2.3.225 Problems 22401 to 22500

Table 2.1023: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
22401	4683	\begin{align*} y^{\prime }&=\left (a +b y \cos \left (k x \right )\right ) y \\ \end{align*}	✓	✓	✓	✓	7.178
22402	21099	\begin{align*} x&=x^{\prime } t -\ln \left (x^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	7.182
22403	19727	\begin{align*} \left (T \ln \left (t \right )-1\right ) T&=t T^{\prime } \\ \end{align*}	✓	✓	✓	✓	7.183
22404	8727	\begin{align*} y^{\prime }&=\frac {2 \left (y+2\right )^{2}}{\left (x +y+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	7.188
22405	14893	\begin{align*} i^{\prime }&=p \left (t \right ) i \\ \end{align*}	✓	✓	✓	✓	7.189
22406	15373	\begin{align*} y^{\prime }+y x&=x^{3} y^{3} \\ \end{align*}	✓	✓	✓	✓	7.189
22407	22569	\begin{align*} x y^{\prime }-3 y&=x^{4} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	7.204
22408	12003	\begin{align*} y^{\prime }&=\frac {\left (18 x^{{3}/{2}}+36 y^{2}-12 x^{3} y+x^{6}\right ) \sqrt {x}}{36} \\ \end{align*}	✓	✓	✓	✓	7.207
22409	19293	\begin{align*} y^{\prime }&=\frac {2+3 x y^{2}}{4 x^{2} y} \\ \end{align*}	✓	✓	✓	✓	7.207
22410	11911	\begin{align*} y^{\prime }&=\frac {x \left (-2+3 \sqrt {x^{2}+3 y}\right )}{3} \\ \end{align*}	✓	✓	✓	✓	7.209
22411	11501	\begin{align*} y y^{\prime }+x^{3}+y&=0 \\ \end{align*}	✗	✗	✗	✗	7.210
22412	12068	\begin{align*} y^{\prime }&=\frac {y \ln \left (x \right )+\cosh \left (x \right ) x a y^{2}+\cosh \left (x \right ) x^{3} b}{x \ln \left (x \right )} \\ \end{align*}	✓	✓	✓	✗	7.211
22413	22054	\begin{align*} y+x^{3}+x y^{2}-x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.211
22414	3409	\begin{align*} y^{\prime }&=x^{2} y^{2} \\ \end{align*}	✓	✓	✓	✓	7.214
22415	12065	\begin{align*} y^{\prime }&=-\frac {y \left (\tanh \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tanh \left (x \right )} \\ \end{align*}	✓	✓	✓	✗	7.220
22416	12172	\begin{align*} y^{\prime }&=\frac {y^{2}+2 y x +x^{2}+{\mathrm e}^{-\frac {2}{x^{2}-y^{2}-1}}}{y^{2}+2 y x +x^{2}-{\mathrm e}^{-\frac {2}{x^{2}-y^{2}-1}}} \\ \end{align*}	✓	✓	✓	✗	7.220
22417	12280	\begin{align*} y^{\prime }&=\frac {2 x^{2} y+x^{3}+x y \ln \left (x \right )-y^{2}-y x}{x^{2} \left (\ln \left (x \right )+x \right )} \\ \end{align*}	✓	✓	✓	✗	7.222
22418	22603	\begin{align*} y^{\prime }&=\frac {x +y^{2}}{2 y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.223
22419	16684	\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y&=6 x^{3} \\ \end{align*}	✓	✓	✓	✓	7.224
22420	13356	\begin{align*} y^{\prime }&=-\left (n +1\right ) x^{n} y^{2}+a \,x^{n +1} \ln \left (x \right )^{m} y-a \ln \left (x \right )^{m} \\ \end{align*}	✓	✓	✓	✗	7.226
22421	5137	\begin{align*} x \left (1-y\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	7.232
22422	742	\begin{align*} y y^{\prime }+x&=\sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	7.233
22423	18736	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\frac {\alpha \left (\alpha +1\right ) \mu ^{2} y}{-x^{2}+1}&=0 \\ y \left (0\right ) &= y_{0} \\ y^{\prime }\left (0\right ) &= y_{1} \\ \end{align*}	✓	✓	✓	✗	7.233
