2.3.213 Problems 21201 to 21300

Table 2.999: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
21201	19765	\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	5.458
21202	5893	\begin{align*} -a^{2} x^{3} y-y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.460
21203	6086	\begin{align*} -\left (2-a \right ) y+a x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.461
21204	12521	\begin{align*} x \left (x -1\right ) y^{\prime \prime }+\left (\left (a +1\right ) x +b \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.461
21205	9190	\begin{align*} y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	5.462
21206	27275	\begin{align*} \left (1-2 y x \right ) y^{\prime }&=y \left (-1+y\right ) \\ \end{align*}	✓	✓	✓	✓	5.463
21207	11915	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x}}{{\mathrm e}^{-x} y+1} \\ \end{align*}	✓	✓	✓	✓	5.466
21208	22467	\begin{align*} x^{2}+y^{2}+y+\left (x^{2}+y^{2}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.468
21209	3606	\begin{align*} y^{\prime }&=y^{3} \sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.473
21210	7681	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=y x +1 \\ \end{align*}	✓	✓	✓	✓	5.473
21211	25780	\begin{align*} y^{\prime }&=\sin \left (x \right ) \cos \left (y\right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.474
21212	27418	\begin{align*} x^{2} y^{\prime }-2 y x&=3 y \\ \end{align*}	✓	✓	✓	✓	5.474
21213	12351	\begin{align*} y^{\prime \prime }-\left (\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}+\frac {\left (2 v -1\right ) g^{\prime }\left (x \right )}{g \left (x \right )}+\frac {2 h^{\prime }\left (x \right )}{h \left (x \right )}\right ) y^{\prime }+\left (\frac {h^{\prime }\left (x \right ) \left (\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}+\frac {\left (2 v -1\right ) g^{\prime }\left (x \right )}{g \left (x \right )}+\frac {2 h^{\prime }\left (x \right )}{h \left (x \right )}\right )}{h \left (x \right )}-\frac {h^{\prime \prime }\left (x \right )}{h \left (x \right )}+{g^{\prime }\left (x \right )}^{2}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	5.476
21214	3659	\begin{align*} y^{\prime }+\frac {2 y}{x}&=6 \sqrt {x^{2}+1}\, \sqrt {y} \\ \end{align*}	✓	✓	✓	✓	5.477
21215	12028	\begin{align*} y^{\prime }&=-\frac {i \left (i x +x^{4}+2 x^{2} y^{2}+y^{4}\right )}{y} \\ \end{align*}	✓	✓	✓	✗	5.479
21216	12327	\begin{align*} b y+a x y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	5.480
21217	11485	\begin{align*} x^{n} y^{\prime }+y^{2}-\left (n -1\right ) x^{n -1} y+x^{2 n -2}&=0 \\ \end{align*}	✓	✓	✓	✗	5.481
21218	12153	\begin{align*} y^{\prime }&=\frac {1+2 y}{x \left (-2+x +x y^{2}+3 x y^{3}+2 y x +2 x y^{4}\right )} \\ \end{align*}	✓	✓	✓	✓	5.482
21219	15125	\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	5.483
21220	17239	\begin{align*} y \left (2 \,{\mathrm e}^{t}+4 t \right )+3 \left ({\mathrm e}^{t}+t^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.483
21221	19990	\begin{align*} x y \left (-x y^{\prime }+y\right )&=y y^{\prime }+x \\ \end{align*}	✓	✓	✓	✓	5.485
21222	20822	\begin{align*} x +y^{2}-2 x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.487
21223	4825	\begin{align*} x y^{\prime }&=\left (1+y^{2}\right ) \left (x^{2}+\arctan \left (y\right )\right ) \\ \end{align*}	✓	✓	✓	✗	5.491
21224	9200	\begin{align*} x y^{\prime }-y&=2 x \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.492
21225	4808	\begin{align*} x y^{\prime }&=y+x \sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✗	5.493
21226	11876	\begin{align*} y^{\prime }&=\frac {F \left (y^{{3}/{2}}-\frac {3 \,{\mathrm e}^{x}}{2}\right ) {\mathrm e}^{x}}{\sqrt {y}} \\ \end{align*}	✗	✓	✓	✗	5.493
21227	21021	\begin{align*} x^{\prime }+x&=4 t \\ x \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.493
21228	15600	\begin{align*} y^{\prime }&=\frac {2 y}{x}+{\mathrm e}^{x} \\ y \left (1\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	5.497
21229	4271	\begin{align*} y^{\prime }+y&=2 x \,{\mathrm e}^{-x}+x^{2} \\ \end{align*}	✓	✓	✓	✓	5.499
21230	20574	\begin{align*} y^{\prime \prime }&=a^{2}+k^{2} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	5.499
21231	18592	\begin{align*} 3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.500
21232	27324	\begin{align*} x^{2}-y^{2}+y+x \left (-1+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.500
