2.3.220 Problems 21901 to 22000

Table 2.1013: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
21901	19097	\begin{align*} \frac {y y^{\prime }+x}{\sqrt {1+x^{2}+y^{2}}}+\frac {-x y^{\prime }+y}{x^{2}+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	6.342
21902	17326	\begin{align*} t^{2} y+\sin \left (t \right )+\left (\frac {t^{3}}{3}-\cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	6.344
21903	15543	\begin{align*} y^{\prime }&=\ln \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	6.345
21904	4676	\begin{align*} y^{\prime }&=x y \left (y+3\right ) \\ \end{align*}	✓	✓	✓	✓	6.349
21905	22087	\begin{align*} y^{\prime }-2 y&=y x \\ \end{align*}	✓	✓	✓	✓	6.350
21906	4777	\begin{align*} x y^{\prime }&=a \,x^{2 n}+\left (n +b y\right ) y \\ \end{align*}	✓	✓	✓	✗	6.352
21907	4760	\begin{align*} x y^{\prime }&=a y \\ \end{align*}	✓	✓	✓	✓	6.353
21908	2964	\begin{align*} x y^{\prime }-2 x^{4}-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	6.355
21909	5612	\begin{align*} {y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	6.358
21910	15359	\begin{align*} x +2 y+1-\left (2 x -3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.358
21911	20156	\begin{align*} {y^{\prime }}^{2}-y y^{\prime \prime }&=n \sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}} \\ \end{align*}	✓	✓	✗	✗	6.359
21912	9933	\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+\left (8+5 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	6.361
21913	14518	\begin{align*} 6 x^{2} y-\left (x^{3}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.363
21914	4765	\begin{align*} x y^{\prime }&=a +b \,x^{n}+c y \\ \end{align*}	✓	✓	✓	✗	6.365
21915	13239	\begin{align*} x y^{\prime }&=a y^{2}+\left (n +b \,x^{n}\right ) y+c \,x^{2 n} \\ \end{align*}	✓	✓	✓	✗	6.365
21916	13303	\begin{align*} y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{2}+b n \,x^{n -1}-a \,b^{2} {\mathrm e}^{\lambda x} x^{2 n} \\ \end{align*}	✓	✗	✗	✗	6.365
21917	18848	\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t \le \pi \\ \pi \,{\mathrm e}^{\pi -t} & \pi <t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	6.368
21918	26408	\begin{align*} 2 x^{5}+4 x^{3} y-2 x y^{2}+\left (y^{2}+2 x^{2} y-x^{4}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.375
21919	12124	\begin{align*} y^{\prime }&=\frac {y+x^{3} \ln \left (x \right )^{3}+2 x^{3} \ln \left (x \right )^{2} y+x^{3} \ln \left (x \right ) y^{2}}{x \ln \left (x \right )} \\ \end{align*}	✓	✓	✓	✗	6.378
21920	22752	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	6.379
21921	9097	\begin{align*} \left (y+1\right ) y^{\prime }&=-x^{2}+1 \\ y \left (-1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	6.381
21922	12882	\begin{align*} y^{\prime \prime }&=a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✗	6.381
21923	3326	\begin{align*} y&=x y^{\prime }-\sqrt {y^{\prime }} \\ \end{align*}	✓	✓	✓	✓	6.382
21924	5046	\begin{align*} y y^{\prime }&=\csc \left (x \right )^{2}-y^{2} \cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	6.382
21925	4917	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=y^{2}-1 \\ \end{align*}	✓	✓	✓	✓	6.384
21926	22964	\begin{align*} y^{\prime }&=\frac {\sin \left (x \right ) \sin \left (y\right )}{\cos \left (x \right ) \cos \left (y\right )} \\ \end{align*}	✓	✓	✓	✓	6.385
21927	12134	\begin{align*} y^{\prime }&=\frac {14 y x +12+2 x +x^{3} y^{3}+6 x^{2} y^{2}}{x^{2} \left (y x +2+x \right )} \\ \end{align*}	✓	✓	✓	✓	6.387
21928	2695	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=2 \delta \left (t -1\right )-\delta \left (t -2\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	6.388
21929	14241	\begin{align*} y^{\prime }&=-y^{2} {\mathrm e}^{-t^{2}} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	6.388
21930	18480	\begin{align*} y^{\prime }&=\frac {x^{2}+{\mathrm e}^{-x}}{y^{2}-{\mathrm e}^{y}} \\ \end{align*}	✓	✓	✓	✓	6.389
21931	14219	\begin{align*} x^{\prime }&=\frac {2 x}{t +1} \\ \end{align*}	✓	✓	✓	✓	6.390
21932	12205	\begin{align*} y^{\prime }&=\frac {y^{2}+2 y x +x^{2}+{\mathrm e}^{2 \left (x -y\right )^{2} \left (x +y\right )^{2}}}{y^{2}+2 y x +x^{2}-{\mathrm e}^{2 \left (x -y\right )^{2} \left (x +y\right )^{2}}} \\ \end{align*}	✓	✓	✓	✗	6.392
