2.3.215 Problems 21401 to 21500

Table 2.961: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
21401	2942	\begin{align*} y \left (y-x^{2}\right )+x^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.410
21402	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*}	✓	✓	✓	✗	4.410
21403	3014	\begin{align*} y-y^{\prime } x&=2 y^{\prime }+2 y^{2} \\ \end{align*}	✓	✓	✓	✓	4.411
21404	3039	\begin{align*} x \sqrt {1-y}-y^{\prime } \sqrt {-x^{2}+1}&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	4.411
21405	5039	\begin{align*} y^{\prime } y+x \,{\mathrm e}^{-x} \left (1+y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.411
21406	9164	\begin{align*} y^{\prime }&=\sin \left (\frac {y}{x}\right )-\cos \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	4.412
21407	14179	\begin{align*} y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	4.412
21408	12282	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	4.415
21409	11493	\begin{align*} x \ln \left (x \right ) y^{\prime }-y^{2} \ln \left (x \right )-\left (2 \ln \left (x \right )^{2}+1\right ) y-\ln \left (x \right )^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	4.417
21410	4848	\begin{align*} \left (x +a \right ) y^{\prime }&=y \left (1-a y\right ) \\ \end{align*}	✓	✓	✓	✓	4.418
21411	4946	\begin{align*} \left (x -a \right ) \left (-b +x \right ) y^{\prime }&=\left (x -a \right ) \left (-b +x \right )+\left (2 x -a -b \right ) y \\ \end{align*}	✓	✓	✓	✓	4.420
21412	2517	\begin{align*} 3 t y+y^{2}+\left (t^{2}+t y\right ) y^{\prime }&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.421
21413	7491	\begin{align*} y^{\prime }+\frac {y}{x}&=x^{3} y^{2} \\ \end{align*}	✓	✓	✓	✓	4.421
21414	4097	\begin{align*} x^{3}+y^{3}-y^{2} y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	4.422
21415	5295	\begin{align*} \left (a -3 x^{2}-y^{2}\right ) y y^{\prime }+x \left (a -x^{2}+y^{2}\right )&=0 \\ \end{align*}	✗	✓	✓	✗	4.422
21416	2971	\begin{align*} 2 y&=\left (y^{4}+x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	4.423
21417	13965	\begin{align*} \left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime \prime }+\left (c \,{\mathrm e}^{\lambda x}+d \right ) y^{\prime }+\left (n \,{\mathrm e}^{\lambda x}+m \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	4.426
21418	8707	\begin{align*} x^{2}+y x +y^{2}&=x^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.427
21419	21313	\begin{align*} x^{\prime }&=\lambda x-x^{5} \\ \end{align*}	✓	✓	✓	✓	4.428
21420	15594	\begin{align*} y^{\prime }&=\frac {y^{2}}{-y x +1} \\ \end{align*}	✓	✓	✓	✓	4.429
21421	14118	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{\left (1-x \right )^{2}} \\ \end{align*}	✓	✓	✓	✗	4.430
21422	25745	\begin{align*} y^{\prime } x +y&=2 x \\ y \left (x_{0} \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.430
21423	1589	\begin{align*} \left (3 y^{2}+4 y\right ) y^{\prime }+2 x +\cos \left (x \right )&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.431
21424	13282	\begin{align*} y^{\prime }&=y^{2}+a \lambda \,{\mathrm e}^{\lambda x}-a^{2} {\mathrm e}^{2 \lambda x} \\ \end{align*}	✓	✓	✓	✗	4.431
21425	729	\begin{align*} \left (x +y\right ) y^{\prime }&=x -y \\ \end{align*}	✓	✓	✓	✓	4.433
21426	4314	\begin{align*} -y+y^{\prime } x&=x \cot \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	4.433
21427	6908	\begin{align*} y x -y^{2}-x^{2} y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.433
21428	13739	\begin{align*} y^{\prime \prime } x -\left (2 a x +1\right ) y^{\prime }+b \,x^{3} y&=0 \\ \end{align*}	✗	✓	✗	✗	4.433
21429	7748	\begin{align*} y^{\prime }+x +x y^{2}&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✗	✓	4.434
21430	20253	\begin{align*} \left (y^{2}+x^{2}\right ) y^{\prime }&=y x \\ \end{align*}	✓	✓	✓	✓	4.436
21431	1706	\begin{align*} x^{2}+y^{2}+2 x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	4.438
21432	21480	\begin{align*} x^{\prime \prime }-4 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	4.438
21433	2941	\begin{align*} \left (x^{3} y^{3}-1\right ) y^{\prime }+x^{2} y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	4.441
