2.3.246 Problems 24501 to 24600

Table 2.1065: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
24501	5894	\begin{align*} \left ({\mathrm e}^{x^{2}}-k^{2}\right ) x^{3} y-y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	13.796
24502	9798	\begin{align*} {y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime }+x^{2}&=0 \\ y \left (0\right ) &= {\frac {1}{2}} \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	13.796
24503	5701	\begin{align*} \ln \left (y^{\prime }\right )+x y^{\prime }+a&=y \\ \end{align*}	✓	✓	✓	✓	13.802
24504	24165	\begin{align*} x -\ln \left (y\right ) y+y \ln \left (x \right )+x \left (\ln \left (y\right )-\ln \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.803
24505	13759	\begin{align*} x y^{\prime \prime }+\left (a b \,x^{n}+b -3 n +1\right ) y^{\prime }+a^{2} n \left (b -n \right ) x^{2 n -1} y&=0 \\ \end{align*}	✗	✗	✗	✗	13.806
24506	4837	\begin{align*} \left (x +1\right ) y^{\prime }&=a y+b x y^{2} \\ \end{align*}	✓	✓	✓	✓	13.807
24507	24170	\begin{align*} x -y+\left (3 x +y\right ) y^{\prime }&=0 \\ y \left (2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	13.809
24508	16341	\begin{align*} x^{3}+y^{3}+x y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.812
24509	11538	\begin{align*} 2 x y y^{\prime }-y^{2}+a \,x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	13.817
24510	17035	\begin{align*} y^{\prime }+t^{2}&=\frac {1}{y^{2}} \\ \end{align*}	✗	✗	✗	✗	13.817
24511	5224	\begin{align*} \left (x +2 y+y^{2}\right ) y^{\prime }+y \left (y+1\right )+\left (x +y\right )^{2} y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	13.826
24512	13721	\begin{align*} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (a b \,x^{n +m}+b c \,x^{m}+a n \,x^{n -1}\right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	13.826
24513	5704	\begin{align*} \ln \left (y^{\prime }\right )+a \left (x y^{\prime }-y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	13.830
24514	792	\begin{align*} x y^{\prime }&=6 y+12 x^{4} y^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✓	13.835
24515	5462	\begin{align*} {y^{\prime }}^{2} x -y y^{\prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✗	13.836
24516	18500	\begin{align*} \sqrt {-x^{2}+1}\, y^{2} y^{\prime }&=\arcsin \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	13.842
24517	24158	\begin{align*} x^{2}+2 y x -4 y^{2}-\left (x^{2}-8 y x -4 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.846
24518	2998	\begin{align*} y+y^{\prime }&=y^{2} {\mathrm e}^{-t} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	13.850
24519	3000	\begin{align*} 2 y&=\left (x^{2} y^{4}+x \right ) y^{\prime } \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	13.859
24520	6492	\begin{align*} 12 y y^{\prime \prime }&=-8 y^{3}+15 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	13.862
24521	26276	\begin{align*} y^{3} y^{\prime }+3 x y^{2}+2 x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	13.871
24522	21395	\begin{align*} x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	13.872
24523	212	\begin{align*} y^{\prime }&=\frac {x +3 y}{y-3 x} \\ \end{align*}	✓	✓	✓	✓	13.902
24524	20682	\begin{align*} 1+y^{2}-x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.916
24525	14916	\begin{align*} x^{\prime }&=k x-x^{2} \\ \end{align*}	✓	✓	✓	✓	13.918
24526	15386	\begin{align*} \frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	13.929
24527	5328	\begin{align*} x \left (x^{3}+y^{5}\right ) y^{\prime }&=\left (x^{3}-y^{5}\right ) y \\ \end{align*}	✓	✓	✓	✗	13.935
24528	5099	\begin{align*} \left (-3 y-2 x +5\right ) y^{\prime }+1-2 x -3 y&=0 \\ \end{align*}	✓	✓	✓	✓	13.943
24529	6350	\begin{align*} a {y^{\prime }}^{3}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.951
24530	17893	\begin{align*} a^{2}+y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime }&=0 \\ y \left (a \right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	13.954
24531	14030	\begin{align*} 5 y x -3 y^{3}+\left (3 x^{2}-7 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	13.957
24532	2332	\begin{align*} y^{\prime }&=\frac {t +y}{t -y} \\ \end{align*}	✓	✓	✓	✓	13.958
24533	17323	\begin{align*} r^{\prime }&=\frac {r^{2}+t^{2}}{r t} \\ \end{align*}	✓	✓	✓	✓	13.959
