2.3.246 Problems 24501 to 24600

Table 2.1023: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
24501	11851	\begin{align*} y \ln \left (y^{\prime }\right )+y^{\prime }-y \ln \left (y\right )-y x&=0 \\ \end{align*}	✓	✓	✓	✓	52.908
24502	13967	\begin{align*} \frac {y^{2}-2 x^{2}}{-x^{3}+x y^{2}}+\frac {\left (2 y^{2}-x^{2}\right ) y^{\prime }}{y^{3}-x^{2} y}&=0 \\ \end{align*}	✓	✓	✓	✓	52.958
24503	24703	\begin{align*} y^{\prime \prime }+16 y&=8 x +8 \sin \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	53.025
24504	14247	\begin{align*} {x^{\prime }}^{2}+t x&=\sqrt {1+t} \\ \end{align*}	✗	✗	✗	✗	53.056
24505	9791	\begin{align*} \left (1+y^{2}\right ) y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	53.083
24506	17914	\begin{align*} y^{\prime } x&=y+\sqrt {y^{2}-x^{2}} \\ \end{align*}	✓	✓	✓	✓	53.094
24507	6123	\begin{align*} 2 y-4 \left (1-x \right ) y^{\prime }+\left (1-x \right )^{2} y^{\prime \prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	53.162
24508	24221	\begin{align*} y \left (y^{2} x^{2}-1\right )+x \left (x^{2} y+2 x +y\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	53.213
24509	17820	\begin{align*} x^{\prime \prime }+\frac {x^{\prime }}{10}+x&=3 \cos \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	53.321
24510	23877	\begin{align*} y^{\prime }&=\frac {2 x^{2}+2 y^{2}-3 y x}{y x} \\ \end{align*}	✓	✓	✓	✓	53.408
24511	13425	\begin{align*} y^{\prime }&=\lambda \arcsin \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\ \end{align*}	✗	✓	✓	✗	53.438
24512	17030	\begin{align*} y^{\prime \prime }+4 y&=t \\ y \left (\frac {\pi }{4}\right ) &= 1 \\ y^{\prime }\left (\frac {\pi }{4}\right ) &= \frac {\pi }{16} \\ \end{align*}	✓	✓	✓	✓	53.452
24513	14065	\begin{align*} \left (x^{2}+y^{2}\right ) \left (1+y^{\prime }\right )^{2}-2 \left (x +y\right ) \left (1+y^{\prime }\right ) \left (y y^{\prime }+x \right )+\left (y y^{\prime }+x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	53.471
24514	17254	\begin{align*} -y+y^{\prime } t&=t y^{3} \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	53.481
24515	13522	\begin{align*} y y^{\prime }-y&=\frac {A}{\sqrt {x}} \\ \end{align*}	✗	✓	✓	✗	53.495
24516	12882	\begin{align*} y^{\prime \prime }&=a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✗	53.524
24517	16620	\begin{align*} y^{\prime \prime }+9 y&=25 x \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	53.579
24518	322	\begin{align*} y^{\prime \prime }+16 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	53.591
24519	13211	\begin{align*} y^{\prime }&=y^{2}+x^{n -1} a n -a^{2} x^{2 n} \\ \end{align*}	✓	✓	✓	✗	53.692
24520	6128	\begin{align*} -\left (2 x +3\right ) y+\left (x^{2}+x +1\right ) y^{\prime }+\left (x^{2}+3 x +4\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	53.710
24521	17277	\begin{align*} y^{2}&=\left (t y-4 t^{2}\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	53.808
24522	11360	\begin{align*} y^{\prime }-a \sqrt {1+y^{2}}-b&=0 \\ \end{align*}	✓	✓	✓	✓	53.836
24523	23086	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=x^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	53.873
24524	24803	\begin{align*} {y^{\prime }}^{2}+4 x^{4} y^{\prime }-12 x^{4} y&=0 \\ \end{align*}	✗	✗	✗	✗	53.900
24525	17524	\begin{align*} y^{\prime \prime }+4 y&=\sec \left (2 t \right )+\tan \left (2 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	53.993
