2.3.229 Problems 22801 to 22900

Table 2.989: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
22801	21683	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	7.213
22802	17111	\begin{align*} y^{\prime }&=\frac {\sqrt {t}}{y} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	7.215
22803	18575	\begin{align*} {\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	7.223
22804	5287	\begin{align*} \left (1-x^{4} y^{2}\right ) y^{\prime }&=x^{3} y^{3} \\ \end{align*}	✓	✓	✓	✓	7.224
22805	21432	\begin{align*} y^{\prime }+q \left (x \right ) y&=0 \\ y \left (\textit {x\_0} \right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	7.226
22806	14532	\begin{align*} x^{2}+y^{2}-2 x y^{\prime } y&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	7.231
22807	24199	\begin{align*} 2 y x +\left (y^{2}+x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.232
22808	19094	\begin{align*} \left (x \left (x +y\right )+a^{2}\right ) y^{\prime }&=y \left (x +y\right )+b^{2} \\ \end{align*}	✓	✓	✓	✓	7.234
22809	12059	\begin{align*} y^{\prime }&=\frac {y \left (1+y\right )}{x \left (-y-1+y^{4} x \right )} \\ \end{align*}	✓	✓	✓	✓	7.238
22810	23956	\begin{align*} y^{\prime }&=\sin \left (y\right )^{3} \cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	7.239
22811	7866	\begin{align*} x +2 y+\left (2 x +3 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.242
22812	21631	\begin{align*} \left (x^{2}-4\right ) y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	7.242
22813	21728	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{4}\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	7.242
22814	13652	\begin{align*} y^{\prime } x&=a \,x^{n +2} y^{3}+\left (b \,x^{n}-1\right ) y+c \,x^{n -1} \\ \end{align*}	✓	✓	✓	✗	7.243
22815	14222	\begin{align*} R^{\prime }&=\left (t +1\right ) \left (1+R^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	7.244
22816	7871	\begin{align*} y \left (2 y x +1\right )+x \left (-y x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.259
22817	11536	\begin{align*} y^{2}-3 y x -2 x^{2}+\left (y x -x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.259
22818	2331	\begin{align*} \left (t -\sqrt {t y}\right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	7.260
22819	11622	\begin{align*} a \,x^{2} y^{n} y^{\prime }-2 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	7.263
22820	25183	\begin{align*} 3 t^{2} y^{\prime \prime }+2 t y^{\prime }+y&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✗	7.269
22821	4993	\begin{align*} x^{4} y^{\prime }+a^{2}+x^{4} y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	7.272
22822	7441	\begin{align*} \left ({\mathrm e}^{4 y}+2 x \right ) y^{\prime }-1&=0 \\ \end{align*}	✓	✓	✓	✓	7.278
22823	13455	\begin{align*} y^{\prime } x&=f \left (x \right ) y^{2}+n y+a \,x^{2 n} f \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	7.282
22824	16362	\begin{align*} x y^{\prime } y&=x^{2}+y x +y^{2} \\ \end{align*}	✓	✓	✓	✗	7.285
22825	19286	\begin{align*} y^{\prime }&=\sin \left (x -y+1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	7.287
22826	7456	\begin{align*} \cos \left (x \right ) \cos \left (y\right )+2 x -\left (\sin \left (x \right ) \sin \left (y\right )+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.289
