2.3.221 Problems 22001 to 22100

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

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
22001	14907	\begin{align*} 2 y x -\sec \left (x \right )^{2}+\left (x^{2}+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.291
22002	4394	\begin{align*} 2 y^{\prime } x -y&=\ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	5.293
22003	15839	\begin{align*} y^{\prime }&=t -y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	5.294
22004	25744	\begin{align*} \left (-2+2 y\right ) y^{\prime }&=2 x -1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	5.294
22005	17926	\begin{align*} 2 x \left (x -y^{2}\right ) y^{\prime }+y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	5.296
22006	4814	\begin{align*} y^{\prime } x&=-x \cos \left (\frac {y}{x}\right )^{2}+y \\ \end{align*}	✓	✓	✓	✗	5.297
22007	25503	\begin{align*} y^{\prime }&=t y^{3} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.298
22008	3470	\begin{align*} x \left (1-2 x^{2} y\right ) y^{\prime }+y&=3 y^{2} x^{2} \\ y \left (1\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	5.303
22009	18626	\begin{align*} x^{\prime }&=\frac {2 x y +x^{2}}{3 y^{2}+2 x y} \\ \end{align*}	✓	✓	✓	✗	5.309
22010	9802	\begin{align*} 4 y {y^{\prime }}^{2} y^{\prime \prime }&=3+{y^{\prime }}^{4} \\ \end{align*}	✓	✓	✓	✗	5.312
22011	12330	\begin{align*} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x +\operatorname {c1} \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	5.312
22012	13661	\begin{align*} y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{3}+3 a b \,{\mathrm e}^{x \left (\lambda +\mu \right )} y^{2}-2 a \,b^{3} {\mathrm e}^{\left (\lambda +3 \mu \right ) x}-{\mathrm e}^{\mu x} b \mu \\ \end{align*}	✓	✓	✓	✗	5.313
22013	12190	\begin{align*} y^{\prime }&=\frac {-2 x -y+1+y^{2} x^{2}+2 x^{3} y+x^{4}+x^{3} y^{3}+3 x^{4} y^{2}+3 x^{5} y+x^{6}}{x} \\ \end{align*}	✓	✓	✓	✗	5.314
22014	13973	\begin{align*} \left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.314
22015	14224	\begin{align*} \left (t +1\right ) x^{\prime }+x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.314
22016	9020	\begin{align*} y^{\prime }&=\frac {x +y+1}{2 x +2 y-1} \\ \end{align*}	✓	✓	✓	✓	5.319
22017	23916	\begin{align*} y^{\prime }-4 y&=x y^{3} \\ \end{align*}	✓	✓	✓	✓	5.319
22018	5074	\begin{align*} \left (a +b x +y\right ) y^{\prime }+a -b x -y&=0 \\ \end{align*}	✓	✓	✓	✓	5.322
22019	14505	\begin{align*} y^{\prime }+\frac {y}{2 x}&=\frac {x}{y^{3}} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.325
22020	15556	\begin{align*} y^{\prime }&=\sqrt {\frac {y-4}{x}} \\ \end{align*}	✓	✓	✓	✓	5.326
22021	2690	\begin{align*} y^{\prime \prime }+y^{\prime }+7 y&=\left \{\begin {array}{cc} t & 0\le t <2 \\ 0 & 2\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	5.327
22022	20267	\begin{align*} x \cos \left (x \right ) y^{\prime }+y \left (x \sin \left (x \right )+\cos \left (x \right )\right )&=1 \\ \end{align*}	✓	✓	✓	✓	5.332
22023	4652	\begin{align*} y^{\prime }&=x^{2}-y^{2} \\ \end{align*}	✓	✓	✓	✗	5.334
22024	22546	\begin{align*} s^{\prime }&=\sqrt {\frac {1-t}{1-s}} \\ s \left (1\right ) &= 0 \\ \end{align*}	✓	✗	✓	✓	5.336
22025	25797	\begin{align*} y^{\prime }&=1-\frac {y}{x} \\ y \left (-\frac {1}{2}\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.337
22026	4681	\begin{align*} y^{\prime }&=x^{n} \left (a +b y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	5.339
22027	19409	\begin{align*} 3 x^{2} {\mathrm e}^{y}-2 x +\left (x^{3} {\mathrm e}^{y}-\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.341
22028	25798	\begin{align*} y^{\prime }&=1-\frac {y}{x} \\ y \left (\frac {3}{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.346
22029	4838	\begin{align*} \left (x +1\right ) y^{\prime }+y+\left (x +1\right )^{4} y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	5.348
22030	9663	\begin{align*} x^{\prime }&=3 x-7 y+4 \sin \left (t \right )+\left (t -4\right ) {\mathrm e}^{4 t} \\ y^{\prime }&=x+y+8 \sin \left (t \right )+\left (2 t +1\right ) {\mathrm e}^{4 t} \\ \end{align*}	✓	✓	✓	✓	5.349
