2.3.215 Problems 21401 to 21500

Table 2.973: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
21401	17126	\begin{align*} y^{\prime }+y f \left (t \right )&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	7.543
21402	806	\begin{align*} y^{\prime }&=\cot \left (x \right ) \left (\sqrt {y}-y\right ) \\ \end{align*}	✓	✓	✓	✓	7.544
21403	15619	\begin{align*} y^{\prime }&=y^{3} \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	7.545
21404	12221	\begin{align*} y^{\prime }&=\frac {-32 y x -72 x^{3}+32 x^{2}-32 x +64 y^{3}+48 y^{2} x^{2}-192 x y^{2}+12 x^{4} y-96 x^{3} y+192 x^{2} y+x^{6}-12 x^{5}+48 x^{4}}{64 y+16 x^{2}-64 x +64} \\ \end{align*}	✓	✓	✓	✗	7.546
21405	21992	\begin{align*} y^{\prime }&=x^{3} y^{2} \\ \end{align*}	✓	✓	✓	✓	7.548
21406	19293	\begin{align*} y^{\prime }&=\frac {2+3 x y^{2}}{4 x^{2} y} \\ \end{align*}	✓	✓	✓	✓	7.553
21407	3548	\begin{align*} x \left (x^{2}-y^{2}\right )-x \left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.555
21408	7020	\begin{align*} x^{2} y^{\prime }+x^{2}+y x +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	7.558
21409	11929	\begin{align*} y^{\prime }&=\frac {x^{3}+x^{2}+2 \sqrt {x^{3}-6 y}}{2 x +2} \\ \end{align*}	✓	✓	✓	✓	7.558
21410	23143	\begin{align*} \left (x^{2}+4\right ) y^{\prime }+3 y x&=0 \\ \end{align*}	✓	✓	✓	✓	7.558
21411	14187	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✓	7.561
21412	5037	\begin{align*} y y^{\prime }+x^{3}+y&=0 \\ \end{align*}	✗	✗	✗	✗	7.563
21413	17905	\begin{align*} \left (x^{2}+1\right ) y^{\prime }-\frac {\cos \left (2 y\right )^{2}}{2}&=0 \\ y \left (-\infty \right ) &= \frac {7 \pi }{2} \\ \end{align*}	✓	✓	✗	✗	7.565
21414	21926	\begin{align*} x^{2} y^{\prime }+y^{2}&=x^{2} y y^{\prime }-x y^{2} \\ \end{align*}	✓	✓	✓	✓	7.569
21415	683	\begin{align*} y^{\prime }&=4 \left (y x \right )^{{1}/{3}} \\ \end{align*}	✓	✓	✓	✗	7.571
21416	16978	\begin{align*} y \cos \left (t \right )+\left (2 y+\sin \left (t \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.573
21417	12080	\begin{align*} y^{\prime }&=\frac {\left (x +y+1\right ) y}{\left (x +y+2 y^{3}\right ) \left (x +1\right )} \\ \end{align*}	✓	✓	✓	✗	7.576
21418	22505	\begin{align*} y^{\prime }&=3 y^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✓	7.581
21419	7693	\begin{align*} y^{\prime }+\frac {2 y}{x}-x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	7.583
21420	12120	\begin{align*} y^{\prime }&=\frac {\left ({\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x +x^{2}\right ) {\mathrm e}^{\frac {y}{x}}}{x} \\ \end{align*}	✓	✓	✓	✓	7.584
21421	19132	\begin{align*} y^{\prime }&=-x +\sqrt {x^{2}+2 y} \\ \end{align*}	✓	✓	✓	✓	7.586
21422	22955	\begin{align*} x \cos \left (y\right ) y^{\prime }-\left (x^{2}+1\right ) \sin \left (y\right )&=0 \\ y \left (1\right ) &= \frac {\pi }{2} \\ \end{align*}	✓	✓	✓	✓	7.587
21423	5041	\begin{align*} y y^{\prime }+4 x \left (x +1\right )+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	7.596
21424	14073	\begin{align*} y&=\left (x +1\right ) {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	7.596
21425	22489	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	7.599
21426	17878	\begin{align*} \sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=0 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.601
21427	7219	\begin{align*} \sin \left (x \right ) y^{\prime }&=y \ln \left (y\right ) \\ y \left (\frac {\pi }{3}\right ) &= {\mathrm e} \\ \end{align*}	✓	✓	✓	✓	7.604
21428	214	\begin{align*} y^{\prime }&=\frac {\sqrt {y}-y}{\tan \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	7.608
21429	7872	\begin{align*} 1+\left (-x^{2}+1\right ) \cot \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.609
21430	21961	\begin{align*} {b^{\prime }}^{7}&=3 p \\ \end{align*}	✓	✓	✓	✗	7.610
21431	13035	\begin{align*} 4 {y^{\prime }}^{2}-2 \left (y+3 y^{\prime } x \right ) y^{\prime \prime }+3 x^{2} {y^{\prime \prime }}^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	7.612
21432	21846	\begin{align*} y^{\prime } x +y&=y^{2} x^{3} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	7.614
21433	25881	\begin{align*} y^{\prime }&=\frac {x^{3}+y^{3}}{y^{2} x} \\ \end{align*}	✓	✓	✓	✓	7.615