21933	23119	\begin{align*} y^{\prime }&=-\frac {x^{2}+y^{2}}{2 y x} \\ \end{align*}	✓	✓	✓	✓	6.395
21934	4785	\begin{align*} x y^{\prime }&=x^{3}+\left (2 x^{2}+1\right ) y+x y^{2} \\ \end{align*}	✓	✓	✓	✓	6.405
21935	21799	\begin{align*} r^{\prime } \sin \left (t \right )+r \cos \left (t \right )&=0 \\ \end{align*}	✓	✓	✓	✓	6.407
21936	3778	\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=\frac {x^{2}}{\ln \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	6.408
21937	14179	\begin{align*} y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	6.408
21938	4717	\begin{align*} y^{\prime }&=a +b \cos \left (y\right ) \\ \end{align*}	✓	✓	✓	✗	6.410
21939	20103	\begin{align*} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	6.410
21940	17113	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{t}}{1+y} \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	6.411
21941	13213	\begin{align*} y^{\prime }&=a \,x^{n} y^{2}+b \,x^{-n -2} \\ \end{align*}	✓	✓	✓	✗	6.412
21942	21802	\begin{align*} r^{\prime }&=r \tan \left (t \right ) \\ r \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	6.412
21943	25020	\begin{align*} y^{\prime }&=\frac {1}{2 t -2 y+1} \\ \end{align*}	✓	✓	✓	✓	6.412
21944	741	\begin{align*} x y^{\prime }&=y+\sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	6.413
21945	1174	\begin{align*} y^{\prime }&=-\frac {4 t}{y} \\ \end{align*}	✓	✓	✓	✓	6.415
21946	13012	\begin{align*} y^{3} y^{\prime \prime }-a&=0 \\ \end{align*}	✓	✓	✓	✓	6.415
21947	8779	\begin{align*} y^{\prime }&=\frac {3 x^{2}+4 x +2}{-2+2 y} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	6.419
21948	4354	\begin{align*} y \left (1+y^{2}\right )+x \left (y^{2}-x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.421
21949	6384	\begin{align*} 2 y^{\prime }+a \,x^{2} {y^{\prime }}^{2}+x y^{\prime \prime }&=b \\ \end{align*}	✓	✓	✓	✗	6.421
21950	7924	\begin{align*} x y^{\prime }+y-x^{3} y^{6}&=0 \\ \end{align*}	✓	✓	✓	✓	6.421
21951	26236	\begin{align*} a^{2}+y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime }&=0 \\ y \left (a \right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	6.431
21952	5480	\begin{align*} \left (x +1\right ) {y^{\prime }}^{2}&=y \\ \end{align*}	✓	✓	✓	✓	6.433
21953	6840	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\ \end{align*}	✓	✓	✓	✓	6.433
21954	7414	\begin{align*} y^{\prime }&=x y^{3} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	6.434
21955	22422	\begin{align*} y^{\prime }&=\frac {2 x -\sin \left (y\right )}{x \cos \left (y\right )} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	6.437
21956	3663	\begin{align*} y^{\prime }+\frac {6 y}{x}&=\frac {3 y^{{2}/{3}} \cos \left (x \right )}{x} \\ \end{align*}	✓	✓	✓	✓	6.441
21957	17931	\begin{align*} x^{2}-x y^{\prime }&=y \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	6.442
21958	24227	\begin{align*} y \left (x^{3} y^{3}+2 x^{2}-y\right )+x^{3} \left (x y^{3}-2\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	6.442
21959	19710	\begin{align*} v^{\prime }+\frac {2 v}{u}&=3 \\ \end{align*}	✓	✓	✓	✓	6.443
21960	14226	\begin{align*} x^{\prime }&=\left (4 t -x\right )^{2} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	6.445
21961	1693	\begin{align*} {\mathrm e}^{x} \left (x^{2} y^{2}+2 x y^{2}\right )+6 x +\left (2 x^{2} y \,{\mathrm e}^{x}+2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	6.449
21962	5539	\begin{align*} 4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9&=0 \\ \end{align*}	✓	✓	✓	✗	6.449
21963	25298	\begin{align*} y^{\prime }-4 y&=\left \{\begin {array}{cc} 12 \,{\mathrm e}^{t} & 0\le t <1 \\ 12 \,{\mathrm e} & 1\le t \end {array}\right . \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	6.450
21964	24832	\begin{align*} {y^{\prime }}^{2}+x y^{2} y^{\prime }+y^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	6.451
21965	22583	\begin{align*} r^{3} r^{\prime }&=\sqrt {a^{8}-r^{8}} \\ \end{align*}	✓	✓	✓	✓	6.455
21966	1676	\begin{align*} \left (y+{\mathrm e}^{x^{2}}\right ) y^{\prime }&=2 x \left (y^{2}+y \,{\mathrm e}^{x^{2}}+{\mathrm e}^{2 x^{2}}\right ) \\ \end{align*}	✓	✓	✓	✗	6.457
