2.3.246 Problems 24501 to 24600

Table 2.1041: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
24501	3777	\begin{align*} x^{2} y^{\prime \prime }+6 y^{\prime } x +6 y&=4 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	24.448
24502	12051	\begin{align*} y^{\prime }&=-\frac {i \left (16 i x^{2}+16 y^{4}+8 y^{2} x^{4}+x^{8}\right ) x}{32 y} \\ \end{align*}	✓	✓	✓	✗	24.451
24503	16362	\begin{align*} y y^{\prime } x&=x^{2}+y x +y^{2} \\ \end{align*}	✓	✓	✓	✗	24.455
24504	12009	\begin{align*} y^{\prime }&=\frac {\left (2 x +2+y\right ) y}{\left (\ln \left (y\right )+2 x -1\right ) \left (x +1\right )} \\ \end{align*}	✓	✓	✓	✗	24.458
24505	3772	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=4 \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	24.459
24506	13475	\begin{align*} y^{\prime }&=-a \ln \left (x \right ) y^{2}+a f \left (x \right ) \left (x \ln \left (x \right )-x \right ) y-f \left (x \right ) \\ \end{align*}	✓	✓	✗	✗	24.460
24507	11633	\begin{align*} \left (\frac {\operatorname {e1} \left (a +x \right )}{\left (\left (a +x \right )^{2}+y^{2}\right )^{{3}/{2}}}+\frac {\operatorname {e2} \left (x -a \right )}{\left (\left (x -a \right )^{2}+y^{2}\right )^{{3}/{2}}}\right ) y^{\prime }-y \left (\frac {\operatorname {e1}}{\left (\left (a +x \right )^{2}+y^{2}\right )^{{3}/{2}}}+\frac {\operatorname {e2}}{\left (\left (x -a \right )^{2}+y^{2}\right )^{{3}/{2}}}\right )&=0 \\ \end{align*}	✓	✗	✗	✗	24.481
24508	13352	\begin{align*} x^{2} \ln \left (a x \right ) \left (y^{\prime }-y^{2}\right )&=1 \\ \end{align*}	✓	✓	✓	✗	24.498
24509	19351	\begin{align*} y^{\prime } y^{2} x +y^{3}&=\cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	24.499
24510	20281	\begin{align*} y^{\prime }+\frac {y \ln \left (y\right )}{x}&=\frac {y}{x^{2}}-\ln \left (y\right )^{2} \\ \end{align*}	✗	✗	✗	✗	24.520
24511	14551	\begin{align*} 10 x -4 y+12-\left (x +5 y+3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	24.529
24512	4806	\begin{align*} y^{\prime } x&=y+\sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	24.539
24513	5105	\begin{align*} 4 \left (-x -y+1\right ) y^{\prime }+2-x&=0 \\ \end{align*}	✓	✓	✓	✓	24.540
24514	5003	\begin{align*} x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3}&=0 \\ \end{align*}	✗	✓	✓	✗	24.545
24515	24200	\begin{align*} \left (y^{2}-x^{2}\right ) y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	24.569
24516	793	\begin{align*} {\mathrm e}^{y}+\cos \left (x \right ) y+\left (x \,{\mathrm e}^{y}+\sin \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	24.571
24517	21863	\begin{align*} 2 {y^{\prime }}^{2}+y y^{\prime }-y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	24.573
24518	26239	\begin{align*} y^{\prime }&=y^{a} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	24.576
24519	10044	\begin{align*} y^{\prime }&=-4 \sin \left (x -y\right )-4 \\ \end{align*}	✓	✓	✓	✓	24.579
24520	4948	\begin{align*} \left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (y-a \right ) \left (y-b \right )&=0 \\ \end{align*}	✓	✓	✓	✓	24.589
24521	7551	\begin{align*} y^{\prime }&=\frac {x -y-1}{x +y+5} \\ \end{align*}	✓	✓	✓	✓	24.590
24522	3460	\begin{align*} 2 y^{\prime } x +3 x +y&=0 \\ \end{align*}	✓	✓	✓	✓	24.596
