2.3.252 Problems 25101 to 25200

Table 2.1035: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
25101	24360	\begin{align*} x -1-\left (3 x -2 y-5\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	79.972
25102	2603	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=\sin \left (t \right )+{\mathrm e}^{2 t} t \\ \end{align*}	✓	✓	✓	✓	79.973
25103	15163	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=1-2 x \\ \end{align*}	✓	✓	✓	✗	79.980
25104	7768	\begin{align*} y^{\prime \prime }-y^{\prime }+10 y&=20-{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	79.986
25105	3118	\begin{align*} y^{\prime \prime }-4 y&=x +{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	80.075
25106	2525	\begin{align*} y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\ y \left (1\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	80.147
25107	12880	\begin{align*} y^{\prime \prime }&=a \sqrt {1+{y^{\prime }}^{2}}+b \\ \end{align*}	✓	✓	✓	✗	80.147
25108	2598	\begin{align*} y^{\prime \prime }+5 y^{\prime }+4 y&=t^{2} {\mathrm e}^{7 t} \\ \end{align*}	✓	✓	✓	✓	80.162
25109	12664	\begin{align*} y^{\prime \prime }&=-\frac {\left (3 x^{2}+a \right ) y^{\prime }}{x^{3}}-\frac {b y}{x^{6}} \\ \end{align*}	✓	✓	✓	✗	80.164
25110	5785	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{-x}+x^{2} \\ \end{align*}	✓	✓	✓	✓	80.199
25111	13225	\begin{align*} x^{n +1} y^{\prime }&=x^{2 n} a y^{2}+c \,x^{m}+d \\ \end{align*}	✓	✓	✓	✗	80.228
25112	12551	\begin{align*} 9 x \left (x -1\right ) y^{\prime \prime }+3 \left (2 x -1\right ) y^{\prime }-20 y&=0 \\ \end{align*}	✓	✓	✓	✗	80.254
25113	1342	\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=\frac {{\mathrm e}^{t}}{t^{2}+1} \\ \end{align*}	✓	✓	✓	✗	80.257
25114	344	\begin{align*} 4 y+y^{\prime \prime }&=3 x \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	80.441
25115	14023	\begin{align*} -y+y^{\prime } x&=\sqrt {x^{2}-y^{2}} \\ \end{align*}	✓	✓	✓	✓	80.471
25116	17290	\begin{align*} t y^{3}-\left (t^{4}+y^{4}\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	80.533
25117	4473	\begin{align*} y^{\prime \prime }+3 y^{\prime }+5 y&=5 \,{\mathrm e}^{-x} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	80.605
25118	24348	\begin{align*} x -4 y-3-\left (x -6 y-5\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	80.707
25119	19202	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=4 \cos \left (\ln \left (x +1\right )\right ) \\ \end{align*}	✓	✓	✓	✗	80.750
25120	882	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=x \left ({\mathrm e}^{-x}-{\mathrm e}^{-2 x}\right ) \\ \end{align*}	✓	✓	✓	✓	80.780
25121	7305	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{x}+\left (1-x \right ) \left ({\mathrm e}^{2 x}-1\right ) \\ \end{align*}	✓	✓	✓	✓	80.803
25122	2351	\begin{align*} y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	80.920
25123	23088	\begin{align*} x^{\prime \prime }+4 x&=\sin \left (2 t \right )+2 t \\ \end{align*}	✓	✓	✓	✓	81.001
25124	13220	\begin{align*} x^{2} y^{\prime }&=a \,x^{2} y^{2}+b \,x^{n}+c \\ \end{align*}	✓	✓	✓	✗	81.127
25125	4456	\begin{align*} y^{\prime \prime }-8 y^{\prime }+17 y&={\mathrm e}^{4 x} \left (x^{2}-3 x \sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	81.166
25126	7782	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	81.168
25127	12519	\begin{align*} x \left (x -1\right ) y^{\prime \prime }+a y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	81.171
25128	5784	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{x}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	81.234
25129	20570	\begin{align*} a^{2} y^{\prime \prime } y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	81.252
25130	20870	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +3 y&=5 x^{2} \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	81.274
25131	17813	\begin{align*} x^{\prime \prime }+x&=\left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✗	✓	✓	✓	81.432
25132	7079	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=8+6 \,{\mathrm e}^{x}+2 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	81.435
25133	1339	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{-2 t}}{t^{2}} \\ \end{align*}	✓	✓	✓	✓	81.466
25134	3775	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +5 y&=8 x \ln \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	81.542
25135	883	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=x \,{\mathrm e}^{3 x} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	81.543
