2.3.214 Problems 21301 to 21400

Table 2.971: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
21301	16757	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	7.355
21302	17122	\begin{align*} y^{\prime }&=\frac {3 y+1}{x +3} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.356
21303	14254	\begin{align*} x^{\prime }+\frac {5 x}{t}&=1+t \\ x \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.358
21304	16364	\begin{align*} x y^{3} y^{\prime }&=y^{4}-x^{2} \\ \end{align*}	✓	✓	✓	✓	7.364
21305	20242	\begin{align*} \left (x +y-1\right ) y^{\prime }&=x +y+1 \\ \end{align*}	✓	✓	✓	✓	7.368
21306	7400	\begin{align*} \frac {y^{\prime }}{\theta }&=\frac {y \sin \left (\theta \right )}{y^{2}+1} \\ y \left (\pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	7.369
21307	12110	\begin{align*} y^{\prime }&=\frac {\left (1+2 y\right ) \left (1+y\right )}{x \left (-2 y-2+x y^{3}+2 y^{4} x \right )} \\ \end{align*}	✓	✓	✓	✓	7.372
21308	1193	\begin{align*} 3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.373
21309	5845	\begin{align*} -\csc \left (x \right )^{2} y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.376
21310	11635	\begin{align*} x \left (3 \,{\mathrm e}^{y x}+2 \,{\mathrm e}^{-y x}\right ) \left (y^{\prime } x +y\right )+1&=0 \\ \end{align*}	✓	✓	✓	✓	7.377
21311	18879	\begin{align*} t^{2} y^{\prime \prime }-2 y^{\prime } t +2 y&=4 t^{2} \\ \end{align*}	✓	✓	✓	✓	7.377
21312	14483	\begin{align*} y^{\prime }+3 y&=3 x^{2} {\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	7.378
21313	4702	\begin{align*} y^{\prime }&=\left (\tan \left (x \right )+y^{3} \sec \left (x \right )\right ) y \\ \end{align*}	✓	✓	✓	✓	7.380
21314	4712	\begin{align*} y^{\prime }&=\sqrt {a +b y^{2}} \\ \end{align*}	✓	✓	✓	✓	7.381
21315	9336	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {2}{x} \\ \end{align*}	✓	✓	✓	✓	7.381
21316	10020	\begin{align*} y^{2}+\frac {2}{x}+2 y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	7.381
21317	19133	\begin{align*} y^{\prime }&=-x -\sqrt {x^{2}+2 y} \\ \end{align*}	✓	✓	✓	✓	7.382
21318	7864	\begin{align*} 1+2 y-\left (4-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.383
21319	19413	\begin{align*} y^{\prime } x +y&=y^{2} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	7.383
21320	4751	\begin{align*} y^{\prime } x +x +y&=0 \\ \end{align*}	✓	✓	✓	✓	7.384
21321	11913	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{b x}}{y \,{\mathrm e}^{-b x}+1} \\ \end{align*}	✓	✓	✓	✓	7.385
21322	17067	\begin{align*} y^{\prime }&=\frac {x}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	7.385
21323	12211	\begin{align*} y^{\prime }&=\frac {-3 x^{2} y-2 x^{3}-2 x -x y^{2}-y+x^{3} y^{3}+3 y^{2} x^{4}+3 y x^{5}+x^{6}}{x \left (x^{2}+y x +1\right )} \\ \end{align*}	✓	✓	✓	✗	7.388
21324	21975	\begin{align*} y^{\prime }&=x +y^{2} \\ \end{align*}	✓	✓	✓	✗	7.394
21325	14543	\begin{align*} 2 x +\tan \left (y\right )+\left (x -x^{2} \tan \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.395
21326	23137	\begin{align*} y^{\prime } x +y&=3 \\ \end{align*}	✓	✓	✓	✓	7.395
21327	17792	\begin{align*} x^{2} y^{\prime \prime }-7 y^{\prime } x +\left (-2 x^{2}+7\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	7.396
