2.3.204 Problems 20301 to 20400

Table 2.957: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
20301	19745	\begin{align*} \frac {y^{\prime }}{x}&=y \sin \left (x^{2}-1\right )-\frac {2 y}{\sqrt {x}} \\ \end{align*}	✓	✓	✓	✓	5.243
20302	21009	\begin{align*} x^{\prime }+\frac {x}{t^{2}-1}&=0 \\ x \left (-2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.247
20303	7711	\begin{align*} x^{2} \left (1+y\right )+y^{2} \left (x -1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.248
20304	4998	\begin{align*} x^{2} \left (-x^{2}+1\right ) y^{\prime }&=\left (x -3 x^{3} y\right ) y \\ \end{align*}	✓	✓	✓	✓	5.249
20305	19132	\begin{align*} y^{\prime }&=-x +\sqrt {x^{2}+2 y} \\ \end{align*}	✓	✓	✓	✓	5.249
20306	7028	\begin{align*} \left (x^{2}-y\right ) y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	5.250
20307	4670	\begin{align*} y^{\prime }&=a \,x^{n -1}+b \,x^{2 n}+c y^{2} \\ \end{align*}	✓	✓	✓	✗	5.251
20308	20768	\begin{align*} y+3 y^{\prime } x +2 y {y^{\prime }}^{2}+\left (x^{2}+2 y^{2} y^{\prime }\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	5.251
20309	14455	\begin{align*} y^{2}+2 y x -x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.253
20310	19088	\begin{align*} y^{\prime }+y^{2}+\frac {y}{x}-\frac {4}{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	5.253
20311	9041	\begin{align*} y^{\prime \prime }&=-\frac {1}{2 {y^{\prime }}^{2}} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	5.254
20312	13243	\begin{align*} y^{\prime } x&=a \,x^{n} y^{2}+m y-a \,b^{2} x^{n +2 m} \\ \end{align*}	✓	✓	✓	✗	5.254
20313	20679	\begin{align*} x^{3}+x y^{2}+a^{2} y+\left (y^{3}+x^{2} y-a^{2} x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.257
20314	1728	\begin{align*} 2 y+3 \left (x^{2}+x^{2} y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.258
20315	527	\begin{align*} y^{\prime }&=x^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✗	5.260
20316	2959	\begin{align*} y^{\prime }+2 y x&=2 x \,{\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.260
20317	9945	\begin{align*} y^{\prime \prime } x -\left (2+x \right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.261
20318	20636	\begin{align*} y^{\prime \prime }+\left (3 \sin \left (x \right )-\cot \left (x \right )\right ) y^{\prime }+2 y \sin \left (x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	5.261
20319	20811	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x}}{2 y} \\ \end{align*}	✓	✓	✓	✓	5.261
20320	4039	\begin{align*} x^{2} y^{\prime \prime }+x^{3} y^{\prime }-\left (2+x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.266
20321	19313	\begin{align*} \frac {-y^{\prime } x +y}{\left (x +y\right )^{2}}+y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✗	5.266
20322	15917	\begin{align*} y^{\prime }&=-\frac {y}{1+t}+t^{2} \\ \end{align*}	✓	✓	✓	✓	5.267
20323	24837	\begin{align*} {y^{\prime }}^{2}+2 x y^{3} y^{\prime }+y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	5.268
20324	14714	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=2 x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.269
20325	17107	\begin{align*} y^{\prime }&=x^{3} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.271
20326	11594	\begin{align*} 6 y^{\prime } y^{2} x +x +2 y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	5.272
20327	11508	\begin{align*} y y^{\prime }+x y^{2}-4 x&=0 \\ \end{align*}	✓	✓	✓	✓	5.275
20328	18491	\begin{align*} y^{\prime }&=2 x y^{2}+4 x^{3} y^{2} \\ y \left (1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	5.277
20329	13019	\begin{align*} \left (-1+y^{2}\right ) \left (y^{2} a^{2}-1\right ) y^{\prime \prime }+b \sqrt {\left (1-y^{2}\right ) \left (1-y^{2} a^{2}\right )}\, {y^{\prime }}^{2}+\left (1+a^{2}-2 y^{2} a^{2}\right ) y {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✗	✓	✗	5.278
20330	19414	\begin{align*} \frac {\cos \left (y\right )}{x +3}-\left (\sin \left (y\right ) \ln \left (5 x +15\right )-\frac {1}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.280
20331	5126	\begin{align*} y y^{\prime } x +x^{4}-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.281
20332	13665	\begin{align*} y^{\prime \prime }-\left (a \,x^{2}+b \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	5.282
