2.3.202 Problems 20101 to 20200

Table 2.977: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
20101	11440	\begin{align*} x^{2} \left (y^{\prime }+y^{2}\right )+a x y+b&=0 \\ \end{align*}	✓	✓	✓	✓	4.416
20102	11888	\begin{align*} y^{\prime }&=-\frac {y^{2} \left (2 x -F \left (-\frac {y x -2}{2 y}\right )\right )}{4 x} \\ \end{align*}	✓	✓	✓	✗	4.416
20103	17245	\begin{align*} 2 t +\tan \left (y\right )+\left (t -t^{2} \tan \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.416
20104	11353	\begin{align*} y^{\prime }-a y^{n}-b \,x^{\frac {n}{1-n}}&=0 \\ \end{align*}	✓	✓	✓	✗	4.417
20105	14903	\begin{align*} y^{\prime }+2 y \cot \left (x \right )&=5 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.418
20106	5500	\begin{align*} {y^{\prime }}^{2} x^{2}+2 a x y^{\prime }+a^{2}+x^{2}-2 a y&=0 \\ \end{align*}	✓	✓	✓	✗	4.419
20107	13231	\begin{align*} y^{\prime }&=y^{2}+\left (\alpha x +\beta \right ) y+a \,x^{2}+b x +c \\ \end{align*}	✓	✓	✓	✗	4.419
20108	9133	\begin{align*} 1+y+\left (1-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.420
20109	16369	\begin{align*} \left (3-x +y\right )^{2} \left (y^{\prime }-1\right )&=1 \\ \end{align*}	✓	✓	✓	✓	4.420
20110	7405	\begin{align*} \sqrt {y}+\left (x +1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	4.421
20111	6972	\begin{align*} 2 y+y^{\prime }&=3 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	4.422
20112	15050	\begin{align*} x^{\prime }-x \cot \left (t \right )&=4 \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	4.422
20113	25866	\begin{align*} y^{\prime }+2 y x&={\mathrm e}^{-x^{2}}-x \\ \end{align*}	✓	✓	✓	✓	4.422
20114	18555	\begin{align*} y^{\prime }&=\frac {t^{2}+1}{3 y-y^{2}} \\ \end{align*}	✓	✓	✓	✓	4.423
20115	4815	\begin{align*} x y^{\prime }&=\left (-2 x^{2}+1\right ) \cot \left (y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.424
20116	24123	\begin{align*} 2 y-3 x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.426
20117	24918	\begin{align*} y^{\prime }&=2 y t \\ \end{align*}	✓	✓	✓	✓	4.427
20118	6934	\begin{align*} \sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\ y \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✓	4.428
20119	14700	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.428
20120	17165	\begin{align*} y^{\prime }+3 t^{2} y&={\mathrm e}^{-t^{3}} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.431
20121	25825	\begin{align*} \csc \left (y\right )+\sec \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.431
20122	24185	\begin{align*} 2 y x -3 x^{2}+\left (x^{2}+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.434
20123	799	\begin{align*} \left (2 x +1\right ) y^{\prime }+y&=\left (2 x +1\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✓	4.435
20124	12963	\begin{align*} 2 \left (y-a \right ) y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✗	4.436
20125	23838	\begin{align*} y^{\prime }&=1-\frac {y^{2}}{x} \\ \end{align*}	✓	✓	✓	✗	4.436
20126	21078	\begin{align*} x +y^{2}+B \left (x \right ) y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.437
20127	22567	\begin{align*} y^{\prime }+y \cot \left (x \right )&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.437
20128	8680	\begin{align*} z^{\prime }&=10^{x +z} \\ \end{align*}	✓	✓	✓	✓	4.438
20129	17978	\begin{align*} y \left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+x \left (-a^{2}+x^{2}+y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	4.438
20130	18726	\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.438
20131	12266	\begin{align*} y^{\prime }&=\frac {y^{3}-3 x y^{2} \ln \left (x \right )+3 x^{2} \ln \left (x \right )^{2} y-x^{3} \ln \left (x \right )^{3}+x^{2}+y x}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	4.439
20132	12376	\begin{align*} x y^{\prime \prime }-x y^{\prime }-a y&=0 \\ \end{align*}	✗	✓	✓	✗	4.439
20133	14073	\begin{align*} y&=\left (x +1\right ) {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	4.440
