2.3.214 Problems 21301 to 21400

Table 2.959: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
21301	22411	\begin{align*} y^{\prime }&=\frac {x -y}{x +y} \\ \end{align*}	✓	✓	✓	✓	4.292
21302	14494	\begin{align*} y \sin \left (2 x \right )-\cos \left (x \right )+\left (1+\sin \left (x \right )^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.293
21303	23970	\begin{align*} y^{\prime }-5 y&=3 x^{3}+4 x \\ \end{align*}	✓	✓	✓	✓	4.293
21304	738	\begin{align*} x y^{\prime } y&=x^{2}+3 y^{2} \\ \end{align*}	✓	✓	✓	✓	4.296
21305	9721	\begin{align*} \left (4 x -y\right ) {y^{\prime }}^{2}+6 \left (x -y\right ) y^{\prime }+2 x -5 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.296
21306	25826	\begin{align*} \sin \left (3 x \right )+2 y \cos \left (3 x \right )^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.296
21307	22557	\begin{align*} \left (x +x \cos \left (y\right )\right ) y^{\prime }-\sin \left (y\right )-y&=0 \\ \end{align*}	✓	✓	✓	✓	4.297
21308	3553	\begin{align*} y^{\prime } y&=\sqrt {y^{2}+x^{2}}-x \\ \end{align*}	✓	✓	✓	✓	4.299
21309	11471	\begin{align*} x^{3} y^{\prime }-x^{4} y^{2}+x^{2} y+20&=0 \\ \end{align*}	✓	✓	✓	✓	4.300
21310	4883	\begin{align*} x^{2} y^{\prime }&=a +b x y+c \,x^{2} y^{2} \\ \end{align*}	✓	✓	✓	✓	4.303
21311	6998	\begin{align*} \left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	4.303
21312	14020	\begin{align*} x \left (1-y\right ) y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	4.303
21313	17125	\begin{align*} y^{\prime }&=\sqrt {y}\, \cos \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	4.303
21314	4079	\begin{align*} 4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.304
21315	5024	\begin{align*} y^{\prime } \sqrt {b \,x^{4}+a \,x^{2}+1}+\sqrt {1+a y^{2}+b y^{4}}&=0 \\ \end{align*}	✓	✓	✓	✓	4.304
21316	23020	\begin{align*} z^{\prime \prime }+g z&=0 \\ z \left (\frac {\pi }{3 \sqrt {g}}\right ) &= 5 \\ z \left (\frac {2 \pi }{3 \sqrt {g}}\right ) &= \frac {\pi }{3} \\ \end{align*}	✓	✓	✓	✓	4.304
21317	4372	\begin{align*} 1+y+\left (x -y \left (1+y\right )^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.306
21318	11351	\begin{align*} y^{\prime }-f_{3} \left (x \right ) y^{3}-f_{2} \left (x \right ) y^{2}-f_{1} \left (x \right ) y-f_{0} \left (x \right )&=0 \\ \end{align*}	✗	✗	✗	✗	4.306
21319	11452	\begin{align*} \left (x^{2}-1\right ) y^{\prime }-y x +a&=0 \\ \end{align*}	✓	✓	✓	✓	4.306
21320	15646	\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✗	4.309
21321	15961	\begin{align*} y^{\prime }&=2 t y^{2}+3 t^{2} y^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	4.309
21322	5054	\begin{align*} \left (x +y\right ) y^{\prime }+x -y&=0 \\ \end{align*}	✓	✓	✓	✓	4.312
21323	14496	\begin{align*} y^{\prime } x +y&=-2 x^{6} y^{4} \\ \end{align*}	✓	✓	✓	✓	4.313
21324	23843	\begin{align*} \left (x +y\right ) y^{\prime }&=x -y \\ \end{align*}	✓	✓	✓	✓	4.313
21325	4889	\begin{align*} x^{2} y^{\prime }&=\left (a x +y^{3} b \right ) y \\ \end{align*}	✓	✓	✓	✓	4.315
21326	20243	\begin{align*} \left (2 x +2 y+1\right ) y^{\prime }&=x +y+1 \\ \end{align*}	✓	✓	✓	✓	4.315
21327	3017	\begin{align*} 2 y x +y^{4}+\left (x y^{3}-2 x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.316