22827	5318	\begin{align*} \left (x^{2}-y^{4}\right ) y^{\prime }&=y x \\ \end{align*}	✓	✓	✓	✓	7.290
22828	18064	\begin{align*} y \cos \left (x \right )+\left (2 y-\sin \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.294
22829	5055	\begin{align*} \left (x +y\right ) y^{\prime }&=x -y \\ \end{align*}	✓	✓	✓	✓	7.295
22830	3038	\begin{align*} y^{\prime } x -5 y-x \sqrt {y}&=0 \\ \end{align*}	✓	✓	✓	✓	7.300
22831	12188	\begin{align*} y^{\prime }&=\frac {4 x \left (a -1\right ) \left (a +1\right )}{4 y+y^{4} a^{2}-2 a^{4} y^{2} x^{2}+4 y^{2} a^{2} x^{2}+a^{6} x^{4}-3 a^{4} x^{4}+3 a^{2} x^{4}-y^{4}-2 y^{2} x^{2}-x^{4}} \\ \end{align*}	✓	✓	✓	✗	7.304
22832	24128	\begin{align*} 1&=b \left (\cos \left (y\right )+x \sin \left (y\right ) y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	7.310
22833	11328	\begin{align*} y^{\prime }-\left (A y-a \right ) \left (B y-b \right )&=0 \\ \end{align*}	✓	✓	✓	✓	7.311
22834	11886	\begin{align*} y^{\prime }&=\frac {2 F \left (y+\ln \left (2 x +1\right )\right ) x +F \left (y+\ln \left (2 x +1\right )\right )-2}{2 x +1} \\ \end{align*}	✗	✓	✓	✗	7.312
22835	17081	\begin{align*} \cosh \left (6 t \right )+5 \sinh \left (4 t \right )+20 \sinh \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.320
22836	24146	\begin{align*} x y^{2}+{\mathrm e}^{x} y^{\prime }&=0 \\ y \left (\infty \right ) &= {\frac {1}{2}} \\ \end{align*}	✗	✓	✓	✗	7.322
22837	8709	\begin{align*} y^{\prime }&=\frac {2 x y}{3 x^{2}-y^{2}} \\ \end{align*}	✓	✓	✓	✗	7.325
22838	14234	\begin{align*} y^{\prime }&=\frac {2 t y^{2}}{t^{2}+1} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	7.325
22839	19921	\begin{align*} y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.326
22840	21438	\begin{align*} y^{\prime }+\frac {y}{x}&=3 x \\ \end{align*}	✓	✓	✓	✓	7.332
22841	9059	\begin{align*} y^{\prime }&=\frac {y^{2}}{y x -x^{2}} \\ \end{align*}	✓	✓	✓	✓	7.336
22842	5052	\begin{align*} \left (x +y\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	7.340
22843	24800	\begin{align*} {y^{\prime }}^{3}+x {y^{\prime }}^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✗	7.348
22844	13553	\begin{align*} y^{\prime } y-y&=a^{2} f^{\prime }\left (x \right ) f^{\prime \prime }\left (x \right )-\frac {\left (f \left (x \right )+b \right )^{2} f^{\prime \prime }\left (x \right )}{{f^{\prime }\left (x \right )}^{3}} \\ \end{align*}	✗	✗	✗	✗	7.352
22845	21680	\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	7.356
22846	22413	\begin{align*} y^{\prime }&=\frac {x}{x +y} \\ \end{align*}	✓	✓	✓	✗	7.357
22847	7489	\begin{align*} 2 t x x^{\prime }+t^{2}-x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	7.367
22848	20979	\begin{align*} \left (y x +1\right ) y&=y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	7.368
22849	12149	\begin{align*} y^{\prime }&=\frac {-x +1-2 y+3 x^{2}-2 x^{2} y+2 x^{4}+x^{3}-2 x^{3} y+2 x^{5}}{x^{2}-y} \\ \end{align*}	✓	✓	✓	✗	7.385
22850	12879	\begin{align*} y^{\prime \prime }&=a \sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✓	7.387
22851	14240	\begin{align*} y^{\prime }&=\frac {y^{2}+2 t y}{t^{2}} \\ \end{align*}	✓	✓	✓	✓	7.387
22852	14466	\begin{align*} v^{3}+\left (u^{3}-u v^{2}\right ) v^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.390