20333	21351	\begin{align*} y^{\prime }&=\frac {x}{y^{2} \sqrt {x^{2}+1}} \\ \end{align*}	✓	✓	✓	✗	5.282
20334	2324	\begin{align*} \sqrt {t^{2}+1}\, y^{\prime }&=\frac {t y^{3}}{\sqrt {t^{2}+1}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.283
20335	17090	\begin{align*} y^{\prime }&=\frac {\left (1+2 \,{\mathrm e}^{y}\right ) {\mathrm e}^{-y}}{t \ln \left (t \right )} \\ \end{align*}	✓	✓	✓	✓	5.283
20336	18105	\begin{align*} y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	5.283
20337	5278	\begin{align*} x \left (1+x y^{2}\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	5.284
20338	15397	\begin{align*} y^{\prime }&=\frac {2 y}{x}-\sqrt {3} \\ \end{align*}	✓	✓	✓	✓	5.285
20339	9928	\begin{align*} y^{\prime \prime } x +\left (3+2 x \right ) y^{\prime }+8 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.286
20340	7001	\begin{align*} y^{2} {\mathrm e}^{x y^{2}}+4 x^{3}+\left (2 x y \,{\mathrm e}^{x y^{2}}-3 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.291
20341	8799	\begin{align*} p \,x^{2} u^{\prime \prime }+q x u^{\prime }+r u&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.292
20342	11709	\begin{align*} x {y^{\prime }}^{2}-2 y y^{\prime }+a&=0 \\ \end{align*}	✓	✓	✓	✗	5.292
20343	21024	\begin{align*} x^{\prime }&=\frac {x}{t^{2}+1} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.293
20344	529	\begin{align*} y^{\prime }&=x^{2}+y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✗	✓	✓	✗	5.294
20345	7321	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=x -\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	5.294
20346	11401	\begin{align*} y^{\prime } x +x y^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✓	5.294
20347	20967	\begin{align*} y^{\prime }&=3 y^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✓	5.296
20348	8743	\begin{align*} \frac {2 y y^{\prime } x}{3}&=\sqrt {x^{6}-y^{4}}+y^{2} \\ \end{align*}	✓	✓	✓	✗	5.300
20349	12420	\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	5.300
20350	21414	\begin{align*} y^{\prime }+\frac {y}{y^{2} x^{2}+x}&=\frac {x y^{2}}{y^{2} x^{2}+x} \\ \end{align*}	✓	✓	✓	✗	5.300
20351	11802	\begin{align*} \left (x^{2}+y^{2}\right ) f \left (\frac {x}{\sqrt {x^{2}+y^{2}}}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (-y+y^{\prime } x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	5.303
20352	17073	\begin{align*} 4 \sinh \left (4 y\right ) y^{\prime }&=6 \cosh \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✗	5.303
20353	22956	\begin{align*} \left (x^{2}-1\right ) y^{\prime }&=\left (-1+y\right ) x \\ \end{align*}	✓	✓	✓	✓	5.303
20354	9136	\begin{align*} 2 y^{4} x +\sin \left (y\right )+\left (4 x^{2} y^{3}+x \cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.304
20355	14542	\begin{align*} 5 y x +4 y^{2}+1+\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.305
20356	25802	\begin{align*} y^{\prime }&=y-y^{3} \\ \end{align*}	✓	✓	✓	✓	5.306
20357	5037	\begin{align*} y y^{\prime }+x^{3}+y&=0 \\ \end{align*}	✗	✗	✗	✗	5.308
20358	26220	\begin{align*} \left (1+y^{2}\right ) {\mathrm e}^{2 x}-\left (1+y^{2}\right ) {\mathrm e}^{y} y^{\prime }-\left (1+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.308
20359	22518	\begin{align*} y^{\prime }&=\frac {y}{x}+\arctan \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	5.310
20360	2957	\begin{align*} y^{\prime } x +2 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	5.312
20361	20573	\begin{align*} a y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	5.313
20362	26172	\begin{align*} y&=y^{\prime } x +y^{2} \sin \left (x^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	5.314
20363	13229	\begin{align*} y^{\prime }&=y^{2}+a \,x^{n} y+a \,x^{n -1} \\ \end{align*}	✓	✓	✓	✗	5.315
20364	16200	\begin{align*} x^{2} y^{\prime }+x y^{2}&=x \\ \end{align*}	✓	✓	✓	✓	5.316
20365	26328	\begin{align*} n \cos \left (x n +m y\right )-m \sin \left (x m +n y\right )+\left (m \cos \left (x n +m y\right )-n \sin \left (x m +n y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.316
20366	4306	\begin{align*} \cos \left (y\right )^{2}+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.319