24523	12041	\begin{align*} y^{\prime }&=-\frac {i \left (54 i x^{2}+81 y^{4}+18 y^{2} x^{4}+x^{8}\right ) x}{243 y} \\ \end{align*}	✓	✓	✓	✗	24.600
24524	11673	\begin{align*} {y^{\prime }}^{2}+a x y^{\prime }-b \,x^{2}-c&=0 \\ \end{align*}	✓	✓	✓	✓	24.612
24525	20115	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +y&=\frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x} \\ \end{align*}	✓	✓	✓	✓	24.636
24526	22348	\begin{align*} y^{\prime }&=\frac {1}{\sqrt {x^{2}+4 y^{2}-4}} \\ y \left (3\right ) &= 2 \\ \end{align*}	✗	✗	✗	✗	24.682
24527	16231	\begin{align*} y^{\prime }&=\sin \left (y\right ) \\ \end{align*}	✓	✓	✓	✗	24.685
24528	8789	\begin{align*} x +y y^{\prime }&=a {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	24.690
24529	12163	\begin{align*} y^{\prime }&=\frac {\left (a^{3}+y^{4} a^{3}+2 a^{2} y^{2} b \,x^{2}+b^{2} x^{4} a +y^{6} a^{3}+3 y^{4} a^{2} b \,x^{2}+3 y^{2} a \,b^{2} x^{4}+b^{3} x^{6}\right ) x}{a^{{7}/{2}} y} \\ \end{align*}	✓	✓	✓	✗	24.694
24530	18846	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=3 x^{2}+2 \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	24.702
24531	6489	\begin{align*} 4 y y^{\prime \prime }&=12 y^{2}+3 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	24.705
24532	23170	\begin{align*} y^{\prime } x +y&=2 x \\ y \left (2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	24.717
24533	20219	\begin{align*} y-x +\left (x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	24.720
24534	23220	\begin{align*} y^{\prime }&=\frac {y}{x -y+1} \\ \end{align*}	✓	✓	✓	✓	24.737
24535	23917	\begin{align*} y^{\prime }+\frac {2 y}{x}&=\frac {x^{2}}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	24.787
24536	7555	\begin{align*} y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\ y \left (1\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	24.793
24537	22433	\begin{align*} y^{2} \cos \left (x \right )-y+\left (x +y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	24.806
24538	24297	\begin{align*} y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\ y \left (0\right ) &= -\frac {\sqrt {3}}{2} \\ \end{align*}	✓	✓	✓	✗	24.860
24539	23179	\begin{align*} x +y+\left (x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	24.879
24540	4316	\begin{align*} y^{\prime } x&=y \left (1+\ln \left (y\right )-\ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	24.882
24541	3775	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +5 y&=8 x \ln \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	24.894
24542	6073	\begin{align*} -p \left (1+p \right ) y+2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	24.907
24543	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*}	✓	✓	✓	✓	24.922
24544	17843	\begin{align*} y^{\prime }&=\frac {1+y}{x -y} \\ \end{align*}	✓	✓	✓	✓	24.937
24545	17345	\begin{align*} y^{\prime }&=y^{2}-x \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	24.956
24546	2348	\begin{align*} y^{\prime }&=t +y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	24.965
24547	12062	\begin{align*} y^{\prime }&=\frac {y x +y+x \sqrt {x^{2}+y^{2}}}{x \left (x +1\right )} \\ \end{align*}	✗	✓	✓	✗	24.996
24548	13804	\begin{align*} x^{2} y^{\prime \prime }+a \,x^{n} y^{\prime }-\left (a b \,x^{n}+a c \,x^{n -1}+b^{2} x^{2}+2 b x c +c^{2}-c \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	25.010
