2.3.253 Problems 25201 to 25300

Table 2.1079: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
25201	2522	\begin{align*} y^{\prime }&=1+y+y^{2} \cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✗	✓	✗	✗	19.711
25202	22398	\begin{align*} 2 x +3 y+4&=\left (4 x +6 y+1\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	19.717
25203	6984	\begin{align*} 2 \cos \left (x \right ) y^{\prime }&=y \sin \left (x \right )-y^{3} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	19.734
25204	11591	\begin{align*} 2 x \left (5 x^{2}+y^{2}\right ) y^{\prime }+y^{3}-x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	19.746
25205	5054	\begin{align*} \left (x +y\right ) y^{\prime }+x -y&=0 \\ \end{align*}	✓	✓	✓	✓	19.753
25206	12476	\begin{align*} x^{2} y^{\prime \prime }-2 x \left (x^{2}-a \right ) y^{\prime }+\left (2 n \,x^{2}+\left (\left (-1\right )^{n}-1\right ) a \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	19.768
25207	18583	\begin{align*} \frac {\sin \left (y\right )}{y}-2 \,{\mathrm e}^{-x} \sin \left (x \right )+\frac {\left (\cos \left (y\right )+2 \cos \left (x \right ) {\mathrm e}^{-x}\right ) y^{\prime }}{y}&=0 \\ \end{align*}	✓	✓	✓	✗	19.779
25208	22463	\begin{align*} y+\left (y^{3}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	19.782
25209	4890	\begin{align*} x^{2} y^{\prime }+y x +\sqrt {y}&=0 \\ \end{align*}	✓	✓	✓	✓	19.783
25210	24220	\begin{align*} \left (-x^{2}+1\right ) y^{2}+x \left (x^{2} y^{2}+2 x +y\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	19.808
25211	2871	\begin{align*} \left (x +y\right ) y^{\prime }+x&=y \\ \end{align*}	✓	✓	✓	✓	19.833
25212	3638	\begin{align*} \sin \left (\frac {y}{x}\right ) \left (x y^{\prime }-y\right )&=x \cos \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	19.837
25213	2334	\begin{align*} y^{\prime }&=\frac {t +y+1}{t -y+3} \\ \end{align*}	✓	✓	✓	✓	19.842
25214	3651	\begin{align*} y^{\prime }&=\frac {2 x -y}{x +4 y} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	19.844
25215	17912	\begin{align*} x y^{\prime }&=y \left (\ln \left (y\right )-\ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	19.852
25216	16976	\begin{align*} 3 y \left (t^{2}+y\right )+t \left (t^{2}+6 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	19.858
25217	13962	\begin{align*} \left (a^{2} {\mathrm e}^{2 \lambda x}+b \right ) y^{\prime \prime }-b \lambda y^{\prime }-a^{2} \lambda ^{2} k^{2} {\mathrm e}^{2 \lambda x} y&=0 \\ \end{align*}	✓	✓	✓	✗	19.867
25218	25022	\begin{align*} y^{\prime }&=\frac {1}{\left (t +y\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	19.882
25219	24382	\begin{align*} 2 x +y-4+\left (x -3 y+12\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	19.888
25220	9166	\begin{align*} y^{\prime }&=\frac {x^{2}-y x}{y^{2} \cos \left (\frac {x}{y}\right )} \\ \end{align*}	✓	✓	✓	✗	19.891
25221	20693	\begin{align*} \left (x y \sin \left (y x \right )+\cos \left (y x \right )\right ) y+\left (x y \sin \left (y x \right )-\cos \left (y x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	19.892
25222	15384	\begin{align*} \frac {x}{\left (x +y\right )^{2}}+\frac {\left (2 x +y\right ) y^{\prime }}{\left (x +y\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	19.905
25223	11930	\begin{align*} y^{\prime }&=\frac {\left (a y^{2}+b \,x^{2}\right )^{2} x}{a^{{5}/{2}} y} \\ \end{align*}	✓	✓	✓	✗	19.907
25224	24357	\begin{align*} 9 x -4 y+4-\left (1+2 x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	19.921