21434	4249	\begin{align*} \left (x +\frac {2}{y}\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	4.442
21435	11446	\begin{align*} x^{2} y^{\prime }+y^{3} a \,x^{2}+b y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	4.443
21436	18059	\begin{align*} x -y+2+\left (x -y+3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.444
21437	8368	\begin{align*} y^{\prime }&=y \,{\mathrm e}^{-x^{2}} \\ y \left (4\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.447
21438	15941	\begin{align*} y^{\prime }&=\frac {\left (t^{2}-4\right ) \left (1+y\right ) {\mathrm e}^{y}}{\left (-1+t \right ) \left (3-y\right )} \\ \end{align*}	✓	✓	✓	✓	4.450
21439	14534	\begin{align*} y^{2} {\mathrm e}^{2 x}-2 x +y \,{\mathrm e}^{2 x} y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.454
21440	21843	\begin{align*} y^{\prime }+3 x^{2} y&=3 x^{2} \\ \end{align*}	✓	✓	✓	✓	4.454
21441	12389	\begin{align*} y^{\prime \prime } x -\left (2 a \,x^{2}+1\right ) y^{\prime }+b \,x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✗	4.455
21442	7224	\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.457
21443	17263	\begin{align*} 2 \ln \left (t \right )-\ln \left (4 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.459
21444	1685	\begin{align*} 4 x +7 y+\left (3 x +4 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.460
21445	23223	\begin{align*} x^{2}+y^{2}-2 x y^{\prime } y&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.462
21446	11501	\begin{align*} y^{\prime } y+x^{3}+y&=0 \\ \end{align*}	✗	✗	✗	✗	4.463
21447	19251	\begin{align*} y^{\prime } x&=\left (-2 x^{2}+1\right ) \tan \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	4.463
21448	1159	\begin{align*} y^{\prime }&=\frac {x^{2}+3 y^{2}}{2 y x} \\ \end{align*}	✓	✓	✓	✓	4.464
21449	7012	\begin{align*} y^{\prime } x&=x +y+{\mathrm e}^{\frac {y}{x}} x \\ \end{align*}	✓	✓	✓	✗	4.464
21450	15351	\begin{align*} -y+y^{\prime } x&=\sqrt {y^{2}+x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.464
21451	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*}	✓	✓	✗	✗	4.464
21452	6989	\begin{align*} y^{\prime }&=1+\frac {y}{x}-\frac {y^{2}}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.465
21453	7254	\begin{align*} y^{\prime }&=\frac {y}{x}-\tan \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	4.467
21454	12373	\begin{align*} y^{\prime \prime } x +\left (x +b \right ) y^{\prime }+a y&=0 \\ \end{align*}	✗	✓	✓	✗	4.467
21455	4701	\begin{align*} y^{\prime }+y^{3} \sec \left (x \right ) \tan \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.470
21456	8886	\begin{align*} y^{\prime }&=1+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✓	4.471
21457	4421	\begin{align*} x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.473
21458	20121	\begin{align*} y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }&=x y^{2} \\ \end{align*}	✗	✗	✗	✗	4.474
21459	18572	\begin{align*} y^{\prime }&=-\frac {4 x +2 y}{2 x +3 y} \\ \end{align*}	✓	✓	✓	✓	4.475
21460	15533	\begin{align*} y^{\prime }&=y^{2}-x^{2} \\ \end{align*}	✓	✓	✓	✗	4.477
21461	61	\begin{align*} 2 y^{\prime } y&=\frac {x}{\sqrt {x^{2}-16}} \\ y \left (5\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.478
21462	3652	\begin{align*} y^{\prime }&=\frac {y-\sqrt {y^{2}+x^{2}}}{x} \\ y \left (3\right ) &= 4 \\ \end{align*}	✓	✓	✓	✗	4.479
21463	12452	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y-x^{3} \sin \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.480
21464	15345	\begin{align*} y^{\prime } \sqrt {-x^{2}+1}-\sqrt {1-y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	4.480
21465	2875	\begin{align*} y^{\prime } y+x&=2 y \\ \end{align*}	✓	✓	✓	✗	4.482
21466	4805	\begin{align*} y^{\prime } x +2 y&=-\sqrt {1+y^{2}} \\ \end{align*}	✓	✓	✓	✓	4.484
21467	23192	\begin{align*} x^{2}+y^{2}+2 x y^{\prime } y&=0 \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	4.485
21468	23187	\begin{align*} 3 x^{2} y+y^{2}-\left (-x^{3}-2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.488