21328	7934	\begin{align*} 1+\sin \left (y\right )&=\left (2 y \cos \left (y\right )-x \left (\sec \left (y\right )+\tan \left (y\right )\right )\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	4.317
21329	111	\begin{align*} y^{2} y^{\prime } x&=x^{3}+y^{3} \\ \end{align*}	✓	✓	✓	✓	4.318
21330	7336	\begin{align*} 2 x -y \sin \left (2 x \right )&=\left (\sin \left (x \right )^{2}-2 y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	4.318
21331	11311	\begin{align*} y^{\prime }-\left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	4.319
21332	16254	\begin{align*} y^{\prime }&=\frac {y^{2}-1}{y x} \\ y \left (1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	4.319
21333	1205	\begin{align*} 2 x -y+\left (-x +2 y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	4.322
21334	5330	\begin{align*} \left (1+a \left (x +y\right )\right )^{n} y^{\prime }+a \left (x +y\right )^{n}&=0 \\ \end{align*}	✓	✓	✓	✓	4.323
21335	12677	\begin{align*} y^{\prime \prime }&=-\frac {\left (-a^{2} \sinh \left (x \right )^{2}-n \left (n -1\right )\right ) y}{\sinh \left (x \right )^{2}} \\ \end{align*}	✗	✓	✓	✗	4.324
21336	11554	\begin{align*} 2 x^{2} y y^{\prime }+y^{2}-2 x^{3}-x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.326
21337	22412	\begin{align*} 2 x y^{\prime } y&=x^{2}-y^{2} \\ \end{align*}	✓	✓	✓	✓	4.328
21338	20250	\begin{align*} x +y+1-\left (2 x +2 y+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.329
21339	733	\begin{align*} x \left (x +y\right ) y^{\prime }&=y \left (x -y\right ) \\ \end{align*}	✓	✓	✓	✓	4.330
21340	5274	\begin{align*} x \left (3 x -7 y^{2}\right ) y^{\prime }+\left (5 x -3 y^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	4.330
21341	9150	\begin{align*} y^{\prime } x&=y+2 \,{\mathrm e}^{-\frac {y}{x}} x \\ \end{align*}	✓	✓	✓	✓	4.333
21342	9163	\begin{align*} y^{\prime }&=\frac {y-x y^{2}}{x +x^{2} y} \\ \end{align*}	✓	✓	✓	✓	4.333
21343	23913	\begin{align*} \sin \left (x \right ) y^{\prime }-y \cos \left (x \right )&=\cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.335
21344	11378	\begin{align*} y^{\prime }-\cos \left (b x +a y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.338
21345	4404	\begin{align*} -y+y^{\prime } x&=\tan \left (\frac {y}{x}\right ) x \\ \end{align*}	✓	✓	✓	✓	4.339
21346	1606	\begin{align*} y^{\prime }-y&=\frac {\left (x +1\right ) {\mathrm e}^{4 x}}{\left ({\mathrm e}^{x}+y\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	4.342
21347	8880	\begin{align*} y^{\prime }+2 y x&=x \,{\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.342
21348	19773	\begin{align*} y-2 y^{\prime } x -y {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.343
21349	23153	\begin{align*} x^{2}+y^{2}-2 x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	4.343
21350	11660	\begin{align*} {y^{\prime }}^{2}+a y+b \,x^{2}&=0 \\ \end{align*}	✓	✗	✓	✗	4.346
21351	7928	\begin{align*} \left (x -x \sqrt {x^{2}-y^{2}}\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	4.347
21352	23222	\begin{align*} y^{\prime }&=-\frac {x +2 y}{y} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	4.347
21353	6572	\begin{align*} y^{\prime } y^{\prime \prime }&=a^{2} x \\ \end{align*}	✓	✓	✓	✓	4.351