20134	4203	\begin{align*} \tan \left (x \right ) y^{\prime }&=y-\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.441
20135	4869	\begin{align*} x^{2} y^{\prime }&=\left (b x +a \right ) y \\ \end{align*}	✓	✓	✓	✓	4.441
20136	21356	\begin{align*} y^{\prime }&=x^{2} y \\ \end{align*}	✓	✓	✓	✓	4.442
20137	6286	\begin{align*} y+3 x^{5} y^{\prime }+x^{6} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.443
20138	11965	\begin{align*} y^{\prime }&=\frac {2 a}{x \left (-y x +2 a x y^{2}-8 a^{2}\right )} \\ \end{align*}	✓	✓	✓	✓	4.443
20139	17151	\begin{align*} y^{\prime }-\frac {3 t y}{t^{2}-4}&=t \\ \end{align*}	✓	✓	✓	✓	4.444
20140	11547	\begin{align*} \left (x^{2} y-1\right ) y^{\prime }+x y^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✗	4.445
20141	14062	\begin{align*} 4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x} y^{\prime }-{\mathrm e}^{2 x}&=0 \\ \end{align*}	✓	✓	✓	✗	4.445
20142	6450	\begin{align*} y y^{\prime \prime }&=b +a {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	4.447
20143	21375	\begin{align*} y^{\prime }&=-\frac {{\mathrm e}^{y}}{x \,{\mathrm e}^{y}+2 y} \\ \end{align*}	✓	✓	✓	✓	4.447
20144	6319	\begin{align*} y^{\prime \prime }&=f \left (x \right ) y^{2}+y^{3}+y \left (-2 f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )+\left (3 f \left (x \right )-y\right ) y^{\prime } \\ \end{align*}	✗	✓	✗	✗	4.448
20145	7543	\begin{align*} y^{\prime }+\frac {y}{x}&=-\frac {4 x}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	4.448
20146	14880	\begin{align*} x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t}&={\mathrm e}^{-t} \\ x \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	4.448
20147	13957	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+c \right ) y^{\prime }+\left (a b \,{\mathrm e}^{\left (\lambda +\mu \right ) x}+{\mathrm e}^{\lambda x} a c +b \mu \,{\mathrm e}^{\mu x}\right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	4.449
20148	18065	\begin{align*} y^{\prime }-1&={\mathrm e}^{x +2 y} \\ \end{align*}	✓	✓	✓	✓	4.449
20149	26251	\begin{align*} 2 \left (x^{2}+1\right ) y^{\prime }-\cos \left (2 y\right )^{2}&=0 \\ y \left (-\infty \right ) &= \frac {7 \pi }{2} \\ \end{align*}	✓	✓	✗	✗	4.450
20150	15054	\begin{align*} x^{2}-y+\left (x^{2} y^{2}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.453
20151	21980	\begin{align*} \sin \left (x \right )+y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.453
20152	5432	\begin{align*} {y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.454
20153	15238	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	4.454
20154	18474	\begin{align*} y^{\prime }&=\frac {x^{2} \left (x^{3}+1\right )}{y} \\ \end{align*}	✓	✓	✓	✓	4.454
20155	12919	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}-a&=0 \\ \end{align*}	✓	✓	✓	✗	4.455
20156	17350	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	4.455
20157	2306	\begin{align*} \sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.456
20158	8876	\begin{align*} y^{\prime }+2 y x&=x \\ \end{align*}	✓	✓	✓	✓	4.456
20159	11637	\begin{align*} \left (-1+2 x +\ln \left (y\right )\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.456
20160	22967	\begin{align*} {\mathrm e}^{x} \left (y^{\prime }+y\right )&=3 \\ \end{align*}	✓	✓	✓	✓	4.456
20161	24878	\begin{align*} -{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.456
20162	4599	\begin{align*} x^{2} y^{\prime \prime }-\left (x^{2}+2 x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.457
20163	4686	\begin{align*} y^{\prime }&=y \sec \left (x \right )+\left (-1+\sin \left (x \right )\right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.457
20164	20223	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-2 y x&=-x^{3}+x \\ \end{align*}	✓	✓	✓	✓	4.457
20165	19305	\begin{align*} 2 x y^{4}+\sin \left (y\right )+\left (4 x^{2} y^{3}+x \cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.458