20367	14544	\begin{align*} \left (x +1\right ) y^{2}+y+\left (2 y x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.319
20368	15548	\begin{align*} y^{\prime }&=\frac {1}{y x} \\ \end{align*}	✓	✓	✓	✓	5.319
20369	1576	\begin{align*} \frac {x y^{\prime }}{y}+2 \ln \left (y\right )&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	5.321
20370	2981	\begin{align*} 3 y^{2} y^{\prime }-x y^{3}&={\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.321
20371	4073	\begin{align*} x^{2} y^{\prime \prime }-x \left (2-x \right ) y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.321
20372	9946	\begin{align*} y^{\prime \prime } x -\left (2+x \right ) y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.321
20373	2950	\begin{align*} 2 x^{2} y y^{\prime }+{\mathrm e}^{x} x^{4}-2 x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.323
20374	21442	\begin{align*} y^{\prime }-2 y x&=x \\ \end{align*}	✓	✓	✓	✓	5.323
20375	12173	\begin{align*} y^{\prime }&=\frac {6 x +x^{3}+x^{3} y^{2}+4 x^{2} y+x^{3} y^{3}+6 y^{2} x^{2}+12 y x +8}{x^{3}} \\ \end{align*}	✓	✓	✓	✗	5.325
20376	24124	\begin{align*} m y-n x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.326
20377	2861	\begin{align*} y^{\prime } x +2 y&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.327
20378	12556	\begin{align*} 50 x \left (x -1\right ) y^{\prime \prime }+25 \left (2 x -1\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	5.327
20379	20326	\begin{align*} \sec \left (y\right )^{2} y^{\prime }+2 x \tan \left (y\right )&=x^{3} \\ \end{align*}	✓	✗	✓	✗	5.329
20380	20776	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=\ln \left (y\right ) y^{2} \\ \end{align*}	✓	✓	✓	✗	5.329
20381	23956	\begin{align*} y^{\prime }&=\sin \left (y\right )^{3} \cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	5.329
20382	8406	\begin{align*} y^{\prime }&=y+\frac {y}{x \ln \left (x \right )} \\ y \left ({\mathrm e}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.331
20383	4720	\begin{align*} y^{\prime }&=\cot \left (x \right ) \cot \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	5.333
20384	3525	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y^{2}&=-1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.334
20385	11759	\begin{align*} \left (x +y\right ) {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	5.334
20386	13996	\begin{align*} y^{\prime }-\frac {1+y}{x +1}&=\sqrt {1+y} \\ \end{align*}	✓	✓	✓	✓	5.334
20387	7391	\begin{align*} y^{\prime }&=\frac {\sec \left (y\right )^{2}}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	5.335
20388	11592	\begin{align*} 3 y^{\prime } y^{2} x +y^{3}-2 x&=0 \\ \end{align*}	✓	✓	✓	✓	5.335
20389	25664	\begin{align*} 2 y^{\prime }&=y^{3} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.335
20390	3044	\begin{align*} \left (-2 x^{2}-3 y x \right ) y^{\prime }+y^{2}&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.336
20391	17325	\begin{align*} t^{2}-y+\left (y-t \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.336
20392	15342	\begin{align*} 1+s^{2}-\sqrt {t}\, s^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.337
20393	9936	\begin{align*} x^{2} y^{\prime \prime }+x \left (1-2 x \right ) y^{\prime }-\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.338
20394	8176	\begin{align*} 2 y^{\prime } x -y&=2 \cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	5.342
20395	9934	\begin{align*} y^{\prime \prime } x +\left (-x +3\right ) y^{\prime }-5 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.343
20396	21402	\begin{align*} 1+3 x \sin \left (y\right )-x^{2} y^{\prime } \cos \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	5.343
20397	22953	\begin{align*} \frac {\tan \left (y\right )}{\cos \left (x \right )}&=\cos \left (x \right ) y^{\prime } \\ y \left (\frac {\pi }{4}\right ) &= \frac {\pi }{2} \\ \end{align*}	✓	✓	✓	✓	5.343
20398	17097	\begin{align*} y^{\prime }&=t^{2} y^{2}+y^{2}-t^{2}-1 \\ \end{align*}	✓	✓	✓	✗	5.344
20399	14232	\begin{align*} y^{\prime }&=t^{2} \tan \left (y\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.348
20400	25743	\begin{align*} 3 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.348