24549	25443	\begin{align*} y^{\prime }-3 y&=5 \,{\mathrm e}^{2 i t} \\ \end{align*}	✓	✓	✓	✓	25.017
24550	3545	\begin{align*} \sin \left (\frac {y}{x}\right ) \left (-y+y^{\prime } x \right )&=x \cos \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	25.020
24551	23212	\begin{align*} x -y+\left (2 x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	25.021
24552	1668	\begin{align*} y^{\prime }&=\frac {-x +3 y-14}{x +y-2} \\ \end{align*}	✓	✓	✓	✓	25.074
24553	5854	\begin{align*} c y+a \cot \left (b x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✗	✗	25.114
24554	14450	\begin{align*} 2 \sin \left (x \right ) \cos \left (x \right ) y+\sin \left (x \right ) y^{2}+\left (\sin \left (x \right )^{2}-2 \cos \left (x \right ) y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✗	25.131
24555	15131	\begin{align*} \cos \left (x \right ) y^{\prime }+y \,{\mathrm e}^{x^{2}}&=\sinh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	25.139
24556	12559	\begin{align*} a \,x^{2} y^{\prime \prime }+b x y^{\prime }+\left (c \,x^{2}+d x +f \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	25.148
24557	23867	\begin{align*} y^{\prime }&=\frac {3 x -y}{x +2 y} \\ \end{align*}	✓	✓	✓	✓	25.188
24558	11930	\begin{align*} y^{\prime }&=\frac {\left (a y^{2}+b \,x^{2}\right )^{2} x}{a^{{5}/{2}} y} \\ \end{align*}	✓	✓	✓	✗	25.193
24559	8159	\begin{align*} \sin \left (x^{\prime }\right )+y^{3} x&=\sin \left (y \right ) \\ \end{align*}	✗	✗	✗	✗	25.211
24560	201	\begin{align*} {\mathrm e}^{y}+\cos \left (x \right ) y+\left (x \,{\mathrm e}^{y}+\sin \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	25.212
24561	6192	\begin{align*} \left (c \,x^{2}+b x +a \right ) y+x^{2} y^{\prime }+x^{3} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✗	✗	25.228
24562	11498	\begin{align*} y^{\prime } \sin \left (2 x \right )+\sin \left (2 y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	25.237
24563	11695	\begin{align*} a {y^{\prime }}^{2}-y y^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✗	25.266
24564	20263	\begin{align*} \left (x -y\right ) y^{\prime }&=x +y+1 \\ \end{align*}	✓	✓	✓	✓	25.304
24565	764	\begin{align*} 1+y \,{\mathrm e}^{y x}+\left (2 y+x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	25.318
24566	2887	\begin{align*} y^{\prime }&=\frac {x +y}{x -y} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	25.320
24567	13623	\begin{align*} x \left (2 a y+b x \right ) y^{\prime }&=a \left (2-m \right ) y^{2}+b \left (-m +1\right ) x y+c \,x^{2}+A \,x^{m +2} \\ \end{align*}	✓	✓	✓	✗	25.325
24568	3553	\begin{align*} y y^{\prime }&=\sqrt {x^{2}+y^{2}}-x \\ \end{align*}	✓	✓	✓	✓	25.332
24569	10119	\begin{align*} y^{\prime \prime }-x^{3} y-x^{4}&=0 \\ \end{align*}	✓	✓	✓	✗	25.343
24570	11884	\begin{align*} y^{\prime }&=\frac {F \left (-\left (x -y\right ) \left (x +y\right )\right ) x}{y} \\ \end{align*}	✗	✓	✓	✗	25.368
24571	16153	\begin{align*} y^{\prime }&=3-\sin \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	25.371
24572	4440	\begin{align*} x +\sin \left (\frac {y}{x}\right )^{2} \left (-y^{\prime } x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	25.373
24573	20252	\begin{align*} x \sin \left (\frac {y}{x}\right ) y^{\prime }&=y \sin \left (\frac {y}{x}\right )-x \\ \end{align*}	✓	✓	✓	✓	25.428