21328	14420	\begin{align*} y^{\prime }+4 y x&=8 x \\ \end{align*}	✓	✓	✓	✓	7.398
21329	23194	\begin{align*} -y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	7.405
21330	21997	\begin{align*} x +y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.406
21331	24956	\begin{align*} {\mathrm e}^{t} y^{\prime }&=y^{3}-y \\ \end{align*}	✓	✓	✓	✓	7.406
21332	12223	\begin{align*} y^{\prime }&=\frac {-128 y x -24 x^{3}+32 x^{2}-128 x +512 y^{3}+192 y^{2} x^{2}-384 x y^{2}+24 x^{4} y-96 x^{3} y+96 x^{2} y+x^{6}-6 x^{5}+12 x^{4}}{512 y+64 x^{2}-128 x +512} \\ \end{align*}	✓	✓	✓	✗	7.407
21333	14213	\begin{align*} y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	7.407
21334	163	\begin{align*} y^{\prime }&=\frac {x -y-1}{x +y+3} \\ \end{align*}	✓	✓	✓	✓	7.408
21335	4315	\begin{align*} x \cos \left (\frac {y}{x}\right )^{2}-y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	7.408
21336	9096	\begin{align*} y^{\prime }&=y^{2} x^{2} \\ y \left (-1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	7.409
21337	110	\begin{align*} \left (x +2 y\right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	7.419
21338	14910	\begin{align*} {\mathrm e}^{x} \sin \left (y\right )+y+\left ({\mathrm e}^{x} \cos \left (y\right )+x +{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.422
21339	26216	\begin{align*} y \ln \left (y\right )+y^{\prime } x&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.424
21340	24961	\begin{align*} y^{\prime }&=t y^{2} \\ \end{align*}	✓	✓	✓	✓	7.425
21341	24372	\begin{align*} y^{2}+\left (3 y x +y^{2}-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.426
21342	25491	\begin{align*} y^{\prime }&=t y \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	7.431
21343	17121	\begin{align*} y^{\prime }&={\mathrm e}^{2 x -y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.433
21344	12219	\begin{align*} y^{\prime }&=\frac {-32 y x +16 x^{3}+16 x^{2}-32 x -64 y^{3}+48 y^{2} x^{2}+96 x y^{2}-12 x^{4} y-48 x^{3} y-48 x^{2} y+x^{6}+6 x^{5}+12 x^{4}}{-64 y+16 x^{2}+32 x -64} \\ \end{align*}	✓	✓	✓	✓	7.434
21345	14252	\begin{align*} \theta ^{\prime }&=-a \theta +{\mathrm e}^{b t} \\ \end{align*}	✓	✓	✓	✓	7.434
21346	19177	\begin{align*} y^{\prime \prime }+\frac {y}{\ln \left (x \right ) x^{2}}&={\mathrm e}^{x} \left (\frac {2}{x}+\ln \left (x \right )\right ) \\ \end{align*}	✗	✓	✓	✗	7.435
21347	7035	\begin{align*} 3 y^{2} y^{\prime } x +y^{3}-2 x&=0 \\ \end{align*}	✓	✓	✓	✓	7.436
21348	19102	\begin{align*} \left (y^{2} x^{2}-1\right ) y^{\prime }+2 x y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	7.436
21349	12194	\begin{align*} y^{\prime }&=\frac {2 a \left (x y^{2}-4 a +x \right )}{-x^{3} y^{3}+4 a \,x^{2} y-x^{3} y+2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}} \\ \end{align*}	✓	✓	✓	✗	7.437
21350	4424	\begin{align*} x^{2}+3 \ln \left (y\right )-\frac {x y^{\prime }}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	7.438
21351	23159	\begin{align*} y^{\prime }+\frac {y}{\sin \left (x \right )}-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	7.440