22031	2973	\begin{align*} \sin \left (\theta \right ) r^{\prime }+1+r \tan \left (\theta \right )&=\cos \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	5.355
22032	6904	\begin{align*} {\mathrm e}^{\frac {y}{x}} x -\sin \left (\frac {y}{x}\right ) y+x \sin \left (\frac {y}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.356
22033	19681	\begin{align*} x^{\prime }+2 t x+t x^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	5.359
22034	4398	\begin{align*} y^{\prime } x&=y-{\mathrm e}^{\frac {y}{x}} x \\ \end{align*}	✓	✓	✓	✗	5.361
22035	14230	\begin{align*} x^{\prime }&={\mathrm e}^{t +x} \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.367
22036	22009	\begin{align*} y^{\prime }&=\frac {2 y^{4}+x^{4}}{x y^{3}} \\ \end{align*}	✓	✓	✓	✓	5.367
22037	23969	\begin{align*} y^{\prime }+\frac {3 y}{2}&=x^{4} \\ \end{align*}	✓	✓	✓	✓	5.379
22038	7551	\begin{align*} y^{\prime }&=\frac {x -y-1}{x +y+5} \\ \end{align*}	✓	✓	✓	✓	5.386
22039	7924	\begin{align*} y^{\prime } x +y-x^{3} y^{6}&=0 \\ \end{align*}	✓	✓	✓	✓	5.390
22040	19675	\begin{align*} x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t}&=2 t \\ \end{align*}	✓	✓	✓	✓	5.391
22041	19890	\begin{align*} z^{\prime }+7 y-9 z&={\mathrm e}^{x} \\ y^{\prime }-y-3 z&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	5.391
22042	21322	\begin{align*} x^{\prime \prime }+4 x^{3}&=0 \\ x \left (0\right ) &= 0 \\ x \left (b \right ) &= 1 \\ \end{align*}	✗	✓	✗	✗	5.397
22043	5147	\begin{align*} x \left (x -y\right ) y^{\prime }+2 x^{2}+3 y x -y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.401
22044	14219	\begin{align*} x^{\prime }&=\frac {2 x}{t +1} \\ \end{align*}	✓	✓	✓	✓	5.404
22045	23853	\begin{align*} y^{3}+y^{\prime } \sqrt {-x^{2}+1}&=0 \\ \end{align*}	✓	✓	✓	✓	5.404
22046	25050	\begin{align*} y^{\prime }&=\frac {t -y}{t +y} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	5.406
22047	19068	\begin{align*} y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	5.407
22048	7412	\begin{align*} y^{\prime }&=\left (x -3\right ) \left (1+y\right )^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✓	5.408
22049	24137	\begin{align*} \cos \left (y\right )&=y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	5.408
22050	4289	\begin{align*} y^{2}-3 y x -2 x^{2}&=\left (x^{2}-y x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	5.410
22051	5490	\begin{align*} 4 x {y^{\prime }}^{2}+4 y^{\prime } y&=1 \\ \end{align*}	✓	✓	✓	✗	5.410
22052	4808	\begin{align*} y^{\prime } x&=y+x \sqrt {y^{2}+x^{2}} \\ \end{align*}	✗	✓	✓	✗	5.414
22053	11524	\begin{align*} \left (4 y-3 x -5\right ) y^{\prime }-3 y+7 x +2&=0 \\ \end{align*}	✓	✓	✓	✓	5.414
22054	22489	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	5.418
22055	19978	\begin{align*} 4 y&={y^{\prime }}^{2}+x^{2} \\ \end{align*}	✓	✓	✓	✗	5.419
22056	17874	\begin{align*} y^{\prime }&=2 y-2 x^{2}-3 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.420
22057	10316	\begin{align*} {y^{\prime }}^{4}&=\frac {1}{x y^{3}} \\ \end{align*}	✓	✓	✓	✗	5.421
22058	19682	\begin{align*} t x^{\prime }+x \ln \left (t \right )&=t^{2} \\ \end{align*}	✓	✓	✓	✓	5.421
22059	13451	\begin{align*} y^{\prime }&=f \left (x \right )+x f \left (x \right ) y+y^{2} \\ \end{align*}	✓	✓	✓	✗	5.423
22060	4400	\begin{align*} 2 \sqrt {y x}-y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	5.424
22061	17961	\begin{align*} y^{\prime }-y \cos \left (x \right )&=y^{2} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.424
22062	24123	\begin{align*} 2 y-3 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	5.424
22063	21799	\begin{align*} r^{\prime } \sin \left (t \right )+r \cos \left (t \right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.425
22064	24397	\begin{align*} 4 y+3 \left (2 x -1\right ) \left (y^{\prime }+y^{4}\right )&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.425
22065	15562	\begin{align*} y^{\prime }&=y x +\frac {1}{x^{2}+1} \\ y \left (-5\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.428
22066	19991	\begin{align*} y^{\prime }+2 y x&=y^{2}+x^{2} \\ \end{align*}	✓	✓	✓	✓	5.429