22853	17152	\begin{align*} y^{\prime }-\frac {4 t y}{4 t^{2}-9}&=t \\ \end{align*}	✓	✓	✓	✓	7.391
22854	18551	\begin{align*} y^{\prime }&=\frac {t -y}{2 t +5 y} \\ \end{align*}	✓	✓	✓	✗	7.395
22855	24402	\begin{align*} 2 x -3 y+1-\left (3 x +2 y-4\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.396
22856	11949	\begin{align*} y^{\prime }&=\left (-\ln \left (y\right )+1+x^{2}+x^{3}\right ) y \\ \end{align*}	✓	✓	✓	✓	7.398
22857	11487	\begin{align*} x^{2 n +1} y^{\prime }-a y^{3}-b \,x^{3 n}&=0 \\ \end{align*}	✓	✓	✓	✗	7.401
22858	24228	\begin{align*} y \left (2-3 y x \right )-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	7.410
22859	13761	\begin{align*} y^{\prime \prime } x +\left (a \,x^{n}+b \,x^{n -1}+2\right ) y^{\prime }+b \,x^{-2+n} y&=0 \\ \end{align*}	✗	✓	✗	✗	7.415
22860	13646	\begin{align*} y^{\prime }&=a \,x^{n} y^{3}+3 a b \,x^{n +m} y^{2}-b m \,x^{m -1}-2 a \,b^{3} x^{n +3 m} \\ \end{align*}	✓	✓	✓	✗	7.417
22861	21341	\begin{align*} y^{\prime }&=-\frac {x}{y} \\ \end{align*}	✓	✓	✓	✓	7.417
22862	23879	\begin{align*} y^{\prime }&=\frac {4 x -3 y-17}{3 x +y-3} \\ \end{align*}	✓	✓	✓	✓	7.420
22863	14016	\begin{align*} y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	7.421
22864	17224	\begin{align*} -\frac {y^{2} {\mathrm e}^{\frac {y}{t}}}{t^{2}}+1+{\mathrm e}^{\frac {y}{t}} \left (1+\frac {y}{t}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.421
22865	7870	\begin{align*} y^{2}-x^{2}+x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	7.424
22866	15593	\begin{align*} y^{\prime }&=-\frac {y \left (2 x +y\right )}{x \left (x +2 y\right )} \\ \end{align*}	✓	✓	✓	✓	7.425
22867	20574	\begin{align*} y^{\prime \prime }&=a^{2}+k^{2} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	7.435
22868	3323	\begin{align*} 2 y&=3 y^{\prime } x +4+2 \ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✗	7.436
22869	1623	\begin{align*} y^{\prime }&=3 x \left (y-1\right )^{{1}/{3}} \\ y \left (0\right ) &= 9 \\ \end{align*}	✓	✓	✓	✗	7.437
22870	17671	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=0 \\ y \left (-1\right ) &= 0 \\ y^{\prime }\left (-1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	7.443
22871	11874	\begin{align*} y^{\prime }&=\frac {F \left (\frac {a y^{2}+b \,x^{2}}{a}\right ) x}{\sqrt {a}\, y} \\ \end{align*}	✗	✓	✓	✗	7.451
22872	12858	\begin{align*} y^{\prime \prime }+3 a y^{\prime }-2 y^{3}+2 a^{2} y&=0 \\ \end{align*}	✗	✓	✓	✗	7.452
22873	8674	\begin{align*} \frac {1}{\sqrt {-x^{2}+1}}+\frac {y^{\prime }}{\sqrt {1-y^{2}}}&=0 \\ \end{align*}	✓	✓	✓	✓	7.463
22874	13629	\begin{align*} \left (A x y+B \,x^{2}+\left (-1+k \right ) A a y-\left (A b k +B a \right ) x \right ) y^{\prime }&=A y^{2}+B y x -\left (B a k +A b \right ) y+\left (-1+k \right ) B b x \\ \end{align*}	✓	✓	✓	✗	7.464
22875	22343	\begin{align*} y^{\prime }&=\frac {x -2 y}{y-2 x} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✗	✗	7.465
22876	11850	\begin{align*} \ln \left (y^{\prime }\right )+a \left (-y+y^{\prime } x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	7.471
22877	11662	\begin{align*} {y^{\prime }}^{2}-y^{3}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	7.473