21434	4336	\begin{align*} y+x \left (y^{2}+\ln \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.620
21435	12215	\begin{align*} y^{\prime }&=-\frac {x}{2}+1+y^{2}+\frac {7 x^{2} y}{2}-2 y x +\frac {13 x^{4}}{16}-\frac {3 x^{3}}{2}+x^{2}+y^{3}+\frac {3 y^{2} x^{2}}{4}-3 x y^{2}+\frac {3 x^{4} y}{16}-\frac {3 x^{3} y}{2}+\frac {x^{6}}{64}-\frac {3 x^{5}}{16} \\ \end{align*}	✓	✓	✓	✓	7.621
21436	23183	\begin{align*} y^{\prime }&=\sqrt {y} \\ \end{align*}	✓	✓	✓	✓	7.622
21437	17880	\begin{align*} y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	7.623
21438	7393	\begin{align*} x^{\prime }-x^{3}&=x \\ \end{align*}	✓	✓	✓	✓	7.624
21439	11986	\begin{align*} y^{\prime }&=\frac {y \left (1-x +y \ln \left (x \right ) x^{2}+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (x -1\right ) x} \\ \end{align*}	✓	✓	✓	✗	7.625
21440	4963	\begin{align*} \left (b \,x^{2}+a \right ) y^{\prime }&=-A -B y^{2} \\ \end{align*}	✓	✓	✓	✓	7.626
21441	14969	\begin{align*} 4 t^{2} x^{\prime \prime }+8 t x^{\prime }+5 x&=0 \\ x \left (1\right ) &= 2 \\ x^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	7.626
21442	14055	\begin{align*} {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	7.628
21443	19815	\begin{align*} 3 x^{2} y^{\prime }+2 x^{2}-3 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	7.629
21444	5251	\begin{align*} x \left (1-y^{2}\right ) y^{\prime }&=\left (x^{2}+1\right ) y \\ \end{align*}	✓	✓	✓	✓	7.631
21445	15799	\begin{align*} y^{\prime }&=-y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	7.631
21446	6567	\begin{align*} \operatorname {f3} \left (y\right )+\operatorname {f2} \left (y\right ) y^{\prime }+\operatorname {f1} \left (y\right ) {y^{\prime }}^{2}+\operatorname {f0} \left (y\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	7.633
21447	5844	\begin{align*} k \left (1+k \right ) y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	7.634
21448	144	\begin{align*} {\mathrm e}^{x} \sin \left (y\right )+\tan \left (y\right )+\left ({\mathrm e}^{x} \cos \left (y\right )+x \sec \left (y\right )^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.635
21449	24975	\begin{align*} y^{\prime }&=\frac {\cot \left (y\right )}{t} \\ y \left (1\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✓	7.640
21450	20029	\begin{align*} y&=y^{\prime } x +\sqrt {b^{2}+a^{2} y^{\prime }} \\ \end{align*}	✓	✓	✓	✗	7.642
21451	16316	\begin{align*} 2 x y^{3}+4 x^{3}+3 x^{2} y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.649
21452	7010	\begin{align*} y^{\prime } x -y^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✓	7.655
21453	23596	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=z \\ z^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	7.655
21454	2924	\begin{align*} \frac {2}{y}-\frac {y}{x^{2}}+\left (\frac {1}{x}-\frac {2 x}{y^{2}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.657
21455	4340	\begin{align*} 2 y \left (x +y+2\right )+\left (y^{2}-x^{2}-4 x -1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.657
21456	136	\begin{align*} 4 x -y+\left (6 y-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.665
21457	16756	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{\left (x +1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	7.665
21458	9164	\begin{align*} y^{\prime }&=\sin \left (\frac {y}{x}\right )-\cos \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✗	7.670
21459	108	\begin{align*} \left (x -y\right ) y^{\prime }&=x +y \\ \end{align*}	✓	✓	✓	✓	7.674
21460	13306	\begin{align*} y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{2}-a b \,x^{n} {\mathrm e}^{\lambda x} y+b n \,x^{n -1} \\ \end{align*}	✓	✓	✓	✗	7.675
21461	19727	\begin{align*} \left (T \ln \left (t \right )-1\right ) T&=t T^{\prime } \\ \end{align*}	✓	✓	✓	✓	7.675
21462	4872	\begin{align*} x^{2} y^{\prime }+x^{2}+y x +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	7.686
21463	23047	\begin{align*} T^{\prime \prime }+{T^{\prime }}^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	7.686
21464	7249	\begin{align*} x^{2} y^{\prime }+y^{2}-y x&=0 \\ \end{align*}	✓	✓	✓	✓	7.691
21465	7338	\begin{align*} 3 x^{3} y^{2} y^{\prime }-x^{2} y^{3}&=1 \\ \end{align*}	✓	✓	✓	✓	7.691