22067	24295	\begin{align*} y&=\left (2 x +1\right ) \left (1-y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	5.430
22068	13644	\begin{align*} y^{\prime }&=a y^{3} x +2 a b \,x^{2} y^{2}-b -2 a \,b^{3} x^{4} \\ \end{align*}	✗	✗	✗	✗	5.435
22069	20736	\begin{align*} \sin \left (y^{\prime } x \right ) \cos \left (y\right )&=\cos \left (y^{\prime } x \right ) \sin \left (y\right )+y^{\prime } \\ \end{align*}	✓	✓	✓	✗	5.439
22070	4945	\begin{align*} \left (x -a \right ) \left (-b +x \right ) y^{\prime }+k y&=0 \\ \end{align*}	✓	✓	✓	✓	5.441
22071	11306	\begin{align*} y^{\prime }+2 y x -x \,{\mathrm e}^{-x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	5.441
22072	19122	\begin{align*} y&=x {y^{\prime }}^{2}+{y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	5.441
22073	1707	\begin{align*} y^{\prime }+\frac {2 y}{x}&=-\frac {2 x y}{x^{2}+2 x^{2} y+1} \\ y \left (1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✗	5.444
22074	2329	\begin{align*} t y^{\prime }&=y+\sqrt {t^{2}+y^{2}} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.444
22075	19741	\begin{align*} n^{\prime }&=\left (n^{2}+1\right ) x \\ \end{align*}	✓	✓	✓	✓	5.446
22076	25484	\begin{align*} y^{\prime }&=a y-y^{3} \\ \end{align*}	✓	✓	✓	✓	5.449
22077	8697	\begin{align*} -y+y^{\prime } x&=\tan \left (\frac {y}{x}\right ) x \\ \end{align*}	✓	✓	✓	✓	5.450
22078	18545	\begin{align*} y \ln \left (t \right )+\left (t -3\right ) y^{\prime }&=2 t \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	5.450
22079	4849	\begin{align*} \left (a -x \right ) y^{\prime }&=y+\left (c x +b \right ) y^{3} \\ \end{align*}	✓	✓	✓	✓	5.451
22080	5221	\begin{align*} \left (3 x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✗	5.451
22081	11974	\begin{align*} y^{\prime }&=\frac {-\sin \left (2 y\right )+\cos \left (2 y\right ) x^{3}+x^{3}}{2 x} \\ \end{align*}	✓	✓	✓	✗	5.454
22082	8379	\begin{align*} y^{\prime } x&=y^{2}-y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	5.456
22083	11520	\begin{align*} \left (-x +2 y\right ) y^{\prime }-y-2 x&=0 \\ \end{align*}	✓	✓	✓	✓	5.458
22084	17069	\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.461
22085	8722	\begin{align*} y^{\prime }&=\frac {x +y-2}{y-x -4} \\ \end{align*}	✓	✓	✓	✓	5.463
22086	5120	\begin{align*} \left (a x +b y\right ) y^{\prime }&=b x +a y \\ \end{align*}	✓	✓	✓	✗	5.464
22087	19806	\begin{align*} x^{3}-3 x^{2} y+5 x y^{2}-7 y^{3}+\left (y^{4}+2 y^{2}-x^{3}+5 x^{2} y-21 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.465
22088	5176	\begin{align*} a x y y^{\prime }&=y^{2}+x^{2} \\ \end{align*}	✓	✓	✓	✓	5.466
22089	7145	\begin{align*} y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-a -1}&=0 \\ \end{align*}	✓	✓	✓	✗	5.466
22090	14015	\begin{align*} x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.466
22091	17274	\begin{align*} y+\left (t +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.467
22092	5847	\begin{align*} \left (\operatorname {a0} -\operatorname {a2} \csc \left (x \right )^{2}+4 \operatorname {a1} \sin \left (x \right )^{2}\right ) y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	5.468
22093	4316	\begin{align*} y^{\prime } x&=y \left (1+\ln \left (y\right )-\ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	5.472
22094	2869	\begin{align*} \left (x^{2}-2 x -8\right ) y^{\prime }&=y^{2}+y-2 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.473
22095	9122	\begin{align*} y^{\prime } x +2&=x^{3} \left (y-1\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	5.474
22096	4432	\begin{align*} 2 y^{\prime }+x&=4 \sqrt {y} \\ \end{align*}	✓	✓	✓	✗	5.475
22097	14465	\begin{align*} 2 y x +3 y^{2}-\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.475
22098	11585	\begin{align*} \left (b \left (\beta y+x \alpha \right )^{2}-\beta \left (a x +b y\right )\right ) y^{\prime }+a \left (\beta y+x \alpha \right )^{2}-\alpha \left (a x +b y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	5.476
22099	19353	\begin{align*} \left ({\mathrm e}^{y}-2 y x \right ) y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	5.476
22100	5102	\begin{align*} \left (3+2 x +4 y\right ) y^{\prime }&=x +2 y+1 \\ \end{align*}	✓	✓	✓	✓	5.480