22878	8776	\begin{align*} \left (-\sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-2 \sin \left (x \right ) y^{\prime }+\left (\cos \left (x \right )+\sin \left (x \right )\right ) y&=\left (-\sin \left (x \right )+\cos \left (x \right )\right )^{2} \\ \end{align*}	✗	✓	✓	✗	7.480
22879	11654	\begin{align*} \left (x \sin \left (y x \right )+\cos \left (x +y\right )-\sin \left (y\right )\right ) y^{\prime }+y \sin \left (y x \right )+\cos \left (x +y\right )+\cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	7.480
22880	12242	\begin{align*} y^{\prime }&=\frac {4 x \left (a -1\right ) \left (a +1\right ) \left (-y^{2}+a^{2} x^{2}-x^{2}-2\right )}{-4 y^{3}+4 y a^{2} x^{2}-4 x^{2} y-8 y-y^{6} a^{2}+3 a^{4} y^{4} x^{2}-6 y^{4} a^{2} x^{2}-3 a^{6} y^{2} x^{4}+9 y^{2} a^{4} x^{4}-9 y^{2} a^{2} x^{4}+a^{8} x^{6}-4 a^{6} x^{6}+6 a^{4} x^{6}-4 a^{2} x^{6}+y^{6}+3 x^{2} y^{4}+3 x^{4} y^{2}+x^{6}} \\ \end{align*}	✓	✓	✓	✗	7.486
22881	3048	\begin{align*} y^{2}+x^{2}&=2 x y^{\prime } y \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	7.489
22882	8732	\begin{align*} \left (1+y^{\prime }\right ) \ln \left (\frac {x +y}{x +3}\right )&=\frac {x +y}{x +3} \\ \end{align*}	✓	✓	✓	✓	7.491
22883	3052	\begin{align*} x -2 y+3&=\left (x -2 y+1\right ) y^{\prime } \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	7.493
22884	2868	\begin{align*} \left (x^{2}+x +1\right ) y^{\prime }&=y^{2}+2 y+5 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.496
22885	25037	\begin{align*} a t +b y-\left (c t +d y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.496
22886	7859	\begin{align*} x y^{2}+y+\left (x^{2} y-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.497
22887	6037	\begin{align*} -y+x \left (x +3\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✓	7.498
22888	20589	\begin{align*} y^{\prime \prime }&={\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✓	7.499
22889	4726	\begin{align*} y^{\prime }&=\tan \left (x \right ) \left (\tan \left (y\right )+\sec \left (x \right ) \sec \left (y\right )\right ) \\ \end{align*}	✗	✓	✓	✓	7.500
22890	19895	\begin{align*} y^{\prime \prime }-k^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	7.502
22891	11885	\begin{align*} y^{\prime }&=\frac {y^{2} \left (2+F \left (\frac {x^{2}-y}{y x^{2}}\right ) x^{2}\right )}{x^{3}} \\ \end{align*}	✗	✓	✓	✗	7.505
22892	24328	\begin{align*} y+x \left (3 y x -2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.511
22893	2685	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	7.513
22894	13639	\begin{align*} y^{\prime }&=-y^{3}+\left (a x +b \right ) y^{2} \\ \end{align*}	✗	✓	✓	✗	7.514
22895	11653	\begin{align*} y^{\prime } \cos \left (a y\right )-b \left (1-c \cos \left (a y\right )\right ) \sqrt {\cos \left (a y\right )^{2}-1+c \cos \left (a y\right )}&=0 \\ \end{align*}	✓	✓	✓	✗	7.526
22896	24285	\begin{align*} x -y-\left (x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.528
22897	19384	\begin{align*} \cos \left (x +y\right )&=x \sin \left (x +y\right )+x \sin \left (x +y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	7.529
22898	682	\begin{align*} y^{\prime }&=3 \sqrt {y x} \\ \end{align*}	✓	✓	✓	✓	7.533
22899	24319	\begin{align*} y^{\prime }&=y-x y^{3} {\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	7.534
22900	20292	\begin{align*} x^{2}+y^{2}-2 x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	7.537