24534	22317	\begin{align*} y^{\prime \prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	13.965
24535	22389	\begin{align*} y^{\prime }&=\frac {y}{x}+\sec \left (\frac {y}{x}\right )^{2} \\ \end{align*}	✓	✓	✓	✗	13.966
24536	12452	\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y-x^{3} \sin \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	13.981
24537	27393	\begin{align*} y&=x y^{\prime }-x^{2} {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✗	✗	13.987
24538	15241	\begin{align*} y^{\prime \prime }+4 \pi ^{2} y&=3 \delta \left (t -\frac {1}{3}\right )-\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	13.989
24539	22596	\begin{align*} y^{\prime }&=\frac {2}{x +2 y-3} \\ \end{align*}	✓	✓	✓	✓	13.992
24540	23210	\begin{align*} y x -\left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	13.997
24541	19199	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+2 y&=x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	14.006
24542	20764	\begin{align*} \sqrt {x}\, y^{\prime \prime }+2 x y^{\prime }+3 y&=x \\ \end{align*}	✗	✓	✓	✗	14.022
24543	24352	\begin{align*} x +y-1+\left (2 x +2 y+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.022
24544	25767	\begin{align*} y^{\prime }&=x^{2}-y^{2} \\ y \left (-2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	14.046
24545	24339	\begin{align*} 12 x +4 y-8-\left (3 x +y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	14.049
24546	15449	\begin{align*} \frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	14.068
24547	8364	\begin{align*} \sqrt {1-y^{2}}-y^{\prime } \sqrt {-x^{2}+1}&=0 \\ y \left (0\right ) &= \frac {\sqrt {3}}{2} \\ \end{align*}	✓	✓	✓	✗	14.072
24548	18300	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+y&=x \left (6-\ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	14.086
24549	24403	\begin{align*} 4 x +3 y-7+\left (4 x +3 y+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.094
24550	4942	\begin{align*} x \left (x +a \right ) y^{\prime }&=\left (b +c y\right ) y \\ \end{align*}	✓	✓	✓	✓	14.095
24551	12164	\begin{align*} y^{\prime }&=-\frac {\left (-1-y^{4}+2 x^{2} y^{2}-x^{4}-y^{6}+3 x^{2} y^{4}-3 y^{2} x^{4}+x^{6}\right ) x}{y} \\ \end{align*}	✓	✓	✓	✗	14.095
24552	13404	\begin{align*} y^{\prime }&=y^{2}+a x \cot \left (b x \right )^{m} y+a \cot \left (b x \right )^{m} \\ \end{align*}	✓	✓	✓	✗	14.111
24553	6824	\begin{align*} x \left (1-y\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	14.122
24554	739	\begin{align*} \left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	14.133
24555	11969	\begin{align*} y^{\prime }&=\frac {y^{3} x \,{\mathrm e}^{2 x^{2}}}{y \,{\mathrm e}^{x^{2}}+1} \\ \end{align*}	✓	✓	✓	✗	14.144
24556	12454	\begin{align*} x^{2} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \\ \end{align*}	✗	✓	✓	✗	14.151
24557	17924	\begin{align*} x -2 y-1+\left (3 x -6 y+2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.153
24558	5032	\begin{align*} \left (a_{0} +a_{1} \sin \left (x \right )^{2}\right ) y^{\prime }+a_{2} x \left (a_{3} +a_{1} \sin \left (x \right )^{2}\right )+a_{1} y \sin \left (2 x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	14.157
24559	6371	\begin{align*} 9 {y^{\prime }}^{4}+8 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.168
24560	5097	\begin{align*} \left (4-x -3 y\right ) y^{\prime }+3-x -3 y&=0 \\ \end{align*}	✓	✓	✓	✓	14.172
24561	2504	\begin{align*} y^{\prime }&=\frac {t +y}{t -y} \\ \end{align*}	✓	✓	✓	✓	14.175
24562	12074	\begin{align*} y^{\prime }&=\frac {y \left (-\cosh \left (\frac {1}{x +1}\right ) x +\cosh \left (\frac {1}{x +1}\right )-x +x^{2} y-x^{2}+x^{3} y\right )}{x \left (x -1\right ) \cosh \left (\frac {1}{x +1}\right )} \\ \end{align*}	✓	✓	✓	✗	14.178
24563	13732	\begin{align*} x y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (\left (a -c \right ) x +b \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	14.201
24564	24372	\begin{align*} y^{2}+\left (3 y x +y^{2}-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.204
24565	7723	\begin{align*} x -x y^{2}&=\left (x +x^{2} y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	14.206
24566	17212	\begin{align*} 2 y t +\left (t^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	14.218
24567	18066	\begin{align*} 2 x^{5}+4 x^{3} y-2 x y^{2}+\left (y^{2}+2 x^{2} y-x^{4}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.225
