2.3.212 Problems 21101 to 21200

Table 2.997: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
21101	14712	\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y&=2 x^{3} \\ \end{align*}	✓	✓	✓	✓	5.350
21102	14502	\begin{align*} 2 x \left (y+1\right )-\left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (1\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	5.355
21103	7023	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+y x -3 x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.357
21104	4994	\begin{align*} x^{4} y^{\prime }+x^{3} y+\csc \left (y x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	5.359
21105	11592	\begin{align*} 3 x y^{2} y^{\prime }+y^{3}-2 x&=0 \\ \end{align*}	✓	✓	✓	✓	5.360
21106	13224	\begin{align*} \left (a \,x^{2}+b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A&=0 \\ \end{align*}	✓	✓	✓	✗	5.360
21107	2977	\begin{align*} y+y^{3}+4 \left (x y^{2}-1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.361
21108	1607	\begin{align*} y^{\prime }-2 y&=\frac {x \,{\mathrm e}^{2 x}}{1-y \,{\mathrm e}^{-2 x}} \\ \end{align*}	✓	✓	✓	✗	5.362
21109	3522	\begin{align*} y^{\prime }&=\frac {x \left (y^{2}-1\right )}{2 \left (x -2\right ) \left (x -1\right )} \\ \end{align*}	✓	✓	✓	✓	5.362
21110	8365	\begin{align*} \left (x^{4}+1\right ) y^{\prime }+x \left (1+4 y^{2}\right )&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✗	✓	5.365
21111	22771	\begin{align*} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	5.366
21112	16306	\begin{align*} y^{\prime }&=2 \sqrt {2 x +y-3} \\ \end{align*}	✓	✓	✓	✓	5.368
21113	17986	\begin{align*} 2 x y^{2}-3 y^{3}+\left (7-3 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.368
21114	21377	\begin{align*} y^{\prime }+\frac {2 \sin \left (y\right ) x +y^{3} {\mathrm e}^{x}}{\cos \left (y\right ) x^{2}+3 y^{2} {\mathrm e}^{x}}&=0 \\ \end{align*}	✓	✓	✓	✗	5.369
21115	4736	\begin{align*} y^{\prime }&={\mathrm e}^{x} \left (a +b \,{\mathrm e}^{-y}\right ) \\ \end{align*}	✓	✓	✓	✓	5.370
21116	9817	\begin{align*} x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✗	5.370
21117	25499	\begin{align*} y^{\prime }&=y t +t +y+1 \\ \end{align*}	✓	✓	✓	✓	5.372
21118	12201	\begin{align*} y^{\prime }&=-\left (-\frac {\ln \left (y\right )}{x}+\frac {\ln \left (y\right )}{x \ln \left (x \right )}-\textit {\_F1} \left (x \right )\right ) y \\ \end{align*}	✓	✓	✓	✓	5.373
21119	27477	\begin{align*} \left (y^{\prime }-x \sqrt {y}\right ) \left (x^{2}-1\right )&=y x \\ \end{align*}	✓	✓	✓	✓	5.374
21120	18724	\begin{align*} a \,x^{2} y^{\prime \prime }+b x y^{\prime }+c y&=d \\ \end{align*}	✓	✓	✓	✓	5.375
21121	12161	\begin{align*} y^{\prime }&=\frac {-18 y x -6 x^{3}-18 x +27 y^{3}+27 x^{2} y^{2}+9 x^{4} y+x^{6}}{27 y+9 x^{2}+27} \\ \end{align*}	✓	✓	✓	✓	5.378
21122	5171	\begin{align*} 2 \left (x +1\right ) y y^{\prime }+2 x -3 x^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.379
21123	12647	\begin{align*} y^{\prime \prime }&=-\frac {\left (-x^{2} \left (a^{2}-1\right )+2 \left (a +3\right ) b x -b^{2}\right ) y}{4 x^{2}} \\ \end{align*}	✗	✓	✓	✗	5.379
21124	11476	\begin{align*} x^{2} \left (x -1\right ) y^{\prime }-y^{2}-x \left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	5.381
21125	8502	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (x -1\right )^{3}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.382
21126	20322	\begin{align*} y \left ({\mathrm e}^{x}+2 y x \right )-{\mathrm e}^{x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.383
21127	1576	\begin{align*} \frac {x y^{\prime }}{y}+2 \ln \left (y\right )&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	5.384
21128	16295	\begin{align*} y^{\prime }+3 y \cot \left (x \right )&=6 \cos \left (x \right ) y^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✓	5.386
21129	2952	\begin{align*} \left (x^{2}-1\right ) y+x \left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.387
21130	5952	\begin{align*} y-x y^{\prime }+\left (-x \cot \left (x \right )+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.387
21131	15518	\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \\ y \left (1\right ) &= 0 \\ y \left (2\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	5.388
