2.3.203 Problems 20201 to 20300

Table 2.937: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
20201	9010	\begin{align*} y^{\prime }&=y^{2} x^{2}-4 x^{2} \\ \end{align*}	✓	✓	✓	✗	3.261
20202	4909	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=2 x \left (x^{2}+1\right )^{2}+2 y x \\ \end{align*}	✓	✓	✓	✓	3.263
20203	17165	\begin{align*} y^{\prime }+3 t^{2} y&={\mathrm e}^{-t^{3}} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.263
20204	19679	\begin{align*} x^{\prime }-x \tan \left (t \right )&=4 \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	3.263
20205	13778	\begin{align*} x^{2} y^{\prime \prime }-\left (a^{2} x^{4}+a \left (2 b -1\right ) x^{2}+b \left (b +1\right )\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.264
20206	8786	\begin{align*} y^{\prime }&=\frac {y}{2 x}+\frac {x^{2}}{2 y} \\ \end{align*}	✓	✓	✓	✓	3.265
20207	6342	\begin{align*} g \left (y\right )+f \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.266
20208	11890	\begin{align*} y^{\prime }&=\frac {2 y+F \left (\frac {y}{x^{2}}\right ) x^{3}}{x} \\ \end{align*}	✓	✓	✓	✗	3.266
20209	15805	\begin{align*} y^{\prime }&=\left (1+y^{2}\right ) t \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	3.266
20210	2974	\begin{align*} y x^{\prime }&=2 y \,{\mathrm e}^{3 y}+x \left (3 y +2\right ) \\ \end{align*}	✓	✓	✓	✓	3.267
20211	8047	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✓	3.269
20212	4940	\begin{align*} x \left (x +1\right ) y^{\prime }&=\left (x +1\right ) \left (x^{2}-1\right )+\left (x^{2}+x -1\right ) y \\ \end{align*}	✓	✓	✓	✓	3.270
20213	21982	\begin{align*} 1+y x +y^{\prime } y&=0 \\ \end{align*}	✗	✓	✓	✗	3.270
20214	22375	\begin{align*} x^{3} {\mathrm e}^{2 x^{2}+3 y^{2}}-y^{3} {\mathrm e}^{-x^{2}-2 y^{2}} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.270
20215	4645	\begin{align*} y^{\prime }&=2+2 \sec \left (2 x \right )+2 y \tan \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	3.273
20216	9162	\begin{align*} y^{\prime }&=\frac {2+3 x y^{2}}{4 x^{2} y} \\ \end{align*}	✓	✓	✓	✓	3.273
20217	4441	\begin{align*} 2 x y^{4} {\mathrm e}^{y}+2 x y^{3}+y+\left (x^{2} y^{4} {\mathrm e}^{y}-y^{2} x^{2}-3 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.274
20218	22958	\begin{align*} x y \left (x^{2}+1\right ) y^{\prime }-y^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	3.275
20219	19929	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	3.276
20220	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*}	✓	✓	✓	✗	3.279
20221	12441	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y-x \sin \left (x \right )-\left (a \,x^{2}+12 a +4\right ) \cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.279
20222	1595	\begin{align*} y^{\prime }&=\frac {2 x}{1+2 y} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.280
20223	8279	\begin{align*} y^{\prime } x +y&=\frac {1}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	3.280
20224	7014	\begin{align*} y^{\prime } x -y \left (\ln \left (y x \right )-1\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.283
20225	11398	\begin{align*} y^{\prime } x +a y^{2}-b y+c \,x^{2 b}&=0 \\ \end{align*}	✓	✓	✓	✗	3.283
20226	15649	\begin{align*} y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.283
20227	17310	\begin{align*} y^{\prime }&=\frac {2 t^{5}}{5 y^{2}} \\ \end{align*}	✓	✓	✓	✓	3.283
20228	20318	\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \left ({\mathrm e}^{x}-{\mathrm e}^{y}\right ) \\ \end{align*}	✗	✓	✓	✓	3.283
20229	3315	\begin{align*} x&=y^{\prime } y+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	3.284
20230	135	\begin{align*} 2 x +3 y+\left (2 y+3 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.286
20231	4870	\begin{align*} x^{2} y^{\prime }+x \left (2+x \right ) y&=x \left (1-{\mathrm e}^{-2 x}\right )-2 \\ \end{align*}	✓	✓	✓	✓	3.286
20232	7026	\begin{align*} \cos \left (x \right ) y^{\prime }+y+\left (1+\sin \left (x \right )\right ) \cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.286
20233	17311	\begin{align*} \cos \left (4 x \right )-8 y^{\prime } \sin \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.286
20234	4861	\begin{align*} 3 y^{\prime } x&=3 x^{{2}/{3}}+\left (1-3 y\right ) y \\ \end{align*}	✓	✓	✓	✗	3.288