21466	12280	\begin{align*} y^{\prime }&=\frac {2 x^{2} y+x^{3}+x y \ln \left (x \right )-y^{2}-y x}{x^{2} \left (\ln \left (x \right )+x \right )} \\ \end{align*}	✓	✓	✓	✗	7.691
21467	23968	\begin{align*} y^{\prime }-2 y&=x^{2}-1 \\ \end{align*}	✓	✓	✓	✓	7.702
21468	4813	\begin{align*} y^{\prime } x +x -y+x \cos \left (\frac {y}{x}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	7.704
21469	3043	\begin{align*} y^{\prime } x -2 y-2 y^{3} x^{4}&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.707
21470	4672	\begin{align*} y^{\prime }&=a_{0} +a_{1} y+a_{2} y^{2} \\ \end{align*}	✓	✓	✓	✓	7.708
21471	8700	\begin{align*} y^{\prime } x&=y \cos \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	7.712
21472	4828	\begin{align*} y^{\prime } x&=y \ln \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	7.714
21473	7726	\begin{align*} \left (y x +1\right ) y+x \left (1+y x +y^{2} x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.715
21474	25779	\begin{align*} y^{\prime }&=\sin \left (x \right ) \cos \left (y\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.715
21475	3007	\begin{align*} x -2 y+1+\left (-2+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.719
21476	22555	\begin{align*} q^{\prime }&=\frac {p \,{\mathrm e}^{p^{2}-q^{2}}}{q} \\ \end{align*}	✓	✓	✓	✓	7.729
21477	24160	\begin{align*} y y^{\prime } x +x^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	7.733
21478	10452	\begin{align*} y^{\prime }&=x -y^{2} \\ \end{align*}	✓	✓	✓	✗	7.734
21479	11836	\begin{align*} {y^{\prime }}^{r}-a y^{s}-b \,x^{\frac {r s}{r -s}}&=0 \\ \end{align*}	✓	✓	✓	✗	7.735
21480	15060	\begin{align*} \left (3+2 x +4 y\right ) y^{\prime }-2 y-x -1&=0 \\ \end{align*}	✓	✓	✓	✓	7.740
21481	5008	\begin{align*} x^{n} y^{\prime }&=x^{n -1} \left (a \,x^{2 n}+n y-b y^{2}\right ) \\ \end{align*}	✓	✓	✓	✗	7.743
21482	15895	\begin{align*} y^{\prime }&=\cos \left (\frac {\pi y}{2}\right ) \\ \end{align*}	✓	✓	✓	✗	7.743
21483	11574	\begin{align*} \left (x +y\right )^{2} y^{\prime }-a^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	7.748
21484	109	\begin{align*} x \left (x +y\right ) y^{\prime }&=y \left (x -y\right ) \\ \end{align*}	✓	✓	✓	✓	7.750
21485	9753	\begin{align*} 2 {y^{\prime }}^{3}+y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✗	✗	7.752
21486	17076	\begin{align*} \frac {3}{t^{2}}&=\left (\frac {1}{\sqrt {y}}+\sqrt {y}\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	7.753
21487	23132	\begin{align*} y^{\prime }&=y x \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	7.755
21488	5547	\begin{align*} y {y^{\prime }}^{2}+a x y^{\prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✓	7.757
21489	25724	\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{6}\right ) &= -1 \\ \end{align*}	✓	✗	✗	✗	7.765
21490	12253	\begin{align*} y^{\prime }&=y \left (y^{2}+y \,{\mathrm e}^{b x}+{\mathrm e}^{2 b x}\right ) {\mathrm e}^{-2 b x} \\ \end{align*}	✓	✓	✓	✓	7.772
21491	4848	\begin{align*} \left (a +x \right ) y^{\prime }&=y \left (1-a y\right ) \\ \end{align*}	✓	✓	✓	✓	7.773
21492	20253	\begin{align*} \left (x^{2}+y^{2}\right ) y^{\prime }&=y x \\ \end{align*}	✓	✓	✓	✓	7.776
21493	18574	\begin{align*} {\mathrm e}^{x} \sin \left (y\right )-2 \sin \left (x \right ) y+\left (2 \cos \left (x \right )+{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.782
21494	5908	\begin{align*} \left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y+a y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✗	✗	✗	7.786
21495	15029	\begin{align*} y&=y^{\prime } x +\frac {1}{y} \\ \end{align*}	✓	✓	✓	✓	7.789
21496	778	\begin{align*} x^{2} y^{\prime }+2 y x&=y^{2} \\ \end{align*}	✓	✓	✓	✓	7.790
21497	5012	\begin{align*} \left (x -\sqrt {x^{2}+1}\right ) y^{\prime }&=y+\sqrt {1+y^{2}} \\ \end{align*}	✓	✓	✓	✓	7.791
21498	23172	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=-2 x \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.794
21499	25783	\begin{align*} y^{\prime }&=x \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	7.796
21500	5027	\begin{align*} y^{\prime } \left (4 x^{3}+a_{1} x +a_{0} \right )^{{2}/{3}}+\left (a_{0} +a_{1} y+4 y^{3}\right )^{{2}/{3}}&=0 \\ \end{align*}	✓	✓	✓	✓	7.798