21132	22068	\begin{align*} y^{\prime }+x^{2} y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	5.388
21133	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*}	✓	✓	✓	✗	5.390
21134	22000	\begin{align*} x +\frac {y^{\prime }}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	5.390
21135	16694	\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	5.391
21136	19925	\begin{align*} x y^{\prime }-a y&=x +1 \\ \end{align*}	✓	✓	✓	✓	5.392
21137	14272	\begin{align*} w^{\prime }&=t w+t^{3} w^{3} \\ \end{align*}	✓	✓	✓	✓	5.393
21138	8168	\begin{align*} 2 y^{\prime }&=y^{3} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.395
21139	14445	\begin{align*} \frac {x}{y^{2}}+x +\left (\frac {x^{2}}{y^{3}}+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.395
21140	11348	\begin{align*} y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-a -1}&=0 \\ \end{align*}	✓	✓	✓	✗	5.397
21141	22079	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	5.398
21142	26904	\begin{align*} y^{\prime }&=\frac {y^{2}}{2 x}-\frac {y}{x}-\frac {4}{x} \\ \end{align*}	✓	✓	✓	✓	5.398
21143	8337	\begin{align*} m v^{\prime }&=m g -k v^{2} \\ \end{align*}	✓	✓	✓	✓	5.399
21144	21340	\begin{align*} 2 x \left (y+1\right )-y y^{\prime }&=0 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	5.399
21145	25035	\begin{align*} t^{2}-y-t y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.399
21146	21068	\begin{align*} a \,x^{p}+b y+\left (b x +d y^{q}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.401
21147	24142	\begin{align*} y-\left ({\mathrm e}^{3 x}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.401
21148	25468	\begin{align*} y^{\prime }&=\frac {y}{t +1} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.401
21149	24992	\begin{align*} y^{\prime }-\frac {2 y}{t}&=\frac {t +1}{t} \\ y \left (1\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	5.403
21150	1595	\begin{align*} y^{\prime }&=\frac {2 x}{1+2 y} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.404
21151	4244	\begin{align*} x y^{\prime }&=y+2 \,{\mathrm e}^{-\frac {y}{x}} \\ \end{align*}	✓	✓	✓	✓	5.405
21152	17121	\begin{align*} y^{\prime }&={\mathrm e}^{2 x -y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.405
21153	18123	\begin{align*} 2 y y^{\prime \prime }-3 {y^{\prime }}^{2}&=4 y^{2} \\ \end{align*}	✓	✓	✓	✗	5.405
21154	20418	\begin{align*} y&=x y^{\prime }+\sqrt {b^{2}-a^{2} {y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	5.405
21155	7509	\begin{align*} y^{\prime }+\frac {y}{x}&=x^{2} y^{2} \\ \end{align*}	✓	✓	✓	✓	5.407
21156	14370	\begin{align*} x^{\prime \prime }+4 x&=\delta \left (t -2\right )-\delta \left (t -5\right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	5.407
21157	15065	\begin{align*} {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	5.408
21158	5443	\begin{align*} 4 {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x -2 y} y^{\prime }-{\mathrm e}^{2 x -2 y}&=0 \\ \end{align*}	✓	✓	✓	✗	5.409
21159	8691	\begin{align*} \left (1+y^{2}\right ) \left ({\mathrm e}^{2 x}-{\mathrm e}^{y} y^{\prime }\right )-\left (y+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.412
21160	6062	\begin{align*} n^{2} y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.413
21161	23178	\begin{align*} x -y+\left (y-x +2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.414
21162	23961	\begin{align*} -y^{2}+x^{2} y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	5.414
21163	15857	\begin{align*} y^{\prime }&=\frac {1}{\left (1+y\right ) \left (t -2\right )} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.416
21164	4673	\begin{align*} y^{\prime }&=f \left (x \right )+a y+b y^{2} \\ \end{align*}	✗	✗	✗	✗	5.418
21165	15562	\begin{align*} y^{\prime }&=y x +\frac {1}{x^{2}+1} \\ y \left (-5\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.418
21166	25869	\begin{align*} y-2 y x -x^{2}+x^{2} y^{\prime }&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.418
21167	6332	\begin{align*} y^{\prime \prime }&=2 x +\left (x^{2}-y^{\prime }\right )^{2} \\ \end{align*}	✓	✓	✓	✓	5.421