20166	8223	\begin{align*} x y^{\prime }&=2 y \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	4.459
20167	4605	\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+2 \left (x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.460
20168	14882	\begin{align*} x^{\prime }&=x \left (2-x\right ) \\ \end{align*}	✓	✓	✓	✓	4.461
20169	15763	\begin{align*} y_{1}^{\prime }&=y_{2} \\ y_{2}^{\prime }&=-3 y_{1}+2 y_{3} \\ y_{3}^{\prime }&=y_{4} \\ y_{4}^{\prime }&=2 y_{1}-5 y_{3} \\ \end{align*}	✓	✓	✓	✓	4.463
20170	4302	\begin{align*} r y^{\prime }&=\frac {\left (a^{2}-r^{2}\right ) \tan \left (y\right )}{a^{2}+r^{2}} \\ \end{align*}	✓	✓	✓	✓	4.464
20171	11864	\begin{align*} y^{\prime }&=\frac {1+2 F \left (\frac {1+4 x^{2} y}{4 x^{2}}\right ) x}{2 x^{3}} \\ \end{align*}	✗	✓	✓	✗	4.466
20172	5838	\begin{align*} -x^{3} y+x^{4} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.467
20173	23202	\begin{align*} 5 x -y+3 x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.467
20174	2319	\begin{align*} y^{\prime }&=1-t +y^{2}-t y^{2} \\ \end{align*}	✓	✓	✓	✓	4.468
20175	5974	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+y&=3 x^{3} \\ \end{align*}	✓	✓	✓	✓	4.468
20176	8179	\begin{align*} x y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.468
20177	22136	\begin{align*} y^{\prime }-5 y&=3 \,{\mathrm e}^{x}-2 x +1 \\ \end{align*}	✓	✓	✓	✓	4.469
20178	20817	\begin{align*} s^{\prime }+2 s&=s t^{2} \\ s \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.470
20179	11408	\begin{align*} x y^{\prime }-y^{2} \ln \left (x \right )+y&=0 \\ \end{align*}	✓	✓	✓	✓	4.471
20180	21009	\begin{align*} x^{\prime }+\frac {x}{t^{2}-1}&=0 \\ x \left (-2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.472
20181	5870	\begin{align*} 3 y+2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.473
20182	9729	\begin{align*} 4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\ \end{align*}	✓	✓	✓	✓	4.473
20183	11396	\begin{align*} x y^{\prime }-y^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✓	4.477
20184	4209	\begin{align*} \sqrt {x^{2}+1}\, y^{\prime }-y&=2 \sqrt {x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	4.480
20185	5215	\begin{align*} \left (x^{2}-y^{2}\right ) y^{\prime }+x \left (x +2 y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	4.480
20186	11887	\begin{align*} y^{\prime }&=\frac {2 y^{3}}{1+2 F \left (\frac {1+4 x y^{2}}{y^{2}}\right ) y} \\ \end{align*}	✗	✓	✓	✗	4.480
20187	4614	\begin{align*} y^{\prime }&=a +b \,{\mathrm e}^{k x}+c y \\ \end{align*}	✓	✓	✓	✓	4.481
20188	19676	\begin{align*} 2 t +3 x+\left (3 t -x\right ) x^{\prime }&=t^{2} \\ \end{align*}	✓	✓	✓	✗	4.481
20189	22585	\begin{align*} x y^{\prime }+2 y-x \cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.481
20190	25645	\begin{align*} y^{\prime }&=1-y^{2} \\ \end{align*}	✓	✓	✓	✓	4.481
20191	2097	\begin{align*} 9 x^{2} y^{\prime \prime }-3 x \left (2 x^{2}+11\right ) y^{\prime }+\left (10 x^{2}+13\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	4.483
20192	18355	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y \left (2 \pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.484
20193	21480	\begin{align*} x^{\prime \prime }-4 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	4.484
20194	23916	\begin{align*} y^{\prime }-4 y&=x y^{3} \\ \end{align*}	✓	✓	✓	✓	4.484
20195	1146	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.487
20196	1222	\begin{align*} y^{\prime }&=\frac {-1-2 y x -y^{2}}{x^{2}+2 y x} \\ \end{align*}	✓	✓	✓	✗	4.487
20197	4341	\begin{align*} 2+y^{2}+2 x +2 y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.487
20198	7932	\begin{align*} 1+y^{2}&=\left (\arctan \left (y\right )-x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.487
20199	14460	\begin{align*} \csc \left (y\right )+\sec \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.488
20200	8199	\begin{align*} y^{\prime }&=\sqrt {1-y^{2}} \\ \end{align*}	✓	✓	✓	✓	4.489