24574	6092	\begin{align*} y+2 y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	25.479
24575	4890	\begin{align*} x^{2} y^{\prime }+y x +\sqrt {y}&=0 \\ \end{align*}	✓	✓	✓	✓	25.489
24576	5273	\begin{align*} x \left (x^{2}-6 y^{2}\right ) y^{\prime }&=4 \left (x^{2}+3 y^{2}\right ) y \\ \end{align*}	✓	✓	✓	✓	25.497
24577	25444	\begin{align*} y^{\prime }&=2 y-{\mathrm e}^{i t} \\ \end{align*}	✓	✓	✓	✓	25.515
24578	3638	\begin{align*} \sin \left (\frac {y}{x}\right ) \left (-y+y^{\prime } x \right )&=x \cos \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	25.519
24579	15798	\begin{align*} y^{\prime }&=t^{2} y^{3} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	25.520
24580	4421	\begin{align*} x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	25.522
24581	7251	\begin{align*} y x +\left (y^{2}-x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	25.533
24582	39	\begin{align*} y^{\prime }&=x^{2}+y^{2}-1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✗	✗	✓	✗	25.602
24583	24003	\begin{align*} y^{\prime \prime \prime }-y&=x^{n} \\ \end{align*}	✓	✓	✓	✓	25.602
24584	11874	\begin{align*} y^{\prime }&=\frac {F \left (\frac {a y^{2}+b \,x^{2}}{a}\right ) x}{\sqrt {a}\, y} \\ \end{align*}	✓	✓	✓	✗	25.626
24585	20760	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +y&=\frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x} \\ \end{align*}	✓	✓	✓	✓	25.636
24586	20260	\begin{align*} \left (3 x^{2}+y^{2}\right ) y y^{\prime }+x \left (x^{2}+3 y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	25.658
24587	23461	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	25.689
24588	6904	\begin{align*} {\mathrm e}^{\frac {y}{x}} x -y \sin \left (\frac {y}{x}\right )+x \sin \left (\frac {y}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	25.706
24589	17274	\begin{align*} y+\left (y+t \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	25.727
24590	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*}	✓	✓	✓	✓	25.731
24591	17278	\begin{align*} y-\left (3 \sqrt {t y}+t \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	25.766
24592	2896	\begin{align*} x -y+2+\left (x +y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	25.770
24593	2893	\begin{align*} x +y-\left (x -y+2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	25.777
24594	6822	\begin{align*} y&=y^{\prime } x +\frac {a y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} \\ \end{align*}	✓	✓	✓	✗	25.811
24595	13474	\begin{align*} y^{\prime }&=f \left (x \right ) y^{2}-a x \ln \left (x \right ) f \left (x \right ) y+a \ln \left (x \right )+a \\ \end{align*}	✗	✗	✗	✗	25.814
24596	7705	\begin{align*} y^{\prime }+\frac {y}{x}&=y^{3} \\ \end{align*}	✓	✓	✓	✓	25.824
24597	13560	\begin{align*} y y^{\prime }&=a \,{\mathrm e}^{\lambda x} y+1 \\ \end{align*}	✗	✓	✓	✗	25.826
24598	12860	\begin{align*} y^{\prime \prime }+a y^{\prime }+b \,{\mathrm e}^{y}-2 a&=0 \\ \end{align*}	✗	✗	✗	✗	25.837
24599	25506	\begin{align*} y^{\prime }&=-\frac {1+{\mathrm e}^{t y} y}{2 y+{\mathrm e}^{t y} t} \\ \end{align*}	✓	✓	✓	✗	25.838
24600	18499	\begin{align*} \sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime }&=0 \\ y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{3} \\ \end{align*}	✓	✓	✗	✓	25.845