22424	7413	\begin{align*} y^{\prime }&=x y^{3} \\ \end{align*}	✓	✓	✓	✓	7.235
22425	11471	\begin{align*} x^{3} y^{\prime }-y^{2} x^{4}+x^{2} y+20&=0 \\ \end{align*}	✓	✓	✓	✓	7.240
22426	23866	\begin{align*} y x -\left (y^{4}+x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.240
22427	3007	\begin{align*} x -2 y+1+\left (-2+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.241
22428	14020	\begin{align*} x \left (1-y\right ) y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	7.241
22429	14433	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= -1 \\ \end{align*}	✓	✗	✗	✗	7.242
22430	8742	\begin{align*} 2 x y^{\prime }+y&=y^{2} \sqrt {x -x^{2} y^{2}} \\ \end{align*}	✓	✓	✓	✗	7.243
22431	11465	\begin{align*} 2 x \left (x -1\right ) y^{\prime }+y^{2} \left (x -1\right )-x&=0 \\ \end{align*}	✓	✓	✓	✗	7.243
22432	15387	\begin{align*} y y^{\prime }+x&=\frac {y}{x^{2}+y^{2}}-\frac {x y^{\prime }}{x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✗	7.246
22433	14033	\begin{align*} \left (1-x \right ) y-x \left (y+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.247
22434	19915	\begin{align*} y \left ({\mathrm e}^{x}+2 y x \right )-{\mathrm e}^{x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.250
22435	6869	\begin{align*} x y^{\prime }-a y+y^{2}&=x^{-\frac {2 a}{3}} \\ \end{align*}	✓	✓	✓	✗	7.252
22436	5348	\begin{align*} \left (1+\left (x +y\right ) \tan \left (y\right )\right ) y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✗	7.257
22437	8382	\begin{align*} x y^{\prime }&=y^{2}-y \\ y \left (2\right ) &= {\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	7.257
22438	12225	\begin{align*} y^{\prime }&=\frac {-32 y x -8 x^{3}-16 a \,x^{2}-32 x +64 y^{3}+48 x^{2} y^{2}+96 a x y^{2}+12 x^{4} y+48 a \,x^{3} y+48 a^{2} x^{2} y+x^{6}+6 x^{5} a +12 a^{2} x^{4}+8 a^{3} x^{3}}{64 y+16 x^{2}+32 a x +64} \\ \end{align*}	✓	✓	✓	✗	7.258
22439	14884	\begin{align*} x^{\prime }&=-x \left (1-x\right ) \left (2-x\right ) \\ \end{align*}	✓	✓	✓	✓	7.259
22440	15124	\begin{align*} x \left (y+1\right )^{2}&=\left (x^{2}+1\right ) y \,{\mathrm e}^{y} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	7.261
22441	3318	\begin{align*} 2 x {y^{\prime }}^{3}+1&=y {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	7.263
22442	23853	\begin{align*} y^{3}+y^{\prime } \sqrt {-x^{2}+1}&=0 \\ \end{align*}	✓	✓	✓	✓	7.263
22443	21010	\begin{align*} x^{\prime }+\sec \left (t \right ) x&=\frac {1}{t -1} \\ x \left (\frac {\pi }{4}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.264
22444	17905	\begin{align*} \left (x^{2}+1\right ) y^{\prime }-\frac {\cos \left (2 y\right )^{2}}{2}&=0 \\ y \left (-\infty \right ) &= \frac {7 \pi }{2} \\ \end{align*}	✓	✓	✗	✗	7.266
22445	22208	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	7.266
22446	21157	\begin{align*} x^{\prime \prime }+\sqrt {t^{6}+3 t^{5}+1}\, x&=0 \\ \end{align*}	✗	✗	✗	✗	7.269
22447	5009	\begin{align*} x^{k} y^{\prime }&=a \,x^{m}+b y^{n} \\ \end{align*}	✗	✗	✗	✗	7.270
22448	9095	\begin{align*} y^{2} y^{\prime }&=x +2 \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	7.277