20235	760	\begin{align*} 4 x -y+\left (6 y-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.289
20236	21467	\begin{align*} y^{\prime }&=-2+3 y-y^{2} \\ \end{align*}	✓	✓	✓	✓	3.289
20237	6801	\begin{align*} {y^{\prime }}^{2}+y^{\prime \prime \prime } y^{\prime }&=2 {y^{\prime \prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	3.290
20238	8301	\begin{align*} y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.292
20239	11418	\begin{align*} y^{\prime } x -y \left (\ln \left (y x \right )-1\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.292
20240	8669	\begin{align*} y^{\prime }&=\frac {3 x^{2}+4 x +2}{-2+2 y} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.293
20241	11572	\begin{align*} \left (y^{2}+4 \sin \left (x \right )\right ) y^{\prime }-\cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.293
20242	25706	\begin{align*} y^{\prime } x&=2 y \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.293
20243	14205	\begin{align*} x^{\prime \prime }&=-3 \sqrt {t} \\ x \left (1\right ) &= 4 \\ x^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.294
20244	12288	\begin{align*} y^{\prime \prime }+a^{2} y-\cot \left (a x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.295
20245	4355	\begin{align*} y^{2}+\left ({\mathrm e}^{x}-y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.296
20246	4937	\begin{align*} x \left (1-x \right ) y^{\prime }+\left (2 x +1\right ) y&=a \\ \end{align*}	✓	✓	✓	✓	3.297
20247	23957	\begin{align*} y x -x&=\left (x y^{2}+x -y^{2}-1\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.297
20248	8657	\begin{align*} y^{\prime }&=\frac {x^{2}}{y} \\ \end{align*}	✓	✓	✓	✓	3.300
20249	17652	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=\ln \left (x \right ) \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.300
20250	5756	\begin{align*} y^{\prime \prime }&=\left (a^{2}+\left (-1+p \right ) p \csc \left (x \right )^{2}+\left (-1+q \right ) q \sec \left (x \right )^{2}\right ) y \\ \end{align*}	✗	✓	✓	✗	3.301
20251	14493	\begin{align*} \cos \left (x \right )^{2}-y \cos \left (x \right )-\left (1+\sin \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.301
20252	20115	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +y&=\frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x} \\ \end{align*}	✓	✓	✓	✓	3.301
20253	4298	\begin{align*} y \sin \left (\frac {x}{y}\right )+x \cos \left (\frac {x}{y}\right )-1+\left (x \sin \left (\frac {x}{y}\right )-\frac {x^{2} \cos \left (\frac {x}{y}\right )}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.302
20254	6360	\begin{align*} y^{\prime \prime }&=a x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✗	3.302
20255	20691	\begin{align*} a^{2}-2 y x -y^{2}-\left (x +y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.304
20256	17328	\begin{align*} t \ln \left (y\right )+\left (\frac {t^{2}}{2 y}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.305
20257	17255	\begin{align*} -2 y+y^{\prime }&=\frac {\cos \left (t \right )}{\sqrt {y}} \\ \end{align*}	✓	✓	✓	✓	3.306
20258	19346	\begin{align*} y-x +x y \cot \left (x \right )+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.307
20259	7628	\begin{align*} \sin \left (x \right ) y^{\prime \prime }+y \cos \left (x \right )&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	3.308
20260	7741	\begin{align*} y^{\prime }&={\mathrm e}^{3 x -2 y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.309
20261	4914	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	3.310
20262	3246	\begin{align*} y^{3} y^{\prime \prime }+4&=0 \\ \end{align*}	✓	✓	✓	✗	3.312
20263	5303	\begin{align*} x y^{3} y^{\prime }&=\left (-x^{2}+1\right ) \left (1+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	3.313
20264	16247	\begin{align*} y^{\prime }-3 y^{2} x^{2}&=3 x^{2} \\ \end{align*}	✓	✓	✓	✓	3.313
20265	3044	\begin{align*} \left (-2 x^{2}-3 y x \right ) y^{\prime }+y^{2}&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.314
20266	3257	\begin{align*} y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	3.314
20267	22359	\begin{align*} y^{\prime }&=-\frac {x}{y} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.315