21354	7529	\begin{align*} 2 x y^{3}-\left (-x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.352
21355	5272	\begin{align*} x \left (x +6 y^{2}\right ) y^{\prime }+y x -3 y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	4.356
21356	18576	\begin{align*} 2 x -2 \,{\mathrm e}^{y x} \sin \left (2 x \right )+{\mathrm e}^{y x} \cos \left (2 x \right ) y+\left (-3+{\mathrm e}^{y x} x \cos \left (2 x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.356
21357	107	\begin{align*} y^{\prime } x&=y+2 \sqrt {y x} \\ \end{align*}	✓	✓	✓	✓	4.359
21358	4679	\begin{align*} y^{\prime }&=x +\left (1-2 x \right ) y-\left (1-x \right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	4.359
21359	6299	\begin{align*} y^{\prime \prime }&=6 y^{2} \\ \end{align*}	✓	✓	✓	✓	4.359
21360	2509	\begin{align*} 2 t \sin \left (y\right )+{\mathrm e}^{t} y^{3}+\left (\cos \left (y\right ) t^{2}+3 \,{\mathrm e}^{t} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.362
21361	23873	\begin{align*} y^{\prime }&=\frac {x^{2} {\mathrm e}^{\frac {y}{x}}+y^{2}}{y x} \\ \end{align*}	✓	✓	✓	✗	4.362
21362	9167	\begin{align*} y^{\prime }&=\frac {y \tan \left (\frac {y}{x}\right )}{x} \\ \end{align*}	✓	✓	✓	✓	4.363
21363	5214	\begin{align*} \left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	4.364
21364	24138	\begin{align*} 1+\ln \left (x \right )+\left (1+\ln \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.364
21365	19098	\begin{align*} \frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}}&=0 \\ \end{align*}	✓	✓	✓	✗	4.365
21366	7857	\begin{align*} y^{2}-x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.369
21367	4970	\begin{align*} x^{3} y^{\prime }&=y \left (y+x^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	4.371
21368	8700	\begin{align*} y^{\prime } x&=y \cos \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	4.371
21369	7163	\begin{align*} a x y^{\prime }+2 y&=x y^{\prime } y \\ \end{align*}	✓	✓	✓	✓	4.372
21370	13969	\begin{align*} y^{\prime } x +x +y&=0 \\ \end{align*}	✓	✓	✓	✓	4.372
21371	7251	\begin{align*} y x +\left (y^{2}-x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.376
21372	13244	\begin{align*} y^{\prime } x&=x^{2 n} y^{2}+\left (m -n \right ) y+x^{2 m} \\ \end{align*}	✓	✓	✓	✗	4.376
21373	25031	\begin{align*} y^{2}+2 t y y^{\prime }+3 t^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.376
21374	1003	\begin{align*} x_{1}^{\prime }&=9 x_{1}+13 x_{2}-13 x_{6} \\ x_{2}^{\prime }&=-14 x_{1}+19 x_{2}-10 x_{3}-20 x_{4}+10 x_{5}+4 x_{6} \\ x_{3}^{\prime }&=-30 x_{1}+12 x_{2}-7 x_{3}-30 x_{4}+12 x_{5}+18 x_{6} \\ x_{4}^{\prime }&=-12 x_{1}+10 x_{2}-10 x_{3}-9 x_{4}+10 x_{5}+2 x_{6} \\ x_{5}^{\prime }&=6 x_{1}+9 x_{2}+6 x_{4}+5 x_{5}-15 x_{6} \\ x_{6}^{\prime }&=-14 x_{1}+23 x_{2}-10 x_{3}-20 x_{4}+10 x_{5} \\ \end{align*}	✓	✓	✓	✓	4.377
21375	9594	\begin{align*} \left (1-2 \sin \left (x \right )\right ) y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.382
21376	15565	\begin{align*} y^{\prime }&=\frac {y}{-x^{2}+4}+\sqrt {x} \\ y \left (3\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	4.384