25225	24200	\begin{align*} \left (y^{2}-x^{2}\right ) y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	19.927
25226	26154	\begin{align*} \left (y x +1\right ) y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	19.937
25227	7938	\begin{align*} 4 x^{2} y y^{\prime }&=3 x \left (3 y^{2}+2\right )+2 \left (3 y^{2}+2\right )^{3} \\ \end{align*}	✓	✓	✓	✓	19.938
25228	25722	\begin{align*} y y^{\prime }&=3 x \\ y \left (-2\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	19.938
25229	17970	\begin{align*} 3 x^{2} \tan \left (y\right )-\frac {2 y^{3}}{x^{3}}+\left (x^{3} \sec \left (y\right )^{2}+4 y^{3}+\frac {3 y^{2}}{x^{2}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✗	✗	19.964
25230	21057	\begin{align*} x^{\prime }&=\frac {t}{x} \\ x \left (\sqrt {2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	19.966
25231	22568	\begin{align*} y^{\prime }&=\frac {\left (y+3\right )^{2}}{4 x^{2}} \\ \end{align*}	✓	✓	✓	✓	19.984
25232	14417	\begin{align*} x^{2}+y^{2}+2 x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	19.989
25233	22537	\begin{align*} y^{\prime }&={\mathrm e}^{\frac {y}{x}}+\frac {y}{x} \\ \end{align*}	✓	✓	✓	✗	20.019
25234	21060	\begin{align*} x^{\prime }&=5 t \sqrt {x} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	20.065
25235	15358	\begin{align*} x +2 y+1-\left (3+2 x +4 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.075
25236	21608	\begin{align*} \frac {x^{2}}{y}+y^{2}-\left (\frac {x^{3}}{y^{2}}+y x +y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✗	✓	✗	✗	20.091
25237	3676	\begin{align*} y^{\prime }&=\frac {x +2 y-1}{2 x -y+3} \\ \end{align*}	✓	✓	✓	✓	20.117
25238	12479	\begin{align*} x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) x y^{\prime }-y&=0 \\ \end{align*}	✗	✓	✓	✗	20.117
25239	19811	\begin{align*} 5 x y y^{\prime }-x^{2}-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	20.125
25240	14155	\begin{align*} x^{4} y^{\prime \prime }+2 x^{3} \left (x +1\right ) y^{\prime }+n^{2} y&=0 \\ \end{align*}	✗	✓	✗	✗	20.143
25241	15616	\begin{align*} y^{\prime }&=y^{2} \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	20.183
25242	16327	\begin{align*} 3 y+3 y^{2}+\left (2 x +4 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.189
25243	11984	\begin{align*} y^{\prime }&=\frac {2 x \,{\mathrm e}^{x}-2 x -\ln \left (x \right )-1+x^{4} \ln \left (x \right )+x^{4}-2 y \ln \left (x \right ) x^{2}-2 x^{2} y+y^{2} \ln \left (x \right )+y^{2}}{{\mathrm e}^{x}-1} \\ \end{align*}	✓	✓	✓	✗	20.198
25244	13979	\begin{align*} y^{3}+x^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.206
25245	27244	\begin{align*} 2 x -4 y+1+\left (-3+x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	20.234
25246	17954	\begin{align*} 3 x y^{2} y^{\prime }-2 y^{3}&=x^{3} \\ \end{align*}	✓	✓	✓	✓	20.244
25247	15819	\begin{align*} S^{\prime }&=S^{3}-2 S^{2}+S \\ S \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✗	✓	20.250
25248	5544	\begin{align*} y {y^{\prime }}^{2}&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	20.270
25249	11504	\begin{align*} y y^{\prime }+a y+b \,{\mathrm e}^{x}-2 a&=0 \\ \end{align*}	✗	✗	✗	✗	20.273
25250	25008	\begin{align*} y^{\prime }&=\frac {t^{2}+y^{2}}{y t} \\ y \left ({\mathrm e}\right ) &= 2 \,{\mathrm e} \\ \end{align*}	✓	✓	✓	✓	20.294
25251	26255	\begin{align*} x^{2} y^{\prime }+\sin \left (2 y\right )&=1 \\ y \left (\infty \right ) &= \frac {11 \pi }{4} \\ \end{align*}	✗	✓	✗	✓	20.300