24568	25830	\begin{align*} y^{\prime }&=\frac {y \left (x \cos \left (x \right )+\sin \left (x \right )-1\right )}{3 x -3 x \sin \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	14.230
24569	5093	\begin{align*} \left (x \,{\mathrm e}^{-x}-2 y\right ) y^{\prime }&=2 \,{\mathrm e}^{-2 x} x -\left ({\mathrm e}^{-x}+x \,{\mathrm e}^{-x}-2 y\right ) y \\ \end{align*}	✓	✓	✓	✗	14.233
24570	13983	\begin{align*} 2 x +y-\left (4 x +2 y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.238
24571	13643	\begin{align*} y^{\prime }&=a x y^{3}+b y^{2} \\ \end{align*}	✓	✓	✓	✓	14.244
24572	729	\begin{align*} \left (x +y\right ) y^{\prime }&=x -y \\ \end{align*}	✓	✓	✓	✓	14.250
24573	24396	\begin{align*} 2 x +4 y-1-\left (x +2 y-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.254
24574	14451	\begin{align*} y \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}+y^{2}+\left ({\mathrm e}^{x}+2 y x \right ) y^{\prime }&=0 \\ y \left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✗	14.275
24575	4695	\begin{align*} y^{\prime }&=x y^{3} \\ \end{align*}	✓	✓	✓	✓	14.282
24576	11676	\begin{align*} {y^{\prime }}^{2}-2 x^{2} y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✗	14.286
24577	3886	\begin{align*} x_{1}^{\prime }&=x_{2}+3 x_{3} \\ x_{2}^{\prime }&=2 x_{1}+3 x_{2}-2 x_{3} \\ x_{3}^{\prime }&=2 x_{2}+2 x_{3} \\ \end{align*}	✓	✓	✓	✗	14.293
24578	6451	\begin{align*} y y^{\prime \prime }&=y^{3} b +a {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	14.306
24579	4240	\begin{align*} x^{2}-y^{2}+x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.314
24580	14202	\begin{align*} x^{\prime }&=t^{2}+x^{2} \\ \end{align*}	✓	✓	✓	✗	14.314
24581	24391	\begin{align*} 3 x +y-2+\left (3 x +y+4\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.323
24582	15605	\begin{align*} x y \left (1-y\right )-2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	14.324
24583	25056	\begin{align*} t y^{\prime }&=2 y-t \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✗	✓	✓	14.329
24584	8787	\begin{align*} y^{\prime }&=-\frac {2}{t}+\frac {y}{t}+\frac {y^{2}}{t} \\ \end{align*}	✓	✓	✓	✓	14.332
24585	17149	\begin{align*} y^{\prime }&=2 x +\frac {x y}{x^{2}-1} \\ \end{align*}	✓	✓	✓	✓	14.337
24586	5089	\begin{align*} \left (6 x -2 y\right ) y^{\prime }&=2+3 x -y \\ \end{align*}	✓	✓	✓	✓	14.340
24587	4920	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+x y \left (1-y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	14.349
24588	13646	\begin{align*} y^{\prime }&=a \,x^{n} y^{3}+3 a b \,x^{n +m} y^{2}-b m \,x^{m -1}-2 a \,b^{3} x^{n +3 m} \\ \end{align*}	✓	✓	✓	✗	14.359
24589	1665	\begin{align*} y^{\prime }&=\frac {x^{2}+y x +y^{2}}{y x} \\ \end{align*}	✓	✓	✓	✗	14.360
24590	11579	\begin{align*} \left (3 x^{2}+2 y x +4 y^{2}\right ) y^{\prime }+2 x^{2}+6 y x +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	14.368
24591	27430	\begin{align*} y^{\prime }+y x -x y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	14.389
24592	22547	\begin{align*} 2 y+3 x +x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.392
24593	6554	\begin{align*} \operatorname {a2} x \left (1-y\right ) y^{2}+\operatorname {a3} \,x^{3} y^{2} \left (y+1\right )+\left (1-y\right )^{3} \left (\operatorname {a0} +\operatorname {a1} y^{2}\right )+2 x \left (1-y\right ) y y^{\prime }-x^{2} \left (1-3 y\right ) {y^{\prime }}^{2}+2 x^{2} \left (1-y\right ) y y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	14.398
24594	27295	\begin{align*} y^{\prime } \sin \left (2 x \right )&=2 y+2 \cos \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✗	✓	✗	14.400
24595	7148	\begin{align*} \left (a x +b \right )^{2} y^{\prime }+\left (a x +b \right ) y^{3}+c y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	14.408
24596	17153	\begin{align*} y^{\prime }-\frac {9 x y}{9 x^{2}+49}&=x \\ \end{align*}	✓	✓	✓	✓	14.408
24597	21852	\begin{align*} 3 x +3 y-2+\left (2 x +2 y+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.410
24598	9082	\begin{align*} x^{5} y^{\prime }+y^{5}&=0 \\ \end{align*}	✓	✓	✓	✓	14.411
24599	23223	\begin{align*} x^{2}+y^{2}-2 x y y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	14.413
24600	4284	\begin{align*} 6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	14.415