	18.282
22942	8672	\begin{align*} x +2 x^{3}+\left (2 y^{3}+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	18.286
22943	17319	\begin{align*} 3 t +\left (t -4 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	18.287
22944	13418	\begin{align*} y^{\prime }&=\lambda \sin \left (\lambda x \right ) y^{2}+a \sin \left (\lambda x \right ) y-a \tan \left (\lambda x \right ) \\ \end{align*}	✓	✓	✗	✗	18.290
22945	19276	\begin{align*} x^{2} y^{\prime }-3 y x -2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	18.293
22946	26336	\begin{align*} x^{2}+y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	18.298
22947	12472	\begin{align*} x^{2} y^{\prime \prime }+\left (2 a x +b \right ) x y^{\prime }+\left (a b x +c \,x^{2}+d \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	18.306
22948	23047	\begin{align*} T^{\prime \prime }+{T^{\prime }}^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	18.309
22949	12146	\begin{align*} y^{\prime }&=-\frac {x}{2}-\frac {a}{2}+\sqrt {x^{2}+2 a x +a^{2}+4 y}+x^{2} \sqrt {x^{2}+2 a x +a^{2}+4 y}+x^{3} \sqrt {x^{2}+2 a x +a^{2}+4 y} \\ \end{align*}	✗	✓	✓	✗	18.315
22950	15083	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	18.323
22951	3646	\begin{align*} y y^{\prime }&=\sqrt {x^{2}+y^{2}}-x \\ \end{align*}	✓	✓	✓	✓	18.347
22952	7488	\begin{align*} 2 x +2 y+2 x^{3} y+4 y^{2} x^{2}+\left (2 x +x^{4}+2 x^{3} y\right ) y^{\prime }&=0 \\ \end{align*}	✗	✓	✓	✗	18.353
22953	15628	\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	18.353
22954	9929	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	18.355
22955	4421	\begin{align*} x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	18.363
22956	15404	\begin{align*} -{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	18.368
22957	27614	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	18.378
22958	16295	\begin{align*} y^{\prime }+3 \cot \left (x \right ) y&=6 \cos \left (x \right ) y^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✓	18.382
22959	6979	\begin{align*} y^{\prime } x +x y^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✓	18.384
22960	25473	\begin{align*} y^{\prime }&=y^{2}+y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	18.391
22961	15627	\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ y \left (-1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	18.392
22962	21048	\begin{align*} x^{\prime }&=x^{2}-t^{2} \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	18.401
22963	25418	\begin{align*} y^{\prime }&=2 y+\delta \left (t -3\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	18.402
22964	24223	\begin{align*} 1+y \tan \left (y x \right )+x \tan \left (y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	18.407
22965	9049	\begin{align*} y^{\prime } x&=2 y \\ \end{align*}	✓	✓	✓	✓	18.408
22966	19311	\begin{align*} \frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\ \end{align*}	✓	✓	✓	✓	18.410
22967	26667	\begin{align*} 4 y^{\prime \prime } x +2 y^{\prime }+y&=1 \\ y \left (\infty \right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	18.412
22968	8400	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{\sqrt {x}}}{y} \\ y \left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	18.419
22969	8666	\begin{align*} 2 x^{2} y y^{\prime }+y^{2}&=2 \\ \end{align*}	✓	✓	✓	✓	18.420
22970	11593	\begin{align*} \left (3 x y^{2}-x^{2}\right ) y^{\prime }+y^{3}-2 y x&=0 \\ \end{align*}	✓	✓	✓	✗	18.420
22971	11490	\begin{align*} y^{\prime } \sqrt {-x^{2}+1}-y \sqrt {-1+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	18.421
22972	15634	\begin{align*} y^{\prime }&=\sqrt {\left (y+2\right ) \left (-1+y\right )} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	18.431