21168	17078	\begin{align*} \cos \left (y\right ) y^{\prime }&=8 \sin \left (8 t \right ) \\ \end{align*}	✓	✓	✓	✓	5.421
21169	19952	\begin{align*} \left (x +1\right ) y^{\prime }+1&=2 \,{\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✓	5.426
21170	5437	\begin{align*} 2 {y^{\prime }}^{2}-2 x^{2} y^{\prime }+3 y x&=0 \\ \end{align*}	✓	✓	✓	✗	5.427
21171	11403	\begin{align*} x y^{\prime }+x y^{2}-\left (2 x^{2}+1\right ) y-x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	5.428
21172	25850	\begin{align*} \frac {2 x}{y}+5 y^{2}-4 x +\left (3 y^{2}-\frac {x^{2}}{y^{2}}+10 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.428
21173	7857	\begin{align*} y^{2}-x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.429
21174	8301	\begin{align*} y^{\prime }&=\sin \left (x \right ) \cos \left (y\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.429
21175	11960	\begin{align*} y^{\prime }&=\frac {y+x^{3} a \ln \left (x +1\right )+a \,x^{4}+a \,x^{3}-x y^{2} \ln \left (x +1\right )-x^{2} y^{2}-x y^{2}}{x} \\ \end{align*}	✓	✓	✓	✗	5.430
21176	6057	\begin{align*} -y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.431
21177	3475	\begin{align*} y^{\prime }-\frac {y^{2}}{x^{2}}&={\frac {1}{4}} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	5.435
21178	7745	\begin{align*} y^{\prime }&=\frac {x -2 y+1}{2 x -4 y} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.435
21179	14458	\begin{align*} y x +2 x +y+2+\left (x^{2}+2 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.437
21180	5346	\begin{align*} \left (a \cos \left (b x +a y\right )-b \sin \left (a x +b y\right )\right ) y^{\prime }+b \cos \left (b x +a y\right )-a \sin \left (a x +b y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	5.438
21181	12140	\begin{align*} y^{\prime }&=-\frac {-x -\textit {\_F1} \left (y^{2}-2 x \right )}{\sqrt {y^{2}}\, x} \\ \end{align*}	✗	✓	✓	✗	5.438
21182	14967	\begin{align*} x^{2} z^{\prime \prime }+3 x z^{\prime }+4 z&=0 \\ z \left (1\right ) &= 0 \\ z^{\prime }\left (1\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	5.438
21183	1728	\begin{align*} 2 y+3 \left (x^{2}+x^{2} y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.440
21184	24127	\begin{align*} y \,{\mathrm e}^{2 x}-\left (4+{\mathrm e}^{2 x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.441
21185	24953	\begin{align*} y^{\prime }&=t y^{2}-y^{2}+t -1 \\ \end{align*}	✓	✓	✓	✓	5.442
21186	14419	\begin{align*} y^{\prime }+3 y&=3 x^{2} {\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	5.443
21187	5486	\begin{align*} \left (5+3 x \right ) {y^{\prime }}^{2}-\left (3+3 y\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	5.448
21188	25901	\begin{align*} y^{\prime }&=y+3 \,{\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	5.448
21189	27485	\begin{align*} x +\left (\cot \left (y\right ) x^{2}-3 \cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.449
21190	17312	\begin{align*} y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t} \\ \end{align*}	✓	✓	✓	✓	5.450
21191	4946	\begin{align*} \left (x -a \right ) \left (x -b \right ) y^{\prime }&=\left (x -a \right ) \left (x -b \right )+\left (2 x -a -b \right ) y \\ \end{align*}	✓	✓	✓	✓	5.452
21192	14965	\begin{align*} t^{2} x^{\prime \prime }-5 x^{\prime } t +10 x&=0 \\ x \left (1\right ) &= 2 \\ x^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.452
21193	22349	\begin{align*} y^{\prime }&=\sqrt {y} \\ \end{align*}	✓	✓	✓	✓	5.452
21194	4116	\begin{align*} \left (x +y^{2}\right ) y^{\prime }+y-x^{2}&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	5.453
21195	17296	\begin{align*} y^{\prime }-\frac {2 y}{x}&=-x^{2} y \\ \end{align*}	✓	✓	✓	✓	5.453
21196	2990	\begin{align*} y^{\prime }-y x&=\frac {x}{y} \\ \end{align*}	✓	✓	✓	✓	5.454
21197	21457	\begin{align*} y \left (6 y^{2}-x -1\right )+2 x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.454
21198	5310	\begin{align*} x \left (x +y+2 y^{3}\right ) y^{\prime }&=y \left (x -y\right ) \\ \end{align*}	✓	✓	✓	✗	5.455
21199	22523	\begin{align*} y^{\prime }&=x^{2}+2 y \\ \end{align*}	✓	✓	✓	✓	5.457
21200	14011	\begin{align*} x y^{\prime }-y+2 x^{2} y-x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	5.458