21352	19918	\begin{align*} 2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	7.443
21353	5021	\begin{align*} y^{\prime } \sqrt {-x^{4}+1}&=\sqrt {1-y^{4}} \\ \end{align*}	✓	✓	✓	✓	7.444
21354	14972	\begin{align*} t^{2} x^{\prime \prime }+3 t x^{\prime }+13 x&=0 \\ x \left (1\right ) &= -1 \\ x^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	7.444
21355	22562	\begin{align*} u v-2 v+\left (-u^{2}+u \right ) v^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.447
21356	19375	\begin{align*} x^{2} y^{3}+y&=\left (x^{3} y^{2}-x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	7.448
21357	10320	\begin{align*} y^{\prime }&=\left (1+6 x +y\right )^{{1}/{4}} \\ \end{align*}	✓	✓	✓	✓	7.466
21358	3318	\begin{align*} 2 x {y^{\prime }}^{3}+1&=y {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	7.468
21359	15490	\begin{align*} y^{\prime }-2 \sqrt {{| y|}}&=0 \\ \end{align*}	✓	✓	✓	✓	7.468
21360	23176	\begin{align*} y^{\prime }&=\left (1-y\right ) \left (\frac {1}{t}-\frac {1}{10}+\frac {y}{10}\right ) \\ \end{align*}	✓	✓	✓	✓	7.469
21361	5127	\begin{align*} y y^{\prime } x&=a \,x^{3} \cos \left (x \right )+y^{2} \\ \end{align*}	✓	✓	✓	✓	7.470
21362	24224	\begin{align*} y \left (y^{2} x^{2}-m \right )+x \left (y^{2} x^{2}+n \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.471
21363	19961	\begin{align*} y y^{\prime }+b y^{2}&=a \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	7.472
21364	24167	\begin{align*} y^{2} y^{\prime }&=x \left (-y+y^{\prime } x \right ) {\mathrm e}^{\frac {x}{y}} \\ \end{align*}	✓	✓	✓	✓	7.472
21365	7467	\begin{align*} {\mathrm e}^{t} y+t \,{\mathrm e}^{t} y+\left ({\mathrm e}^{t} t +2\right ) y^{\prime }&=0 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	7.475
21366	4881	\begin{align*} x^{2} y^{\prime }&=a +b \,x^{2} y^{2} \\ \end{align*}	✓	✓	✓	✓	7.477
21367	5498	\begin{align*} x^{2} {y^{\prime }}^{2}+y^{2}-y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	7.477
21368	14721	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=-6 x^{3}+4 x^{2} \\ y \left (2\right ) &= 4 \\ y^{\prime }\left (2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	7.477
21369	12224	\begin{align*} y^{\prime }&=\frac {-32 a x y-8 a^{2} x^{3}-16 a b \,x^{2}-32 a x +64 y^{3}+48 a \,x^{2} y^{2}+96 b x y^{2}+12 a^{2} x^{4} y+48 y a \,x^{3} b +48 b^{2} x^{2} y+a^{3} x^{6}+6 a^{2} x^{5} b +12 b^{2} x^{4} a +8 b^{3} x^{3}}{64 y+16 a \,x^{2}+32 b x +64} \\ \end{align*}	✓	✓	✓	✗	7.483
21370	13759	\begin{align*} y^{\prime \prime } x +\left (x^{n} a b +b -3 n +1\right ) y^{\prime }+a^{2} n \left (b -n \right ) x^{2 n -1} y&=0 \\ \end{align*}	✗	✗	✗	✗	7.484
21371	17730	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (16 x^{2}-25\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	7.484
21372	19915	\begin{align*} y \left ({\mathrm e}^{x}+2 y x \right )-{\mathrm e}^{x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.484
21373	22374	\begin{align*} r^{\prime }&=\frac {\sin \left (t \right )+{\mathrm e}^{r} \sin \left (t \right )}{3 \,{\mathrm e}^{r}+{\mathrm e}^{r} \cos \left (2 t \right )} \\ r \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	7.484