21967	2950	\begin{align*} 2 x^{2} y y^{\prime }+{\mathrm e}^{x} x^{4}-2 x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	6.457
21968	23354	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 2 \\ \end{align*}	✓	✗	✗	✗	6.459
21969	15492	\begin{align*} y^{\prime }-y^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	6.461
21970	21620	\begin{align*} y^{\prime \prime }+\omega ^{2} y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= v \\ \end{align*}	✓	✓	✓	✓	6.464
21971	26906	\begin{align*} x y^{\prime }&=x \cos \left (\frac {y}{x}\right )+y \\ \end{align*}	✓	✓	✓	✓	6.464
21972	12116	\begin{align*} y^{\prime }&=\frac {\left (x^{4}+3 x y^{2}+3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x \left (x +1\right )} \\ \end{align*}	✗	✓	✓	✗	6.465
21973	12466	\begin{align*} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-v \left (v -1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	6.466
21974	2340	\begin{align*} \frac {y^{2}}{2}-2 \,{\mathrm e}^{t} y+\left (-{\mathrm e}^{t}+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.467
21975	5751	\begin{align*} \left (a +b \cos \left (2 x \right )\right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	6.467
21976	4326	\begin{align*} 2 x^{2}-x y^{2}-2 y+3-\left (x^{2} y+2 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	6.470
21977	4916	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=1-y^{2} \\ \end{align*}	✓	✓	✓	✓	6.471
21978	26174	\begin{align*} y^{\prime }&=x^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✗	6.471
21979	14486	\begin{align*} \left (u^{2}+1\right ) v^{\prime }+4 u v&=3 u \\ \end{align*}	✓	✓	✓	✓	6.472
21980	15317	\begin{align*} y^{\prime \prime }-\alpha ^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	6.472
21981	27333	\begin{align*} x^{2}-y+x \left (y+1\right ) y^{\prime }&=0 \\ \end{align*}	✗	✓	✗	✗	6.477
21982	13463	\begin{align*} y^{\prime }&=f \left (x \right ) y^{2}+\lambda y+a^{2} {\mathrm e}^{2 \lambda x} f \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	6.479
21983	4852	\begin{align*} 2 x y^{\prime }&=y \left (1+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	6.481
21984	20226	\begin{align*} x \cos \left (y\right )^{2}&=y \cos \left (x \right )^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✗	6.483
21985	26264	\begin{align*} \left (y^{4}-3 x^{2}\right ) y^{\prime }&=-y x \\ \end{align*}	✓	✓	✓	✗	6.483
21986	2967	\begin{align*} x y^{\prime }&=5 y+x +1 \\ \end{align*}	✓	✓	✓	✓	6.484
21987	4761	\begin{align*} x y^{\prime }&=-a y \\ \end{align*}	✓	✓	✓	✓	6.484
21988	23959	\begin{align*} x y y^{\prime }+2 x +\frac {y^{2}}{2}&=0 \\ \end{align*}	✓	✓	✓	✓	6.486
21989	20299	\begin{align*} \left (x +y\right )^{2} y^{\prime }&=a^{2} \\ \end{align*}	✓	✓	✓	✓	6.488
21990	6274	\begin{align*} B y+\left (-x +a \right ) \left (-x +b \right ) \left (A +2 x \right ) y^{\prime }+\left (-x +a \right )^{2} \left (-x +b \right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	6.490
21991	27326	\begin{align*} \left (2 x^{2} y^{3}-1\right ) y+\left (4 x^{2} y^{3}-1\right ) x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	6.493
21992	1636	\begin{align*} y^{\prime }-y x&=x y^{{3}/{2}} \\ y \left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✗	6.500
21993	22531	\begin{align*} \sin \left (x \right ) y^{\prime }&=\cos \left (x \right ) y+\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	6.500
21994	12046	\begin{align*} y^{\prime }&=\frac {\left (-x \ln \left (y\right )-\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )} \\ \end{align*}	✗	✓	✓	✓	6.505
21995	15339	\begin{align*} y-a +x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.507
21996	17243	\begin{align*} 5 y t +4 y^{2}+1+\left (t^{2}+2 y t \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	6.514
21997	4780	\begin{align*} x y^{\prime }+a +x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	6.516
21998	6968	\begin{align*} y^{\prime }-\frac {2 x y}{x^{2}+1}&=1 \\ \end{align*}	✓	✓	✓	✓	6.516
21999	4964	\begin{align*} \left (b \,x^{2}+a \right ) y^{\prime }&=c x y \ln \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	6.520
22000	11922	\begin{align*} y^{\prime }&=\left (-\ln \left (\ln \left (y\right )\right )+\ln \left (x \right )\right )^{2} y \\ \end{align*}	✗	✓	✓	✗	6.520