22973	25223	\begin{align*} 2 t^{2} y^{\prime \prime }-5 y^{\prime } t +3 y&=0 \\ \end{align*}	✓	✓	✓	✓	18.434
22974	19767	\begin{align*} y^{\prime \prime }&=c \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✗	18.444
22975	3652	\begin{align*} y^{\prime }&=\frac {y-\sqrt {x^{2}+y^{2}}}{x} \\ y \left (3\right ) &= 4 \\ \end{align*}	✓	✓	✓	✗	18.447
22976	8675	\begin{align*} 2 x \sqrt {1-y^{2}}+y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	18.453
22977	19823	\begin{align*} \left (6 x -4 y+1\right ) y^{\prime }&=3 x -2 y+1 \\ \end{align*}	✓	✓	✓	✓	18.457
22978	14451	\begin{align*} {\mathrm e}^{x} y+2 \,{\mathrm e}^{x}+y^{2}+\left ({\mathrm e}^{x}+2 y x \right ) y^{\prime }&=0 \\ y \left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✗	18.464
22979	26480	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	18.464
22980	7336	\begin{align*} 2 x -y \sin \left (2 x \right )&=\left (\sin \left (x \right )^{2}-2 y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	18.470
22981	12164	\begin{align*} y^{\prime }&=-\frac {\left (-1-y^{4}+2 y^{2} x^{2}-x^{4}-y^{6}+3 x^{2} y^{4}-3 y^{2} x^{4}+x^{6}\right ) x}{y} \\ \end{align*}	✓	✓	✓	✗	18.483
22982	17094	\begin{align*} y^{\prime }&=\frac {\left (5-2 \cos \left (x \right )\right )^{3} \sin \left (x \right ) \cos \left (y\right )^{4}}{\sin \left (y\right )} \\ \end{align*}	✓	✓	✓	✓	18.483
22983	9040	\begin{align*} y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	18.488
22984	3772	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=4 \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	18.492
22985	20309	\begin{align*} {x^{\prime }}^{2}&=k^{2} \left (1-{\mathrm e}^{-\frac {2 g x}{k^{2}}}\right ) \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	18.497
22986	20500	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{m} \\ \end{align*}	✓	✓	✓	✓	18.503
22987	16288	\begin{align*} y^{\prime }&=1+\left (-x +y\right )^{2} \\ y \left (0\right ) &= {\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	18.505
22988	13927	\begin{align*} y^{\prime \prime }+a \left (\lambda \,{\mathrm e}^{\lambda x}-a \,{\mathrm e}^{2 \lambda x}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	18.507
22989	26659	\begin{align*} y^{\prime \prime }+y^{\prime }+y \,{\mathrm e}^{-2 x}&={\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✗	18.507
22990	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*}	✓	✓	✓	✗	18.516
22991	7145	\begin{align*} y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-a -1}&=0 \\ \end{align*}	✓	✓	✓	✗	18.519
22992	12696	\begin{align*} y^{\prime \prime }&=-\frac {\sin \left (x \right ) y^{\prime }}{\cos \left (x \right )}-\frac {\left (2 x^{2}+x^{2} \sin \left (x \right )^{2}-24 \cos \left (x \right )^{2}\right ) y}{4 x^{2} \cos \left (x \right )^{2}}+\sqrt {\cos \left (x \right )} \\ \end{align*}	✗	✓	✓	✗	18.519
22993	17051	\begin{align*} y^{\prime }&=\sqrt {25-y^{2}} \\ y \left (3\right ) &= -6 \\ \end{align*}	✓	✓	✓	✗	18.523
22994	24268	\begin{align*} y^{\prime }&={\mathrm e}^{x +y} \\ \end{align*}	✓	✓	✓	✓	18.525
22995	11630	\begin{align*} \left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	18.527
22996	19307	\begin{align*} 2 x \left (1+\sqrt {x^{2}-y}\right )&=\sqrt {x^{2}-y}\, y^{\prime } \\ \end{align*}	✓	✓	✓	✓	18.527
22997	15856	\begin{align*} y^{\prime }&=y^{3} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	18.531
22998	21260	\begin{align*} x^{\prime \prime }&=x-x^{3} \\ x \left (0\right ) &= \frac {\sqrt {2}}{2} \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	18.534
22999	18580	\begin{align*} 2 x -y+\left (-x +2 y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	18.536
23000	25421	\begin{align*} y+y^{\prime }&=\delta \left (-2+t \right ) \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	18.537