2.3.252 Problems 25101 to 25200

Table 2.1077: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
25101	9656	\begin{align*} x^{\prime }&=-3 x+4 y-9 z \\ y^{\prime }&=6 x-y \\ z^{\prime }&=10 x+4 y+3 z \\ \end{align*}	✓	✓	✓	✗	18.575
25102	1678	\begin{align*} y^{\prime }+\frac {3 y}{x}&=\frac {3 y^{2} x^{4}+10 x^{2} y+6}{x^{3} \left (2 x^{2} y+5\right )} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	18.579
25103	15646	\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✗	18.581
25104	14002	\begin{align*} x +y-\left (x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	18.590
25105	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*}	✓	✓	✓	✗	18.595
25106	27327	\begin{align*} y \left (x +y^{2}\right )+x^{2} \left (-1+y\right ) y^{\prime }&=0 \\ \end{align*}	✗	✓	✓	✗	18.607
25107	20247	\begin{align*} x^{2}-y^{2}+2 x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	18.635
25108	25870	\begin{align*} x^{\prime }-\frac {2 x}{y}&=x^{4} \\ \end{align*}	✓	✓	✓	✓	18.639
25109	7895	\begin{align*} x +y+1-\left (-3+x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	18.641
25110	4718	\begin{align*} y^{\prime }+x \left (\sin \left (2 y\right )-x^{2} \cos \left (y\right )^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	18.645
25111	5252	\begin{align*} x \left (3 x -y^{2}\right ) y^{\prime }+\left (5 x -2 y^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	18.645
25112	15060	\begin{align*} \left (3+2 x +4 y\right ) y^{\prime }-2 y-x -1&=0 \\ \end{align*}	✓	✓	✓	✓	18.650
25113	18568	\begin{align*} 3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	18.656
25114	25787	\begin{align*} y y^{\prime }&=-x \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	18.670
25115	25723	\begin{align*} y y^{\prime }&=3 x \\ y \left (2\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	18.672
25116	12473	\begin{align*} x^{2} y^{\prime \prime }+\left (a x +b \right ) y^{\prime } x +\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x +\operatorname {c1} \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	18.675
25117	15039	\begin{align*} 2 x +2 y-1+\left (x +y-2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	18.685
25118	15821	\begin{align*} S^{\prime }&=S^{3}-2 S^{2}+S \\ S \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	18.746
25119	12232	\begin{align*} y^{\prime }&=-\frac {-y+\sqrt {x^{2}+y^{2}}\, x^{2}-x \sqrt {x^{2}+y^{2}}\, y+x^{4} \sqrt {x^{2}+y^{2}}-x^{3} \sqrt {x^{2}+y^{2}}\, y+x^{5} \sqrt {x^{2}+y^{2}}-x^{4} \sqrt {x^{2}+y^{2}}\, y}{x} \\ \end{align*}	✗	✓	✓	✗	18.749
25120	13053	\begin{align*} y^{\prime \prime } y^{\prime \prime \prime }-a \sqrt {1+b^{2} {y^{\prime \prime }}^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	18.752
25121	5975	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	18.761
25122	17264	\begin{align*} \frac {2}{t}+\frac {1}{y}+\frac {t y^{\prime }}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	18.784
25123	3018	\begin{align*} y+\left (3 x -2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	18.785
25124	22033	\begin{align*} \left (x +y\right ) y^{\prime }+x -y&=0 \\ \end{align*}	✓	✓	✓	✓	18.795
25125	11544	\begin{align*} \left (3 x +2\right ) \left (y-2 x -1\right ) y^{\prime }-y^{2}+y x -7 x^{2}-9 x -3&=0 \\ \end{align*}	✓	✓	✓	✗	18.800
25126	6594	\begin{align*} {y^{\prime }}^{2} \left (1-b^{2} {y^{\prime }}^{2}\right )+2 b^{2} y {y^{\prime }}^{2} y^{\prime \prime }+\left (a^{2}-b^{2} y^{2}\right ) {y^{\prime \prime }}^{2}&=0 \\ \end{align*}	✓	✓	✗	✗	18.813
25127	17339	\begin{align*} 2 x -y-2+\left (-x +2 y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	18.851
25128	26271	\begin{align*} 4 x y^{2}+\left (3 x^{2} y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	18.910
25129	3545	\begin{align*} \sin \left (\frac {y}{x}\right ) \left (x y^{\prime }-y\right )&=x \cos \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	18.925
25130	14554	\begin{align*} 2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime }&=0 \\ y \left (-2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	18.925
25131	4239	\begin{align*} x y y^{\prime }&=2 x^{2}-y^{2} \\ \end{align*}	✓	✓	✓	✓	18.926
25132	17281	\begin{align*} y^{\prime }&=\frac {1}{\frac {2 y \,{\mathrm e}^{-\frac {t}{y}}}{t}+\frac {t}{y}} \\ \end{align*}	✓	✓	✓	✓	18.944