25136	20430	\begin{align*} \left (-y+y^{\prime } x \right )^{2}&=a \left (1+{y^{\prime }}^{2}\right ) \left (x^{2}+y^{2}\right )^{{3}/{2}} \\ \end{align*}	✗	✓	✓	✗	81.651
25137	5923	\begin{align*} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✓	✓	✗	81.653
25138	24180	\begin{align*} 16 x +15 y+\left (3 x +y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= -3 \\ \end{align*}	✓	✓	✓	✗	81.763
25139	3745	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{-2 x}}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	81.898
25140	1664	\begin{align*} y^{\prime }&=\frac {2 y^{2}-y x +2 x^{2}}{y x +2 x^{2}} \\ \end{align*}	✓	✓	✓	✗	81.908
25141	7578	\begin{align*} y^{\prime \prime }+2 y^{\prime }+4 y&=6 \cos \left (2 t \right )+8 \sin \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	81.988
25142	8949	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	81.994
25143	10195	\begin{align*} {y^{\prime }}^{2}+y^{2}&=\sec \left (x \right )^{4} \\ \end{align*}	✗	✗	✗	✗	82.002
25144	5615	\begin{align*} {y^{\prime }}^{3}+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	82.097
25145	3171	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	82.105
25146	5999	\begin{align*} \left (b \,x^{2}+a \right ) y+2 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	82.118
25147	6261	\begin{align*} b y+a x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✗	✗	82.178
25148	8907	\begin{align*} y^{\prime \prime }+2 i y^{\prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	82.181
25149	3759	\begin{align*} y^{\prime \prime }+2 y^{\prime }+17 y&=\frac {64 \,{\mathrm e}^{-x}}{3+\sin \left (4 x \right )^{2}} \\ \end{align*}	✓	✓	✓	✗	82.218
25150	13399	\begin{align*} \left (a \tan \left (\lambda x \right )+b \right ) y^{\prime }&=y^{2}+k \tan \left (\mu x \right ) y-d^{2}+k d \tan \left (\mu x \right ) \\ \end{align*}	✓	✓	✓	✗	82.405
25151	7577	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=-50 \sin \left (5 t \right ) \\ \end{align*}	✓	✓	✓	✓	82.411
25152	7811	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x^{5}} \\ \end{align*}	✓	✓	✓	✓	82.427
25153	6283	\begin{align*} -y+y^{\prime } x +x^{5} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	82.446
25154	6074	\begin{align*} p \left (1+p \right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	82.457
25155	11912	\begin{align*} y^{\prime }&=\frac {\left (2 y \ln \left (x \right )-1\right )^{2}}{x} \\ \end{align*}	✓	✓	✓	✗	82.506
25156	7854	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{x} \left (1-x \right ) \\ \end{align*}	✓	✓	✓	✓	82.524
25157	3209	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }-2 y&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	82.556
25158	844	\begin{align*} y^{\prime \prime }+2 y&=6 x +4 \\ \end{align*}	✓	✓	✓	✓	82.576
25159	1834	\begin{align*} \left (x -1\right )^{2} y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+2 y&=\left (x -1\right )^{2} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -6 \\ \end{align*}	✓	✓	✓	✗	82.674
25160	20745	\begin{align*} \left (2 x^{2}+1\right ) {y^{\prime }}^{2}+\left (y^{2}+2 y x +x^{2}+2\right ) y^{\prime }+2 y^{2}+1&=0 \\ \end{align*}	✗	✗	✓	✗	82.694
25161	3756	\begin{align*} y^{\prime \prime }-2 m y^{\prime }+m^{2} y&=\frac {{\mathrm e}^{x m}}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✗	82.695
25162	4953	\begin{align*} 2 x^{2} y^{\prime }&=2 y x +\left (-x \cot \left (x \right )+1\right ) \left (x^{2}-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✗	82.721
25163	20177	\begin{align*} a^{2} {y^{\prime \prime }}^{2}&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	82.781
25164	6992	\begin{align*} \left (x +1\right ) y^{\prime }-1-y&=\left (x +1\right ) \sqrt {1+y} \\ \end{align*}	✓	✓	✓	✓	82.820
25165	6072	\begin{align*} n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=\frac {2 \left (-1-n \right ) x \operatorname {LegendreP}\left (n , x\right )+2 \left (n +1\right ) \operatorname {LegendreP}\left (n +1, x\right )}{x^{2}-1} \\ \end{align*}	✗	✓	✓	✗	82.848
25166	18341	\begin{align*} x^{3} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x^{2} y^{\prime }+y x&=2 \ln \left (x \right ) \\ y \left (\infty \right ) &= 0 \\ \end{align*}	✗	✓	✗	✗	82.930
25167	4988	\begin{align*} 2 x^{3} y^{\prime }&=y \left (x^{2}-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	82.931