25252	21086	\begin{align*} x^{\prime }&=\frac {3 x^{2}-2 t^{2}}{x t} \\ \end{align*}	✓	✓	✓	✓	20.326
25253	6563	\begin{align*} 2 \left (1-x \right )^{2} x^{2} \left (1-y\right ) \left (x -y\right ) y y^{\prime \prime }&=\operatorname {a0} x \left (1-y\right )^{2} \left (x -y\right )^{2}+\left (-1+\operatorname {a2} \right ) \left (1-x \right ) x \left (1-y\right )^{2} y^{2}+\operatorname {a1} \left (1-x \right ) \left (x -y\right )^{2} y^{2}+\operatorname {a3} \left (1-y\right )^{2} \left (x -y\right )^{2} y^{2}+2 \left (1-x \right ) x \left (1-y\right )^{2} y \left (x^{2}+y-2 y x \right ) y^{\prime }+\left (1-x \right )^{2} x^{2} \left (x -2 y-2 y x +3 y^{2}\right ) {y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	20.343
25254	22410	\begin{align*} 3 x +4 y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.371
25255	15121	\begin{align*} y^{\prime }&=t \ln \left (y^{2 t}\right )+t^{2} \\ \end{align*}	✗	✗	✓	✗	20.394
25256	5081	\begin{align*} \left (x +2 y\right ) y^{\prime }+2 x -y&=0 \\ \end{align*}	✓	✓	✓	✓	20.416
25257	24318	\begin{align*} y^{\prime }&=\left (9 x +4 y+1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	20.426
25258	18579	\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*}	✓	✓	✓	✓	20.427
25259	15490	\begin{align*} y^{\prime }-2 \sqrt {{| y|}}&=0 \\ \end{align*}	✓	✓	✓	✓	20.428
25260	13765	\begin{align*} x y^{\prime \prime }+\left (a b \,x^{n +m}+a n \,x^{n}+b \,x^{m}+1-2 n \right ) y^{\prime }+a^{2} b n \,x^{2 n +m -1} y&=0 \\ \end{align*}	✗	✗	✗	✗	20.434
25261	17285	\begin{align*} y^{\prime }&=\frac {4 y^{2}-t^{2}}{2 y t} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	20.437
25262	10053	\begin{align*} 3 y y^{\prime \prime }+y&=5 \\ \end{align*}	✓	✓	✓	✓	20.455
25263	15569	\begin{align*} y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\ y \left (6\right ) &= -9 \\ \end{align*}	✓	✓	✓	✓	20.479
25264	24368	\begin{align*} y \left (4 x +y\right )-2 \left (x^{2}-y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	20.484
25265	15541	\begin{align*} y^{\prime }&={| y|} \\ \end{align*}	✓	✓	✓	✓	20.489
25266	4959	\begin{align*} 2 \left (x^{2}+x +1\right ) y^{\prime }&=1+8 x^{2}-\left (2 x +1\right ) y \\ \end{align*}	✓	✓	✓	✓	20.510
25267	12168	\begin{align*} y^{\prime }&=\frac {6 x^{2} y-2 x +1-5 x^{3} y^{2}-2 y x +x^{4} y^{3}}{x^{2} \left (x^{2} y-x +1\right )} \\ \end{align*}	✓	✓	✓	✗	20.512
25268	21451	\begin{align*} \frac {x^{2}}{y}+y^{2}-\left (\frac {x^{3}}{y^{2}}+y x +y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✗	✓	✗	✗	20.517
25269	11656	\begin{align*} \left (x y^{\prime }-y\right ) \cos \left (\frac {y}{x}\right )^{2}+x&=0 \\ \end{align*}	✓	✓	✓	✗	20.518
25270	3654	\begin{align*} y^{\prime }&=\frac {x +a y}{a x -y} \\ \end{align*}	✓	✓	✓	✗	20.522
25271	20260	\begin{align*} \left (3 x^{2}+y^{2}\right ) y y^{\prime }+x \left (x^{2}+3 y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	20.524
25272	25212	\begin{align*} \sin \left (t \right ) y^{\prime \prime }+y&=\cos \left (t \right ) \\ y \left (\frac {\pi }{2}\right ) &= y_{1} \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= y_{1} \\ \end{align*}	✗	✗	✗	✗	20.525
25273	21061	\begin{align*} x^{\prime }&=4 t^{3} \sqrt {x} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	20.529
25274	25718	\begin{align*} y^{\prime }&=\sqrt {y^{2}-9} \\ y \left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	20.565