25133	17989	\begin{align*} x -y x +\left (x^{2}+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	18.956
25134	13335	\begin{align*} \left (a \cosh \left (\lambda x \right )+b \right ) \left (y^{\prime }-y^{2}\right )+a \,\lambda ^{2} \cosh \left (\lambda x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	18.967
25135	2331	\begin{align*} \left (t -\sqrt {y t}\right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	18.984
25136	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*}	✗	✓	✓	✗	18.997
25137	17293	\begin{align*} 5 t +2 y+1+\left (2 t +y+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	18.999
25138	27521	\begin{align*} \tan \left (y\right ) y^{\prime }+4 \cos \left (y\right ) x^{3}&=2 x \\ \end{align*}	✓	✓	✓	✓	19.034
25139	8835	\begin{align*} x^{2}+y^{2}-2 x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	19.046
25140	27229	\begin{align*} 3 y^{2} y^{\prime }+16 x&=2 x y^{3} \\ y \left (\infty \right ) &= y_{0} \\ \end{align*}	✗	✓	✗	✗	19.071
25141	25031	\begin{align*} y^{2}+2 t y y^{\prime }+3 t^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	19.092
25142	9279	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	19.096
25143	21838	\begin{align*} x y \left (x y^{\prime }+y\right )&=4 x^{3} \\ \end{align*}	✓	✓	✓	✓	19.104
25144	6345	\begin{align*} h \left (y\right )+f \left (y\right ) y^{\prime }+g \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	19.116
25145	11961	\begin{align*} y^{\prime }&=\frac {x^{2} \left (x +1+2 x \sqrt {x^{3}-6 y}\right )}{2 x +2} \\ \end{align*}	✗	✓	✓	✗	19.180
25146	14022	\begin{align*} x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	19.194
25147	15820	\begin{align*} S^{\prime }&=S^{3}-2 S^{2}+S \\ S \left (1\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✗	✓	19.204
25148	22372	\begin{align*} y^{\prime }&=\frac {\left (-1+y\right ) \left (y+3\right )}{\left (-2+y\right ) \left (x +3\right )} \\ \end{align*}	✓	✓	✓	✓	19.217
25149	12075	\begin{align*} y^{\prime }&=-\frac {y \left (y x +1\right )}{x \left (y x +1-y\right )} \\ \end{align*}	✓	✓	✓	✗	19.227
25150	21370	\begin{align*} y+x y^{\prime }+\frac {y^{3} \left (-x y^{\prime }+y\right )}{x}&=0 \\ \end{align*}	✓	✓	✓	✗	19.236
25151	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*}	✓	✓	✓	✓	19.237
25152	24828	\begin{align*} y&=x y^{\prime }+x^{3} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	19.255
25153	18501	\begin{align*} y^{\prime }&=\frac {3 x^{2}+1}{12 y^{2}-12 y} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	19.260
25154	20288	\begin{align*} x^{2} y-2 x y^{2}-\left (x^{3}-3 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	19.260
25155	7546	\begin{align*} y-x +\left (x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	19.263
25156	24164	\begin{align*} x +\sin \left (\frac {y}{x}\right )^{2} \left (-x y^{\prime }+y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	19.274
25157	5703	\begin{align*} \ln \left (y^{\prime }\right )+4 x y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	19.299
25158	15456	\begin{align*} 2 x +2 y-1+\left (x +y-2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	19.314
25159	24353	\begin{align*} 3 x +2 y+7+\left (2 x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	19.316
25160	12053	\begin{align*} y^{\prime }&=\frac {-4 a x y-a^{2} x^{3}-2 a b \,x^{2}-4 a x +8}{8 y+2 a \,x^{2}+4 b x +8} \\ \end{align*}	✓	✓	✓	✓	19.337
25161	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*}	✗	✓	✓	✗	19.344
25162	20251	\begin{align*} y^{2}&=\left (y x -x^{2}\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	19.349
25163	14337	\begin{align*} t^{2} x^{\prime \prime }-3 x^{\prime } t +3 x&=4 t^{7} \\ \end{align*}	✓	✓	✓	✓	19.352
25164	2919	\begin{align*} \cos \left (x \right ) y-2 \sin \left (y\right )&=\left (2 x \cos \left (y\right )-\sin \left (x \right )\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	19.356
25165	4797	\begin{align*} x y^{\prime }+y \left (1-x y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	19.365
25166	11519	\begin{align*} \left (2 y+x +7\right ) y^{\prime }-y+2 x +4&=0 \\ \end{align*}	✓	✓	✓	✓	19.391
25167	8701	\begin{align*} y+\sqrt {y x}-x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	19.392