25168	3012	\begin{align*} \sin \left (x \right ) y-2 \cos \left (y\right )+\tan \left (x \right )-\left (\cos \left (x \right )-2 x \sin \left (y\right )+\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	82.965
25169	9888	\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +5 y&=0 \\ \end{align*}	✓	✓	✓	✓	82.997
25170	13598	\begin{align*} y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (3 x +7\right )}{5 x^{{3}/{5}}} \\ \end{align*}	✗	✗	✗	✗	83.000
25171	5769	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\left (x -6\right ) x^{2} \\ \end{align*}	✓	✓	✓	✓	83.013
25172	527	\begin{align*} y^{\prime }&=x^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✗	83.036
25173	2600	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=\left (3 t^{7}-5 t^{4}\right ) {\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	83.047
25174	7533	\begin{align*} 1+\frac {1}{1+x^{2}+4 y x +y^{2}}+\left (\frac {1}{\sqrt {y}}+\frac {1}{1+x^{2}+2 y x +y^{2}}\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	83.207
25175	3189	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=x^{2}-8 \\ \end{align*}	✓	✓	✓	✓	83.371
25176	3667	\begin{align*} 2 y^{\prime }+\cot \left (x \right ) y&=\frac {8 \cos \left (x \right )^{3}}{y} \\ \end{align*}	✓	✓	✓	✓	83.427
25177	20443	\begin{align*} \left (a {y^{\prime }}^{2}-b \right ) x y+\left (b \,x^{2}-a y^{2}+c \right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✓	✗	83.655
25178	7687	\begin{align*} y^{\prime \prime } x +\frac {y^{\prime }}{2}+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	83.726
25179	24311	\begin{align*} x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	83.734
25180	7784	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	83.796
25181	7970	\begin{align*} y^{\prime \prime }+9 y&=\cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	83.815
25182	13579	\begin{align*} y y^{\prime }+\frac {a \left (13 x -18\right ) y}{15 x^{{7}/{5}}}&=-\frac {4 a^{2} \left (x -1\right ) \left (x -6\right )}{15 x^{{9}/{5}}} \\ \end{align*}	✗	✗	✗	✗	83.901
25183	21789	\begin{align*} x^{\prime \prime }&=x^{2}-4 x+\lambda \\ \end{align*}	✓	✓	✓	✗	84.101
25184	21393	\begin{align*} x^{2}-3 y^{2}+2 y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	84.206
25185	5740	\begin{align*} y^{\prime \prime }+a^{2} y&=\cot \left (a x \right ) \\ \end{align*}	✓	✓	✓	✓	84.326
25186	2605	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{t}+{\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	84.342
25187	7302	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{x}+6 x -5 \\ \end{align*}	✓	✓	✓	✓	84.378
25188	8771	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (4 x +3\right ) y^{\prime }-y&=x +\frac {1}{x} \\ \end{align*}	✗	✓	✓	✗	84.526
25189	13582	\begin{align*} y y^{\prime }+\frac {3 a \left (13 x -8\right ) y}{20 x^{{7}/{5}}}&=-\frac {a^{2} \left (x -1\right ) \left (27 x -32\right )}{20 x^{{9}/{5}}} \\ \end{align*}	✗	✗	✗	✗	84.536
25190	6585	\begin{align*} a^{2} {y^{\prime \prime }}^{2}&=\left (1+{y^{\prime }}^{2}\right )^{3} \\ \end{align*}	✓	✓	✓	✗	84.609
25191	24162	\begin{align*} v^{2}+x \left (x +v\right ) v^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	84.643
25192	2604	\begin{align*} y^{\prime \prime }+y^{\prime }+4 y&=t^{2}+\left (2 t +3\right ) \left (1+\cos \left (t \right )\right ) \\ \end{align*}	✓	✓	✓	✓	84.746
25193	2955	\begin{align*} y-x^{2} \sqrt {x^{2}-y^{2}}-y^{\prime } x&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	84.755
25194	3747	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {2 \,{\mathrm e}^{-3 x}}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✗	84.765
25195	13850	\begin{align*} x \left (a \,x^{2}+b \right ) y^{\prime \prime }+2 \left (a \,x^{2}+b \right ) y^{\prime }-2 a x y&=0 \\ \end{align*}	✓	✓	✓	✗	84.894
25196	1755	\begin{align*} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	85.113
25197	4500	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\sin \left ({\mathrm e}^{-x}\right ) \\ \end{align*}	✓	✓	✓	✓	85.202
25198	13520	\begin{align*} y y^{\prime }-y&=-\frac {3 x}{16}+\frac {A}{x^{{5}/{3}}} \\ \end{align*}	✗	✗	✗	✗	85.275
25199	23085	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&={\mathrm e}^{2 x} \sin \left (3 x \right ) \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -{\frac {25}{6}} \\ \end{align*}	✓	✓	✓	✓	85.401
25200	11847	\begin{align*} f \left (x^{2}+y^{2}\right ) \sqrt {1+{y^{\prime }}^{2}}-y^{\prime } x +y&=0 \\ \end{align*}	✗	✓	✓	✗	85.413