20268	3467	\begin{align*} y^{\prime }&=\frac {1}{x +2 y+1} \\ \end{align*}	✓	✓	✓	✓	3.316
20269	5268	\begin{align*} x \left (x -3 y^{2}\right ) y^{\prime }+\left (2 x -y^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	3.316
20270	11426	\begin{align*} y^{\prime } x -y f \left (x^{a} y^{b}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	3.316
20271	24114	\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}-5 x \right ) y^{\prime }+\left (5-6 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	3.316
20272	8400	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{\sqrt {x}}}{y} \\ y \left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	3.317
20273	8687	\begin{align*} y^{\prime }+\sin \left (x +y\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.317
20274	12335	\begin{align*} y^{\prime \prime }+a \,x^{-1+q} y^{\prime }+b \,x^{q -2} y&=0 \\ \end{align*}	✗	✓	✓	✗	3.318
20275	12405	\begin{align*} 16 y^{\prime \prime } x +8 y^{\prime }-\left (x +a \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.318
20276	1822	\begin{align*} \sin \left (x \right ) y^{\prime \prime }+\left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime }+\left (\sin \left (x \right )-\cos \left (x \right )\right ) y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✗	3.319
20277	4344	\begin{align*} 2 x \left (x^{2}-\sin \left (y\right )+1\right )+\left (x^{2}+1\right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.320
20278	2917	\begin{align*} 3 x^{2} y+x y^{2}+{\mathrm e}^{x}+\left (x^{3}+x^{2} y+\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.323
20279	19986	\begin{align*} y&=x \left (1+y^{\prime }\right )+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	3.323
20280	25780	\begin{align*} y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.323
20281	1607	\begin{align*} y^{\prime }-2 y&=\frac {x \,{\mathrm e}^{2 x}}{1-y \,{\mathrm e}^{-2 x}} \\ \end{align*}	✓	✓	✓	✗	3.324
20282	21101	\begin{align*} x&=t \left (1+x^{\prime }\right )+x^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.324
20283	4306	\begin{align*} \cos \left (y\right )^{2}+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.325
20284	6371	\begin{align*} 9 {y^{\prime }}^{4}+8 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.326
20285	22038	\begin{align*} y^{\prime }&=\frac {3 y x^{2}}{x^{3}+2 y^{4}} \\ \end{align*}	✓	✓	✓	✓	3.326
20286	1186	\begin{align*} y^{\prime }&=-\frac {2 \arctan \left (y\right )}{1+y^{2}} \\ \end{align*}	✓	✓	✓	✓	3.328
20287	8365	\begin{align*} \left (x^{4}+1\right ) y^{\prime }+x \left (1+4 y^{2}\right )&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✗	✓	3.329
20288	15377	\begin{align*} y^{\prime } x&=\left (y \ln \left (x \right )-2\right ) y \\ \end{align*}	✓	✓	✓	✓	3.329
20289	15911	\begin{align*} y^{\prime }+2 y&=t^{2}+2 t +1+{\mathrm e}^{4 t} \\ \end{align*}	✓	✓	✓	✓	3.329
20290	17247	\begin{align*} -1+{\mathrm e}^{t y} y+y \cos \left (t y\right )+\left (1+{\mathrm e}^{t y} t +t \cos \left (t y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.329
20291	2932	\begin{align*} y \,{\mathrm e}^{y x}+2 y x +\left (x \,{\mathrm e}^{y x}+x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.330
20292	11603	\begin{align*} \left (2 y^{3}+y\right ) y^{\prime }-2 x^{3}-x&=0 \\ \end{align*}	✓	✓	✓	✓	3.330
20293	4926	\begin{align*} \left (a^{2}+x^{2}\right ) y^{\prime }&=b +y x \\ \end{align*}	✓	✓	✓	✓	3.331
20294	759	\begin{align*} 2 x +3 y+\left (2 y+3 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.332
20295	5616	\begin{align*} y^{\prime }+{y^{\prime }}^{3}&={\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✗	3.332
20296	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*}	✗	✓	✓	✗	3.332
20297	3472	\begin{align*} y^{\prime }&=\frac {4 y^{2}}{x^{2}}-y^{2} \\ \end{align*}	✓	✓	✓	✓	3.333
20298	11505	\begin{align*} y^{\prime } y+4 x \left (x +1\right )+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.335
20299	21123	\begin{align*} x^{\prime \prime }+\lambda ^{2} x&=0 \\ x \left (0\right ) &= 0 \\ x \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.337
20300	22464	\begin{align*} y+x^{3}+x y^{2}-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.337