21233	13261	\begin{align*} \left (a \,x^{2}+b \right ) y^{\prime }+y^{2}-2 y x +\left (1-a \right ) x^{2}-b&=0 \\ \end{align*}	✓	✓	✓	✗	5.503
21234	5458	\begin{align*} {y^{\prime }}^{2} x -y y^{\prime }+a&=0 \\ \end{align*}	✓	✓	✓	✗	5.504
21235	22490	\begin{align*} y^{\prime \prime }&=\left (y+1\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	5.505
21236	5488	\begin{align*} 4 {y^{\prime }}^{2} x +2 x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	5.506
21237	1585	\begin{align*} y^{\prime }&=\left (x -1\right ) \left (-1+y\right ) \left (-2+y\right ) \\ \end{align*}	✓	✓	✓	✓	5.507
21238	19318	\begin{align*} {\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 \csc \left (y\right ) y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.507
21239	7399	\begin{align*} x^{2} y^{\prime }&=\frac {4 x^{2}-x -2}{\left (x +1\right ) \left (y+1\right )} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.508
21240	15333	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }-a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	5.508
21241	3674	\begin{align*} y^{\prime }&=\frac {y \left (\ln \left (y x \right )-1\right )}{x} \\ \end{align*}	✓	✓	✓	✓	5.510
21242	11902	\begin{align*} y^{\prime }&=\frac {6 y}{8 y^{4}+9 y^{3}+12 y^{2}+6 y-F \left (-\frac {y^{4}}{3}-\frac {y^{3}}{2}-y^{2}-y+x \right )} \\ \end{align*}	✗	✓	✓	✗	5.510
21243	25493	\begin{align*} y^{\prime }&=a \left (t \right ) y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.511
21244	3552	\begin{align*} x^{2} y^{\prime }&=y^{2}+3 y x +x^{2} \\ \end{align*}	✓	✓	✓	✓	5.512
21245	9362	\begin{align*} x^{2} y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	5.513
21246	24191	\begin{align*} 1+y^{2}+x y^{2}+\left (x^{2} y+y+2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.515
21247	22549	\begin{align*} \left (\sin \left (y\right )-x \right ) y^{\prime }&=2 x +y \\ y \left (1\right ) &= \frac {\pi }{2} \\ \end{align*}	✓	✓	✓	✗	5.516
21248	19801	\begin{align*} y^{\prime }-y \tan \left (x \right )&=y^{4} \sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.517
21249	9182	\begin{align*} y^{\prime \prime }-k^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	5.518
21250	12362	\begin{align*} x y^{\prime \prime }+y^{\prime }+\left (x +a \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	5.518
21251	19872	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	5.519
21252	1708	\begin{align*} y^{\prime }-\frac {3 y}{x}&=\frac {2 x^{4} \left (4 x^{3}-3 y\right )}{3 x^{5}+3 x^{3}+2 y} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	5.520
21253	24995	\begin{align*} y^{\prime }+a y&=t^{n} {\mathrm e}^{-a t} \\ \end{align*}	✓	✓	✓	✓	5.520
21254	14029	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y&=\arctan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.521
21255	12345	\begin{align*} b y+a \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	5.522
21256	11987	\begin{align*} y^{\prime }&=\frac {x y \ln \left (x \right )-y+2 x^{5} b +2 x^{3} a y^{2}}{\left (x \ln \left (x \right )-1\right ) x} \\ \end{align*}	✓	✓	✓	✗	5.523
21257	11452	\begin{align*} \left (x^{2}-1\right ) y^{\prime }-y x +a&=0 \\ \end{align*}	✓	✓	✓	✓	5.528
21258	20751	\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=2 x^{2} \\ \end{align*}	✓	✓	✓	✓	5.528
21259	8305	\begin{align*} y^{\prime }&=x \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.529
21260	11380	\begin{align*} y^{\prime }+f \left (x \right ) \cos \left (a y\right )+g \left (x \right ) \sin \left (a y\right )+h \left (x \right )&=0 \\ \end{align*}	✗	✗	✗	✗	5.530
21261	15395	\begin{align*} y&=x y^{\prime }+\frac {1}{y^{\prime }} \\ \end{align*}	✓	✓	✓	✗	5.531
21262	15668	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-4 y&=-3 x -\frac {3}{x} \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= -6 \\ \end{align*}	✓	✓	✓	✓	5.531
21263	14972	\begin{align*} t^{2} x^{\prime \prime }+3 x^{\prime } t +13 x&=0 \\ x \left (1\right ) &= -1 \\ x^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.534
21264	27451	\begin{align*} y^{\prime }&=\frac {x \,{\mathrm e}^{2 x}}{y}+y \\ \end{align*}	✓	✓	✓	✓	5.534
21265	6537	\begin{align*} \left (1+y^{2}\right ) y^{\prime \prime }&=\left (a +3 y\right ) {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	5.536
21266	9816	\begin{align*} {y^{\prime }}^{4}+x y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✗	✗	5.536