21377	17293	\begin{align*} 5 t +2 y+1+\left (2 t +y+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.384
21378	19678	\begin{align*} x^{\prime }+x \tan \left (t \right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.384
21379	8434	\begin{align*} y-4 \left (x +y^{6}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.385
21380	15775	\begin{align*} y^{\prime }&=t^{2} y^{2} \\ \end{align*}	✓	✓	✓	✓	4.385
21381	23199	\begin{align*} x^{4}+y^{4}-x y^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.387
21382	19267	\begin{align*} {\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.392
21383	21267	\begin{align*} t x^{\prime \prime }&=x \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	4.394
21384	20261	\begin{align*} x^{2}+3 y^{2}-2 x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	4.397
21385	17099	\begin{align*} 4 \left (x -1\right )^{2} y^{\prime }-3 \left (3+y\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.398
21386	19205	\begin{align*} y^{\prime \prime }+\frac {2 p y^{\prime }}{x}+y&=0 \\ \end{align*}	✓	✓	✓	✗	4.400
21387	743	\begin{align*} x \left (x +y\right ) y^{\prime }+y \left (3 x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.401
21388	14220	\begin{align*} \theta ^{\prime }&=t \sqrt {t^{2}+1}\, \sec \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	4.402
21389	8061	\begin{align*} 2 \left (1+y\right ) y^{\prime \prime }+2 {y^{\prime }}^{2}+y^{2}+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	4.403
21390	21265	\begin{align*} x^{\prime \prime }-x+3 x^{2}&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	4.403
21391	4874	\begin{align*} x^{2} y^{\prime }&=a +b y^{2} \\ \end{align*}	✓	✓	✓	✓	4.404
21392	6560	\begin{align*} \left (\left (-y+a \right ) \left (-y+b \right )+\left (-y+a \right ) \left (c -y\right )+\left (-y+b \right ) \left (c -y\right )\right ) {y^{\prime }}^{2}+2 \left (-y+a \right ) \left (-y+b \right ) \left (c -y\right ) y^{\prime \prime }&=\operatorname {a3} \left (-y+a \right )^{2} \left (-y+b \right )^{2}+2 \operatorname {a2} \left (-y+a \right )^{2} \left (c -y\right )^{2}+\operatorname {a1} \left (-y+b \right )^{2} \left (c -y\right )^{2}+\operatorname {a0} \left (-y+a \right )^{2} \left (-y+b \right )^{2} \left (c -y\right )^{2} \\ \end{align*}	✓	✓	✓	✗	4.405
21393	11804	\begin{align*} {y^{\prime }}^{3}-\left (y-a \right )^{2} \left (y-b \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.405
21394	14211	\begin{align*} x^{\prime }&=\sqrt {x} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	4.405
21395	19742	\begin{align*} v^{\prime }+\frac {2 v}{u}&=3 v \\ \end{align*}	✓	✓	✓	✓	4.406
21396	21435	\begin{align*} y^{\prime }&={\mathrm e}^{x}+y \\ \end{align*}	✓	✓	✓	✓	4.406
21397	12174	\begin{align*} y^{\prime }&=-\frac {i \left (i x +1+x^{4}+2 y^{2} x^{2}+y^{4}+x^{6}+3 x^{4} y^{2}+3 x^{2} y^{4}+y^{6}\right )}{y} \\ \end{align*}	✗	✗	✗	✗	4.407
21398	20980	\begin{align*} y^{\prime }+p \left (x \right ) y&=q \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.407
21399	17051	\begin{align*} y^{\prime }&=\sqrt {25-y^{2}} \\ y \left (3\right ) &= -6 \\ \end{align*}	✓	✓	✓	✗	4.408
21400	8254	\begin{align*} 2 y^{\prime \prime }-3 y^{2}&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	4.409