24526	23888	\begin{align*} \frac {8 x^{4} y+12 x^{3} y^{2}+2}{2 x +3 y}+\frac {\left (2 x^{5}+3 x^{4} y+3\right ) y^{\prime }}{1+x^{2} y^{4}}&=0 \\ \end{align*}	✗	✗	✗	✗	54.088
24527	12514	\begin{align*} \left (-a^{2}+x^{2}\right ) y^{\prime \prime }+8 y^{\prime } x +12 y&=0 \\ \end{align*}	✓	✓	✓	✗	54.136
24528	11658	\begin{align*} \left (y f \left (x^{2}+y^{2}\right )-x \right ) y^{\prime }+y+x f \left (x^{2}+y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	54.177
24529	20001	\begin{align*} \left (x^{2}+y^{2}\right ) \left (1+y^{\prime }\right )^{2}-2 \left (x +y\right ) \left (1+y^{\prime }\right ) \left (y y^{\prime }+x \right )+\left (y y^{\prime }+x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	54.179
24530	11502	\begin{align*} y y^{\prime }+a y+x&=0 \\ \end{align*}	✓	✓	✓	✗	54.229
24531	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*}	✓	✓	✓	✗	54.361
24532	24030	\begin{align*} y^{\prime \prime }+3 y&=-x^{6}+x^{4} \\ \end{align*}	✓	✓	✓	✓	54.398
24533	17250	\begin{align*} 2 t +\frac {19 y}{10}+\left (\frac {19 t}{10}+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	54.496
24534	6400	\begin{align*} x^{2} y^{\prime \prime }&=f \left (\frac {x y^{\prime }}{y}\right ) y \\ \end{align*}	✗	✓	✗	✗	54.551
24535	16303	\begin{align*} \left (2 y x +2 x^{2}\right ) y^{\prime }&=x^{2}+2 y x +2 y^{2} \\ \end{align*}	✓	✓	✓	✗	54.557
24536	7974	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✓	54.601
24537	367	\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=3 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	54.674
24538	19770	\begin{align*} 1+{y^{\prime }}^{2}+\frac {m y^{\prime \prime }}{\sqrt {1+{y^{\prime }}^{2}}}&=0 \\ \end{align*}	✓	✓	✓	✗	54.683
24539	4668	\begin{align*} y^{\prime }&=a x +b y^{2} \\ \end{align*}	✓	✓	✓	✗	54.694
24540	10946	\begin{align*} \left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y&=0 \\ \end{align*}	✓	✓	✓	✗	54.827
24541	5528	\begin{align*} \left (-a^{2}+1\right ) x^{2} {y^{\prime }}^{2}-2 y y^{\prime } x -a^{2} x^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	54.856
24542	20961	\begin{align*} x^{\prime }&=x^{3}+a x^{2}-b x \\ \end{align*}	✓	✓	✓	✗	54.865
24543	8758	\begin{align*} x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	54.899
24544	20799	\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*}	✓	✓	✓	✗	54.942
24545	8772	\begin{align*} x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-y^{\prime } x +y&=x \left (1-\ln \left (x \right )\right )^{2} \\ \end{align*}	✓	✓	✓	✗	55.007
24546	140	\begin{align*} 1+y \,{\mathrm e}^{y x}+\left (2 y+x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	55.048
24547	6076	\begin{align*} -a y-3 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	55.048
24548	23509	\begin{align*} y^{\prime \prime }-y&=x \,{\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	55.079
24549	13907	\begin{align*} x^{n} y^{\prime \prime }+\left (a \,x^{n}-x^{n -1}+a b x +b \right ) y^{\prime }+a^{2} b x y&=0 \\ \end{align*}	✗	✗	✗	✗	55.085
24550	13575	\begin{align*} y y^{\prime }-a \left (1-\frac {b}{\sqrt {x}}\right ) y&=\frac {a^{2} b}{\sqrt {x}} \\ \end{align*}	✗	✓	✓	✗	55.093
24551	1754	\begin{align*} \left (2 x +1\right ) y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (x +1\right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	55.171