21469	20819	\begin{align*} y^{\prime }+y&=\sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.489
21470	19792	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+x^{2} y&=x^{3}-x^{2} \arctan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.490
21471	8839	\begin{align*} x +y^{\prime } y+y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	4.492
21472	18580	\begin{align*} 2 x -y+\left (-x +2 y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	4.493
21473	4804	\begin{align*} y^{\prime } x +2 y&=\sqrt {1+y^{2}} \\ \end{align*}	✓	✓	✓	✓	4.494
21474	25779	\begin{align*} y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.494
21475	19376	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}-2 y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✗	4.496
21476	1801	\begin{align*} \left (3 x -1\right ) \left (y^{\prime }+y^{2}\right )-\left (3 x +2\right ) y-6 x +8&=0 \\ \end{align*}	✓	✓	✓	✓	4.498
21477	17220	\begin{align*} 1-y^{2} \cos \left (t y\right )+\left (t y \cos \left (t y\right )+\sin \left (t y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	4.499
21478	17948	\begin{align*} 2 y^{\prime } x -y&=1-\frac {2}{\sqrt {x}} \\ y \left (\infty \right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	4.500
21479	12334	\begin{align*} -x^{3} y+x^{4} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.501
21480	24129	\begin{align*} y x -\left (2+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.502
21481	4407	\begin{align*} 2 y-x \left (\ln \left (x^{2} y\right )-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.503
21482	3469	\begin{align*} y^{\prime }&=\tan \left (x \right ) \cos \left (y\right ) \left (\cos \left (y\right )+\sin \left (y\right )\right ) \\ \end{align*}	✓	✓	✓	✓	4.504
21483	4954	\begin{align*} 2 \left (-x^{2}+1\right ) y^{\prime }&=\sqrt {-x^{2}+1}+\left (x +1\right ) y \\ \end{align*}	✓	✓	✓	✓	4.505
21484	1201	\begin{align*} 2 x -2 \,{\mathrm e}^{y x} \sin \left (2 x \right )+{\mathrm e}^{y x} \cos \left (2 x \right ) y+\left (-3+{\mathrm e}^{y x} x \cos \left (2 x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.510
21485	25051	\begin{align*} y^{\prime }&=\frac {t -y}{t +y} \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	4.513
21486	21357	\begin{align*} {\mathrm e}^{x}-y^{\prime } y&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.518
21487	20324	\begin{align*} y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}}&=\frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	4.519
21488	5191	\begin{align*} x \left (1-2 y x \right ) y^{\prime }+y \left (2 y x +1\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.520
21489	14056	\begin{align*} x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right )&=0 \\ \end{align*}	✓	✓	✗	✗	4.520
21490	12495	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+a x y^{\prime }+\left (a -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	4.522
21491	22382	\begin{align*} x^{2}-y^{2}-2 x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	4.524
21492	11353	\begin{align*} y^{\prime }-a y^{n}-b \,x^{\frac {n}{1-n}}&=0 \\ \end{align*}	✓	✓	✓	✗	4.525
21493	119	\begin{align*} x \left (x +y\right ) y^{\prime }+y \left (3 x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.526
21494	5344	\begin{align*} \left (x \sqrt {1+x^{2}+y^{2}}-y \left (y^{2}+x^{2}\right )\right ) y^{\prime }&=\left (y^{2}+x^{2}\right ) x +y \sqrt {1+x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✗	4.527
21495	4895	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=5-y x \\ \end{align*}	✓	✓	✓	✓	4.532
21496	13286	\begin{align*} y^{\prime }&=y^{2}+a \,{\mathrm e}^{\lambda x} y-a b \,{\mathrm e}^{\lambda x}-b^{2} \\ \end{align*}	✓	✓	✓	✗	4.533
21497	4806	\begin{align*} y^{\prime } x&=y+\sqrt {y^{2}+x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.534
21498	8874	\begin{align*} L y^{\prime }+R y&=E \,{\mathrm e}^{i \omega x} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.535
21499	24126	\begin{align*} v^{\prime }&=-\frac {v}{p} \\ \end{align*}	✓	✓	✓	✓	4.536
21500	21035	\begin{align*} x^{\prime }&=x^{p} \\ \end{align*}	✓	✓	✓	✓	4.538