22449	14448	\begin{align*} 2 y x -3+\left (x^{2}+4 y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	7.278
22450	15589	\begin{align*} y-x^{2} y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.286
22451	19357	\begin{align*} y^{\prime } \sin \left (2 x \right )&=2 y+2 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	7.289
22452	13653	\begin{align*} x^{2} y^{\prime }&=y^{3}-3 y a^{2} x^{4}+2 a^{3} x^{6}+2 a \,x^{3} \\ \end{align*}	✗	✓	✓	✗	7.292
22453	6892	\begin{align*} y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}}&=x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} \\ \end{align*}	✓	✓	✓	✓	7.301
22454	17080	\begin{align*} \left (5 x^{5}-4 \cos \left (x\right )\right ) x^{\prime }+2 \cos \left (9 t \right )+2 \sin \left (7 t \right )&=0 \\ \end{align*}	✓	✓	✓	✓	7.301
22455	11416	\begin{align*} x y^{\prime }-{\mathrm e}^{\frac {y}{x}} x -y-x&=0 \\ \end{align*}	✓	✓	✓	✗	7.305
22456	2822	\begin{align*} z^{\prime \prime }+\frac {z}{1+z^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	7.306
22457	19672	\begin{align*} 1+2 x+\left (-t^{2}+4\right ) x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.307
22458	4872	\begin{align*} x^{2} y^{\prime }+x^{2}+y x +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	7.309
22459	4848	\begin{align*} \left (x +a \right ) y^{\prime }&=y \left (1-a y\right ) \\ \end{align*}	✓	✓	✓	✓	7.314
22460	14888	\begin{align*} x^{\prime }&=x t^{2} \\ \end{align*}	✓	✓	✓	✓	7.314
22461	2991	\begin{align*} x y^{\prime }+y&=y^{2} x^{2} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	7.316
22462	4691	\begin{align*} y^{\prime }&=\left (a \,{\mathrm e}^{x}+y\right ) y^{2} \\ \end{align*}	✗	✓	✓	✗	7.318
22463	11945	\begin{align*} y^{\prime }&=\frac {x}{2}+\frac {1}{2}+x^{2} \sqrt {x^{2}+2 x +1-4 y} \\ \end{align*}	✓	✓	✓	✗	7.319
22464	14014	\begin{align*} x y^{\prime }-a y+b y^{2}&=c \,x^{2 a} \\ \end{align*}	✓	✓	✓	✗	7.320
22465	17090	\begin{align*} y^{\prime }&=\frac {\left (1+2 \,{\mathrm e}^{y}\right ) {\mathrm e}^{-y}}{t \ln \left (t \right )} \\ \end{align*}	✓	✓	✓	✓	7.322
22466	23164	\begin{align*} y y^{\prime }+x&=y \\ \end{align*}	✓	✓	✓	✓	7.324
22467	22514	\begin{align*} s^{2} t s^{\prime }+t^{2}+4&=0 \\ \end{align*}	✓	✓	✓	✓	7.330
22468	17883	\begin{align*} \ln \left (y\right ) y+x y^{\prime }&=1 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	7.334
22469	13657	\begin{align*} y^{\prime }&=-y^{3}+3 a^{2} {\mathrm e}^{2 \lambda x} y-2 a^{3} {\mathrm e}^{3 \lambda x}+a \lambda \,{\mathrm e}^{\lambda x} \\ \end{align*}	✗	✓	✓	✗	7.339
22470	19103	\begin{align*} a x y^{\prime }+b y+x^{m} y^{n} \left (\alpha x y^{\prime }+\beta y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	7.340
22471	4887	\begin{align*} x^{2} y^{\prime }&=a \,x^{2} y^{2}-a y^{3} \\ \end{align*}	✗	✓	✓	✗	7.342
22472	12471	\begin{align*} x^{2} y^{\prime \prime }+a \,x^{2} y^{\prime }+f \left (x \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	7.345
22473	2999	\begin{align*} y^{\prime }&=x \left (1-{\mathrm e}^{2 y-x^{2}}\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	7.346