25275	2910	\begin{align*} x -2 y+3+\left (1-x +2 y\right ) y^{\prime }&=0 \\ y \left (-4\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	20.568
25276	21983	\begin{align*} 3 x^{2} y+\left (y+x^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.576
25277	18285	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=8 \,{\mathrm e}^{x}+9 \\ y \left (-\infty \right ) &= 3 \\ \end{align*}	✗	✓	✗	✓	20.605
25278	12486	\begin{align*} x^{2} y^{\prime \prime }+\left (x -2 x^{2} f \left (x \right )\right ) y^{\prime }+\left (x^{2} \left (1+f \left (x \right )^{2}-f^{\prime }\left (x \right )\right )-f \left (x \right ) x -v^{2}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	20.617
25279	27392	\begin{align*} y^{\prime }&={\mathrm e}^{\frac {x y^{\prime }}{y}} \\ \end{align*}	✓	✓	✓	✗	20.619
25280	19280	\begin{align*} x -y-\left (x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.634
25281	19900	\begin{align*} x^{2}+y^{2}-2 x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.672
25282	6825	\begin{align*} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.681
25283	15374	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-y x +a x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	20.723
25284	11931	\begin{align*} y^{\prime }&=-\frac {x^{3} \left (\sqrt {a}\, x +\sqrt {a}-2 \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2 \left (x +1\right )} \\ \end{align*}	✗	✓	✓	✗	20.740
25285	15547	\begin{align*} y^{\prime }&=\frac {y x}{x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	20.741
25286	14169	\begin{align*} \left (x -1\right )^{2} y^{\prime \prime }+4 \left (x -1\right ) y^{\prime }+2 y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	20.750
25287	8789	\begin{align*} y y^{\prime }+x&=a {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	20.769
25288	2511	\begin{align*} \sec \left (t \right ) \tan \left (t \right )+\sec \left (t \right )^{2} y+\left (\tan \left (t \right )+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	20.782
25289	20120	\begin{align*} \sqrt {x}\, y^{\prime \prime }+2 x y^{\prime }+3 y&=x \\ \end{align*}	✗	✓	✓	✗	20.802
25290	15406	\begin{align*} {y^{\prime \prime }}^{2}+{y^{\prime }}^{2}&=a^{2} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	20.819
25291	21826	\begin{align*} x^{2} y^{\prime }-y x&=x^{2}-y^{2} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	20.820
25292	8231	\begin{align*} \left (-x +y\right ) y^{\prime }&=x +y \\ \end{align*}	✓	✓	✓	✓	20.824
25293	14237	\begin{align*} x^{\prime }&=\frac {4 t^{2}+3 x^{2}}{2 x t} \\ \end{align*}	✓	✓	✓	✓	20.826
25294	4082	\begin{align*} x -2 y-3+\left (2 x +y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.860
25295	6322	\begin{align*} y^{\prime \prime }&=f^{\prime }\left (x \right ) y+\left (f \left (x \right )-2 y\right ) y^{\prime } \\ \end{align*}	✗	✗	✗	✗	20.873
25296	15618	\begin{align*} y^{\prime }&=y^{3} \\ y \left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	20.897
25297	5213	\begin{align*} \left (x^{2}+y^{2}\right ) y^{\prime }&=y x \\ \end{align*}	✓	✓	✓	✓	20.928
25298	15556	\begin{align*} y^{\prime }&=\sqrt {\frac {y-4}{x}} \\ \end{align*}	✓	✓	✓	✓	20.937
25299	2928	\begin{align*} \frac {2 y}{x^{3}}+\frac {2 x}{y^{2}}&=\left (\frac {1}{x^{2}}+\frac {2 x^{2}}{y^{3}}\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	20.960
25300	11946	\begin{align*} y^{\prime }&=\frac {2 a +x^{2} \sqrt {-y^{2}+4 a x}}{y} \\ \end{align*}	✓	✓	✓	✗	20.972