25168	24958	\begin{align*} 1-y^{2}-t y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	19.438
25169	6811	\begin{align*} \sqrt {1+{y^{\prime \prime }}^{2}}\, \left (1-y^{\prime \prime \prime }\right )&=y^{\prime \prime } y^{\prime \prime \prime } \\ \end{align*}	✓	✓	✓	✓	19.484
25170	15620	\begin{align*} y^{\prime }&=y^{3} \\ y \left (-1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	19.490
25171	12678	\begin{align*} y^{\prime \prime }&=-\frac {2 n \cosh \left (x \right ) y^{\prime }}{\sinh \left (x \right )}-\left (-a^{2}+n^{2}\right ) y \\ \end{align*}	✗	✓	✓	✗	19.519
25172	19962	\begin{align*} \left (y^{2}-x^{2}\right ) y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	19.536
25173	15362	\begin{align*} y+\frac {x}{y^{\prime }}&=\sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	19.545
25174	25004	\begin{align*} y^{\prime }&=\frac {4 t -3 y}{t -y} \\ \end{align*}	✓	✓	✓	✗	19.551
25175	26914	\begin{align*} y^{\prime }&=\frac {3 x -y-9}{x +y+1} \\ \end{align*}	✓	✓	✓	✓	19.551
25176	26376	\begin{align*} y&=x y^{\prime }+\frac {a y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} \\ \end{align*}	✓	✓	✓	✗	19.556
25177	11693	\begin{align*} a {y^{\prime }}^{2}+b \,x^{2} y^{\prime }+c x y&=0 \\ \end{align*}	✓	✓	✓	✗	19.558
25178	11630	\begin{align*} \left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	19.564
25179	4831	\begin{align*} x y^{\prime }&=y-2 x \tanh \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✗	19.565
25180	5438	\begin{align*} 2 {y^{\prime }}^{2}+2 \left (6 y-1\right ) y^{\prime }+3 y \left (6 y-1\right )&=0 \\ \end{align*}	✓	✓	✓	✓	19.569
25181	15049	\begin{align*} y^{\prime }&=\frac {3 x -4 y-2}{3 x -4 y-3} \\ \end{align*}	✓	✓	✓	✓	19.574
25182	21817	\begin{align*} 4 x -2 y+3+\left (5 y-2 x +7\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	19.582
25183	8245	\begin{align*} y y^{\prime }&=3 x \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	19.594
25184	6599	\begin{align*} f \left (y^{\prime \prime }, y^{\prime }-x y^{\prime \prime }, y-x y^{\prime }+\frac {x^{2} y^{\prime \prime }}{2}\right )&=0 \\ \end{align*}	✗	✓	✗	✗	19.605
25185	26892	\begin{align*} 1+{\mathrm e}^{\frac {y}{x}}-\frac {y \,{\mathrm e}^{\frac {y}{x}}}{x}+{\mathrm e}^{\frac {y}{x}} y^{\prime }&=0 \\ y \left (1\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	19.619
25186	5319	\begin{align*} \left (x^{3}-y^{4}\right ) y^{\prime }&=3 x^{2} y \\ \end{align*}	✓	✓	✓	✓	19.623
25187	3049	\begin{align*} 3 y x +\left (3 x^{2}+y^{2}\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	19.636
25188	4351	\begin{align*} y^{2}+\left (y x +\tan \left (y x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	19.643
25189	26905	\begin{align*} \left (x -2 y\right ) y^{\prime }&=2 x -y \\ \end{align*}	✓	✓	✓	✓	19.646
25190	5053	\begin{align*} \left (x -y\right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	19.658
25191	16286	\begin{align*} y^{\prime }&=\frac {\left (3 x -2 y\right )^{2}+1}{3 x -2 y}+\frac {3}{2} \\ \end{align*}	✓	✓	✓	✓	19.673
25192	13875	\begin{align*} x^{4} y^{\prime \prime }+a \,x^{n} y^{\prime }-\left (a \,x^{n -1}+a b \,x^{-2+n}+b^{2}\right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	19.677
25193	27334	\begin{align*} y^{2} \left (y-2 x y^{\prime }\right )&=x^{3} \left (x y^{\prime }-2 y\right ) \\ \end{align*}	✓	✓	✓	✗	19.677
25194	24291	\begin{align*} x y \left (1-y^{\prime }\right )&=x^{2} y^{\prime }+y^{2} \\ \end{align*}	✓	✓	✓	✓	19.693
25195	4238	\begin{align*} \left (x +y-1\right ) y^{\prime }&=x -y+1 \\ \end{align*}	✓	✓	✓	✓	19.694
25196	8225	\begin{align*} y^{\prime }&=\sqrt {y x} \\ \end{align*}	✓	✓	✓	✓	19.694
25197	12054	\begin{align*} y^{\prime }&=\frac {\left (x +1+x \ln \left (y\right )\right ) \ln \left (y\right ) y}{x \left (x +1\right )} \\ \end{align*}	✗	✓	✓	✓	19.699
25198	27344	\begin{align*} y^{\prime }&=\frac {x +2 y-4}{x -y-1} \\ \end{align*}	✓	✓	✓	✓	19.704
25199	18733	\begin{align*} y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+3 \ln \left (t \right ) y&=0 \\ y \left (2\right ) &= 3 \\ y^{\prime }\left (2\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	19.705
25200	23867	\begin{align*} y^{\prime }&=\frac {3 x -y}{x +2 y} \\ \end{align*}	✓	✓	✓	✓	19.710