22474	4241	\begin{align*} x^{2} y^{\prime }-2 y x -2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	7.348
22475	8291	\begin{align*} y^{\prime }&=x^{2}-y^{2} \\ y \left (0\right ) &= 2 \\ \end{align*}	✗	✓	✓	✗	7.348
22476	11412	\begin{align*} x y^{\prime }-y-\sqrt {x^{2}+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	7.350
22477	22581	\begin{align*} \cos \left (x \right ) y^{\prime }&=y-\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	7.352
22478	3468	\begin{align*} y^{\prime }&=-\frac {x +y}{3 x +3 y-4} \\ \end{align*}	✓	✓	✓	✓	7.353
22479	21872	\begin{align*} y&=x y^{\prime }+\ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	7.355
22480	5754	\begin{align*} a \csc \left (x \right )^{2} y+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	7.357
22481	11448	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y x -x \left (x^{2}+1\right )&=0 \\ \end{align*}	✓	✓	✓	✓	7.357
22482	17842	\begin{align*} y^{\prime }&=\sqrt {1-y^{2}} \\ \end{align*}	✓	✓	✓	✓	7.357
22483	12335	\begin{align*} y^{\prime \prime }+a \,x^{-1+q} y^{\prime }+b \,x^{q -2} y&=0 \\ \end{align*}	✗	✓	✓	✗	7.358
22484	22171	\begin{align*} \left (x^{2}-4\right ) y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	7.359
22485	19375	\begin{align*} x^{2} y^{3}+y&=\left (x^{3} y^{2}-x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	7.361
22486	6843	\begin{align*} 3 z^{2} z^{\prime }-a z^{3}&=x +1 \\ \end{align*}	✓	✓	✓	✓	7.362
22487	22977	\begin{align*} y^{\prime }+2 y x&=x \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.365
22488	6138	\begin{align*} -3 y+3 x y^{\prime }+\left (2 x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.368
22489	15481	\begin{align*} x^{\prime \prime }&=\left (2 \cos \left (x\right )-1\right ) \sin \left (x\right ) \\ \end{align*}	✓	✓	✓	✗	7.370
22490	6499	\begin{align*} 2 y y^{\prime }+{y^{\prime }}^{2} x +x y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.372
22491	25504	\begin{align*} \left (t +1\right ) y^{\prime }&=4 y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.372
22492	24319	\begin{align*} y^{\prime }&=y-x y^{3} {\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	7.374
22493	16310	\begin{align*} y^{\prime }+2 x&=2 \sqrt {x^{2}+y} \\ \end{align*}	✓	✓	✓	✓	7.375
22494	4442	\begin{align*} x y^{3}-1+x^{2} y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.378
22495	4762	\begin{align*} x y^{\prime }&=1+x +a y \\ \end{align*}	✓	✓	✓	✓	7.378
22496	13310	\begin{align*} y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+a \,x^{1+k} {\mathrm e}^{\lambda x} y-a \,{\mathrm e}^{\lambda x} \\ \end{align*}	✓	✓	✓	✗	7.382
22497	5155	\begin{align*} y \left (1-x \right ) y^{\prime }+\left (1-y\right ) x&=0 \\ \end{align*}	✓	✓	✓	✓	7.386
22498	6978	\begin{align*} x y^{\prime }-y&=x^{2} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	7.387
22499	24378	\begin{align*} y^{2}-3 y-x +\left (2 y-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.387
22500	7846	\begin{align*} y y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	7.390