24552	19333	\begin{align*} y^{\prime } x +y&=y^{\prime } \sqrt {y x} \\ \end{align*}	✓	✓	✓	✓	55.186
24553	13568	\begin{align*} y y^{\prime }&=\left (\left (3-m \right ) x -1\right ) y-\left (m -1\right ) a x \\ \end{align*}	✗	✗	✗	✗	55.187
24554	11917	\begin{align*} y^{\prime }&=\frac {1+2 x^{5} \sqrt {4 x^{2} y+1}}{2 x^{3}} \\ \end{align*}	✗	✓	✓	✗	55.192
24555	13587	\begin{align*} y y^{\prime }-\frac {2 a \left (3 x -10\right ) y}{5 x^{4}}&=\frac {a^{2} \left (x -1\right ) \left (8 x -5\right )}{5 x^{7}} \\ \end{align*}	✗	✗	✗	✗	55.194
24556	4789	\begin{align*} y^{\prime } x +a \,x^{2} y^{2}+2 y&=b \\ \end{align*}	✓	✓	✓	✗	55.243
24557	17112	\begin{align*} y^{\prime }&=\sqrt {\frac {y}{t}} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	55.246
24558	170	\begin{align*} r y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✗	55.293
24559	13586	\begin{align*} y y^{\prime }-\frac {a \left (5 x -4\right ) y}{x^{4}}&=\frac {a^{2} \left (x -1\right ) \left (3 x -1\right )}{x^{7}} \\ \end{align*}	✗	✓	✗	✗	55.449
24560	21368	\begin{align*} x^{2}-2 y^{2}+y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	55.469
24561	2629	\begin{align*} \left (t -1\right )^{2} y^{\prime \prime }-2 \left (t -1\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	55.487
24562	12600	\begin{align*} y^{\prime \prime }&=-\frac {\left (3 x +a +2 b \right ) y^{\prime }}{2 \left (a +x \right ) \left (x +b \right )}-\frac {\left (a -b \right ) y}{4 \left (a +x \right )^{2} \left (x +b \right )} \\ \end{align*}	✓	✓	✓	✗	55.568
24563	17472	\begin{align*} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 10 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	55.596
24564	20129	\begin{align*} y^{\prime \prime }-\frac {a^{2}}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	55.656
24565	20958	\begin{align*} y^{\prime }&=y \left (\mu -y\right ) \left (\mu -2 y\right ) \\ \end{align*}	✓	✓	✓	✓	55.703
24566	330	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=1+x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	55.706
24567	23524	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{a x} \\ y \left (0\right ) &= y_{0} \\ y^{\prime }\left (0\right ) &= y_{1} \\ \end{align*}	✓	✓	✓	✓	55.750
24568	23402	\begin{align*} y^{\prime \prime }+\frac {5 y^{\prime }}{x -1}+\frac {4 y}{\left (x -1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	55.839
24569	25580	\begin{align*} r^{\prime \prime }+r^{\prime }+r&=1 \\ r \left (0\right ) &= 0 \\ r^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	55.858
24570	17494	\begin{align*} y^{\prime \prime }-10 y^{\prime }+34 y&={\mathrm e}^{5 t} \cot \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	55.905
24571	12639	\begin{align*} y^{\prime \prime }&=-\frac {\left (2 x^{2}+a \right ) y^{\prime }}{x \left (x^{2}+a \right )}-\frac {b y}{x^{2} \left (x^{2}+a \right )} \\ \end{align*}	✓	✓	✓	✗	55.972
24572	12095	\begin{align*} y^{\prime }&=\frac {\left (-\sqrt {a}\, x^{3}+2 \sqrt {a \,x^{4}+8 y}+2 x^{2} \sqrt {a \,x^{4}+8 y}+2 x^{3} \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2} \\ \end{align*}	✗	✓	✓	✗	55.975
24573	10526	\begin{align*} \left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y&=0 \\ \end{align*}	✓	✓	✓	✗	56.039
24574	11817	\begin{align*} {y^{\prime }}^{2}-\left (y^{4}+x y^{2}+x^{2}\right ) {y^{\prime }}^{2}+\left (x y^{6}+x^{2} y^{4}+x^{3} y^{2}\right ) y^{\prime }-x^{3} y^{6}&=0 \\ \end{align*}	✗	✗	✗	✗	56.059