21374	25902	\begin{align*} 3 x^{2} y+y^{3}+\left (x^{3}+3 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.484
21375	17999	\begin{align*} y&={y^{\prime }}^{2} {\mathrm e}^{y^{\prime }} \\ \end{align*}	✓	✓	✓	✓	7.486
21376	11646	\begin{align*} x \cos \left (y\right ) y^{\prime }+\sin \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	7.487
21377	12261	\begin{align*} y^{\prime }&=\frac {a^{3} x^{3} y^{3}+3 y^{2} a^{2} x^{2}+3 a x y+1+a^{2} x}{x^{3} a^{3}} \\ \end{align*}	✓	✓	✓	✓	7.488
21378	14484	\begin{align*} y^{\prime }+4 y x&=8 x \\ \end{align*}	✓	✓	✓	✓	7.490
21379	23880	\begin{align*} x^{2} y-2 x +\left (\frac {x^{3}}{3}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.490
21380	5545	\begin{align*} y {y^{\prime }}^{2}+2 a x y^{\prime }-a y&=0 \\ \end{align*}	✓	✓	✓	✓	7.491
21381	18362	\begin{align*} y^{\prime \prime }+\alpha ^{2} y&=1 \\ y^{\prime }\left (0\right ) &= \alpha \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✗	✓	7.492
21382	3052	\begin{align*} x -2 y+3&=\left (x -2 y+1\right ) y^{\prime } \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	7.493
21383	2991	\begin{align*} y^{\prime } x +y&=y^{2} x^{2} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	7.499
21384	22610	\begin{align*} y^{\prime }&=x y^{2}-2 y+4-4 x \\ \end{align*}	✓	✓	✓	✓	7.499
21385	9162	\begin{align*} y^{\prime }&=\frac {2+3 x y^{2}}{4 x^{2} y} \\ \end{align*}	✓	✓	✓	✓	7.501
21386	20574	\begin{align*} y^{\prime \prime }&=a^{2}+k^{2} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	7.506
21387	19797	\begin{align*} y^{\prime }+\sin \left (x \right ) y&=\sin \left (x \right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	7.509
21388	5483	\begin{align*} 2 x {y^{\prime }}^{2}+\left (2 x -y\right ) y^{\prime }+1-y&=0 \\ \end{align*}	✓	✓	✓	✗	7.510
21389	19738	\begin{align*} y^{\prime \prime }&=\frac {m \sqrt {1+{y^{\prime }}^{2}}}{k} \\ \end{align*}	✓	✓	✓	✗	7.513
21390	25819	\begin{align*} y^{\prime } x&=4 y \\ \end{align*}	✓	✓	✓	✓	7.514
21391	13249	\begin{align*} \left (a x +c \right ) y^{\prime }&=\alpha \left (a y+b x \right )^{2}+\beta \left (a y+b x \right )-b x +\gamma \\ \end{align*}	✓	✓	✓	✓	7.518
21392	12041	\begin{align*} y^{\prime }&=-\frac {i \left (54 i x^{2}+81 y^{4}+18 y^{2} x^{4}+x^{8}\right ) x}{243 y} \\ \end{align*}	✓	✓	✓	✗	7.519
21393	13236	\begin{align*} y^{\prime }&=a \,x^{n} y^{2}+b \,x^{m} y+c k \,x^{-1+k}-b c \,x^{m +k}-a \,c^{2} x^{n +2 k} \\ \end{align*}	✓	✗	✗	✗	7.519
21394	23233	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	7.520
21395	13226	\begin{align*} \left (a \,x^{n}+b \right ) y^{\prime }&=b y^{2}+a \,x^{-2+n} \\ \end{align*}	✓	✓	✓	✗	7.524
21396	4328	\begin{align*} 3 \left (x^{2}-1\right ) y+\left (x^{3}+8 y-3 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.527
21397	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*}	✓	✓	✓	✗	7.528
21398	25656	\begin{align*} y^{2}-1+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	7.533
21399	16227	\begin{align*} y y^{\prime }&=3 \sqrt {x y^{2}+9 x} \\ y \left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✗	7.537
21400	17312	\begin{align*} y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t} \\ \end{align*}	✓	✓	✓	✓	7.538