21267	22561	\begin{align*} u^{\prime }&=-a \left (u-100 t \right ) \\ u \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.536
21268	1243	\begin{align*} x y^{\prime }&={\mathrm e}^{\frac {y}{x}} x +y \\ \end{align*}	✓	✓	✓	✗	5.537
21269	11458	\begin{align*} \left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.537
21270	12922	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✗	5.538
21271	24825	\begin{align*} 2 {y^{\prime }}^{2} x +\left (2 x -y\right ) y^{\prime }+1-y&=0 \\ \end{align*}	✓	✓	✓	✗	5.538
21272	20235	\begin{align*} \csc \left (x \right ) \ln \left (y\right ) y^{\prime }+x^{2} y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.539
21273	1648	\begin{align*} y^{\prime }&=\frac {2 y^{2}+x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}}{2 y x} \\ \end{align*}	✓	✓	✓	✓	5.540
21274	3046	\begin{align*} x y^{\prime }+y&=x^{3} y^{6} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.540
21275	5242	\begin{align*} 3 \left (x^{2}-y^{2}\right ) y^{\prime }+3 \,{\mathrm e}^{x}+6 \left (x +1\right ) x y-2 y^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	5.540
21276	21986	\begin{align*} y^{\prime }&=y x \\ \end{align*}	✓	✓	✓	✓	5.540
21277	8397	\begin{align*} y^{\prime }&=\frac {\sin \left (\sqrt {x}\right )}{\sqrt {y}} \\ \end{align*}	✓	✓	✓	✓	5.541
21278	2842	\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.543
21279	6011	\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.543
21280	15877	\begin{align*} w^{\prime }&=\left (1-w\right ) \sin \left (w\right ) \\ \end{align*}	✓	✓	✓	✓	5.545
21281	11913	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{b x}}{y \,{\mathrm e}^{-b x}+1} \\ \end{align*}	✓	✓	✓	✓	5.546
21282	20429	\begin{align*} y&=\frac {2 a {y^{\prime }}^{2}}{\left (1+{y^{\prime }}^{2}\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	5.546
21283	8675	\begin{align*} 2 x \sqrt {1-y^{2}}+y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.548
21284	5972	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=a \,x^{2} \\ \end{align*}	✓	✓	✓	✓	5.549
21285	25844	\begin{align*} y^{\prime }+\left (-1+y\right ) \cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.549
21286	18511	\begin{align*} -2 y+y^{\prime }&={\mathrm e}^{2 t} t^{2} \\ \end{align*}	✓	✓	✓	✓	5.550
21287	26381	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=y^{n} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	5.550
21288	14187	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✓	5.557
21289	12244	\begin{align*} y^{\prime }&=-\frac {8 x \left (a -1\right ) \left (a +1\right )}{8+x^{6}+2 x^{4}-8 y+2 y^{4}-8 a^{2}-4 a^{2} x^{6}-y^{6} a^{2}-6 y^{4} a^{2} x^{2}-9 y^{2} a^{2} x^{4}+4 x^{2} y^{2}+y^{6}+4 a^{4} y^{2} x^{2}+3 x^{2} y^{4}-8 y^{2} a^{2} x^{2}+3 y^{2} x^{4}-2 y^{4} a^{2}+a^{8} x^{6}-4 a^{6} x^{6}+6 a^{4} x^{6}-6 a^{2} x^{4}+3 a^{4} y^{4} x^{2}-3 a^{6} y^{2} x^{4}+9 y^{2} a^{4} x^{4}-2 a^{6} x^{4}+6 a^{4} x^{4}} \\ \end{align*}	✓	✓	✓	✗	5.558
21290	13251	\begin{align*} 2 x^{2} y^{\prime }&=2 y^{2}+3 y x -2 a^{2} x \\ \end{align*}	✓	✓	✓	✗	5.559
21291	12679	\begin{align*} y^{\prime \prime }&=-\frac {\left (1+2 n \right ) \cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\left (v +n +1\right ) \left (v -n \right ) y \\ \end{align*}	✗	✓	✓	✗	5.560
21292	5253	\begin{align*} x \left (x^{2}+y^{2}\right ) y^{\prime }&=\left (x^{2}+x^{4}+y^{2}\right ) y \\ \end{align*}	✓	✓	✓	✗	5.562
21293	14213	\begin{align*} y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	5.562
21294	15599	\begin{align*} y^{\prime }&=\frac {y}{x}+\sin \left (x^{2}\right ) \\ y \left (-1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	5.562
21295	3022	\begin{align*} x y^{\prime }-y-\sqrt {x^{2}+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	5.563
21296	8246	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{4}\right ) &= 3 \\ \end{align*}	✓	✗	✗	✗	5.563
21297	22577	\begin{align*} r^{\prime }&={\mathrm e}^{t}-3 r \\ r \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	5.569
21298	25038	\begin{align*} y^{\prime }&=y t \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.570
21299	12271	\begin{align*} y^{\prime }&=-F \left (x \right ) \left (x^{2}+2 y x -y^{2}\right )+\frac {y}{x} \\ \end{align*}	✓	✓	✓	✗	5.571
21300	4261	\begin{align*} y x -1+\left (x^{2}-y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.572