24575	2771	\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2}-x_{3}+{\mathrm e}^{3 t} \\ x_{2}^{\prime }&=x_{1}+3 x_{2}+x_{3}-{\mathrm e}^{3 t} \\ x_{3}^{\prime }&=-3 x_{1}+x_{2}-x_{3}-{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	56.211
24576	10075	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	56.251
24577	17324	\begin{align*} x^{\prime }&=\frac {5 t x}{t^{2}+x^{2}} \\ \end{align*}	✓	✓	✓	✓	56.277
24578	7518	\begin{align*} -4 x -y-1+\left (x +y+3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	56.295
24579	20128	\begin{align*} y^{\prime \prime }+\frac {a^{2}}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	56.439
24580	13527	\begin{align*} y y^{\prime }-y&=2 A^{2}-A \sqrt {x} \\ \end{align*}	✗	✓	✗	✗	56.460
24581	24302	\begin{align*} y^{2}-\left (y x +2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	56.517
24582	893	\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=3 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	56.635
24583	22776	\begin{align*} y^{\prime \prime }+3 y&=x^{2}+1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	56.646
24584	6256	\begin{align*} -a^{2} y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✗	✗	56.697
24585	18043	\begin{align*} x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	56.744
24586	22653	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=x \\ \end{align*}	✓	✓	✓	✗	56.819
24587	14068	\begin{align*} \left (x -y^{\prime }-y\right )^{2}&=x^{2} \left (2 y x -x^{2} y^{\prime }\right ) \\ \end{align*}	✗	✗	✗	✗	56.862
24588	4778	\begin{align*} y^{\prime } x&=a \,x^{n}+b y+c y^{2} \\ \end{align*}	✓	✓	✓	✗	56.903
24589	9686	\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{3}-\frac {9 x_{4}}{5} \\ x_{2}^{\prime }&=\frac {51 x_{2}}{10}-x_{4}+3 x_{5} \\ x_{3}^{\prime }&=x_{1}+2 x_{2}-3 x_{3} \\ x_{4}^{\prime }&=x_{2}-\frac {31 x_{3}}{10}+4 x_{4} \\ x_{5}^{\prime }&=-\frac {14 x_{1}}{5}+\frac {3 x_{4}}{2}-x_{5} \\ \end{align*}	✓	✓	✓	✗	56.934
24590	13619	\begin{align*} y y^{\prime } x&=a y^{2}+b y+c \,x^{n}+s \\ \end{align*}	✗	✗	✗	✗	56.951
24591	8399	\begin{align*} y^{\prime }&=y^{{2}/{3}}-y \\ \end{align*}	✓	✓	✓	✓	56.970
24592	17531	\begin{align*} y^{\prime \prime }+4 y&=f \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	56.988
24593	6167	\begin{align*} -\left (4 p^{2}+1\right ) y-8 y^{\prime } x +4 \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	57.059
24594	11837	\begin{align*} {y^{\prime }}^{n}-f \left (x \right )^{n} \left (y-a \right )^{n +1} \left (y-b \right )^{n -1}&=0 \\ \end{align*}	✓	✓	✓	✗	57.075
24595	3749	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{2 x} \tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	57.125
24596	2632	\begin{align*} \left (-2+t \right )^{2} y^{\prime \prime }+5 \left (-2+t \right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	57.129
24597	2934	\begin{align*} \frac {x^{2}-y^{2}}{x \left (2 x^{2}+y^{2}\right )}+\frac {\left (x^{2}+2 y^{2}\right ) y^{\prime }}{y \left (2 x^{2}+y^{2}\right )}&=0 \\ \end{align*}	✓	✓	✓	✗	57.144
24598	5786	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{a x} x \\ \end{align*}	✓	✓	✓	✓	57.158
24599	11993	\begin{align*} y^{\prime }&=-\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-1\right ) y}{x +1} \\ \end{align*}	✗	✓	✓	✓	57.256
24600	17841	\begin{align*} y^{\prime }&=\sqrt {x^{2}-y}-x \\ \end{align*}	✓	✓	✓	✗	57.466