2.3.213 Problems 21201 to 21300

Table 2.969: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
21201	3640	\begin{align*} -y+y^{\prime } x&=\sqrt {9 x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	7.140
21202	3480	\begin{align*} \left (2 \sin \left (y\right )-x \right ) y^{\prime }&=\tan \left (y\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	7.141
21203	11335	\begin{align*} y^{\prime }-\frac {y^{2} f^{\prime }\left (x \right )}{g \left (x \right )}+\frac {g^{\prime }\left (x \right )}{f \left (x \right )}&=0 \\ \end{align*}	✗	✓	✓	✗	7.143
21204	21062	\begin{align*} x^{\prime }&=2 t \sqrt {x} \\ x \left (a \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	7.143
21205	13457	\begin{align*} y^{\prime }&=f \left (x \right ) y^{2}+g \left (x \right ) y-a^{2} f \left (x \right )-g \left (x \right ) a \\ \end{align*}	✓	✓	✓	✗	7.145
21206	4775	\begin{align*} y^{\prime } x&=a +b y^{2} \\ \end{align*}	✓	✓	✓	✓	7.147
21207	22367	\begin{align*} 2 \cos \left (x \right ) y+3 \sin \left (x \right ) y^{\prime }&=0 \\ y \left (\frac {\pi }{2}\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	7.148
21208	25897	\begin{align*} x -2 y+1&=\left (x -2 y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	7.148
21209	5155	\begin{align*} y \left (1-x \right ) y^{\prime }+\left (1-y\right ) x&=0 \\ \end{align*}	✓	✓	✓	✓	7.149
21210	16253	\begin{align*} y^{\prime } x&=y^{2}-y \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✗	✓	7.149
21211	16695	\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	7.152
21212	25883	\begin{align*} 2 x +y-\left (4 x +2 y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.152
21213	7121	\begin{align*} y y^{\prime \prime }&=-1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	7.154
21214	16377	\begin{align*} y^{\prime }&=\tan \left (6 x +3 y+1\right )-2 \\ \end{align*}	✓	✓	✓	✓	7.154
21215	14493	\begin{align*} \cos \left (x \right )^{2}-\cos \left (x \right ) y-\left (1+\sin \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.156
21216	16340	\begin{align*} x y^{2}-6+x^{2} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.156
21217	17317	\begin{align*} y^{\prime }&=\frac {\left (4-7 x \right ) \left (2 y-3\right )}{\left (x -1\right ) \left (2 x -5\right )} \\ \end{align*}	✓	✓	✓	✓	7.156
21218	2931	\begin{align*} \frac {x \cos \left (\frac {x}{y}\right )}{y}+\sin \left (\frac {x}{y}\right )+\cos \left (x \right )-\frac {x^{2} \cos \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	7.162
21219	7741	\begin{align*} y^{\prime }&={\mathrm e}^{3 x -2 y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	7.164
21220	4229	\begin{align*} x \cos \left (y\right ) y^{\prime }&=1+\sin \left (y\right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	7.170
21221	22986	\begin{align*} y^{\prime }-\sin \left (x \right ) y&=\sin \left (x \right ) \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	7.170
21222	19801	\begin{align*} y^{\prime }-\tan \left (x \right ) y&=y^{4} \sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	7.171
21223	6886	\begin{align*} y&=y^{\prime } x +\sqrt {b^{2}-a^{2} {y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	7.172
21224	11647	\begin{align*} \left (x \sin \left (y\right )-1\right ) y^{\prime }+\cos \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	7.174
21225	11957	\begin{align*} y^{\prime }&=-\frac {x^{2}-x -2-2 \sqrt {x^{2}-4 x +4 y}}{2 \left (x +1\right )} \\ \end{align*}	✓	✓	✓	✓	7.174
21226	8786	\begin{align*} y^{\prime }&=\frac {y}{2 x}+\frac {x^{2}}{2 y} \\ \end{align*}	✓	✓	✓	✓	7.175
21227	21795	\begin{align*} y^{\prime }&=-\frac {x}{4 y} \\ \end{align*}	✓	✓	✓	✓	7.175
21228	7607	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 2 \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	7.178
21229	26252	\begin{align*} 2 \left (x^{2}+1\right ) y^{\prime }-\cos \left (2 y\right )^{2}&=0 \\ y \left (-\infty \right ) &= \frac {7 \pi }{2} \\ \end{align*}	✓	✓	✗	✗	7.180
21230	1693	\begin{align*} {\mathrm e}^{x} \left (y^{2} x^{2}+2 x y^{2}\right )+6 x +\left (2 x^{2} y \,{\mathrm e}^{x}+2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.181
21231	7129	\begin{align*} r^{\prime \prime }&=\frac {h^{2}}{r^{3}}-\frac {k}{r^{2}} \\ \end{align*}	✓	✓	✓	✓	7.188
21232	25011	\begin{align*} -y+y^{\prime }&=t y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.189
21233	22970	\begin{align*} y^{\prime }&=1+\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	7.190
21234	4343	\begin{align*} y \left (x +y\right )+\left (x +2 y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.193
21235	5669	\begin{align*} {y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	7.201
21236	129	\begin{align*} y^{2} \left (y^{\prime } x +y\right ) \sqrt {x^{4}+1}&=x \\ \end{align*}	✓	✓	✓	✓	7.204
21237	5066	\begin{align*} \left (2 x -y+3\right ) y^{\prime }+2&=0 \\ \end{align*}	✓	✓	✓	✓	7.204
21238	18561	\begin{align*} y^{3}+y^{\prime }&=0 \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	7.205
21239	5190	\begin{align*} 2 x^{2} y y^{\prime }&=x^{2} \left (2 x +1\right )-y^{2} \\ \end{align*}	✓	✓	✓	✓	7.208
21240	4858	\begin{align*} \left (2 x +1\right ) y^{\prime }&=4 \,{\mathrm e}^{-y}-2 \\ \end{align*}	✓	✓	✓	✓	7.211
21241	17964	\begin{align*} y^{\prime } \cos \left (y\right )+\sin \left (y\right )&=x +1 \\ \end{align*}	✓	✓	✓	✓	7.211
21242	14746	\begin{align*} \left (x^{3}+x^{2}\right ) y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	7.213
21243	18493	\begin{align*} y^{\prime }&=\left (1+y^{2}\right ) \tan \left (2 x \right ) \\ y \left (0\right ) &= -\sqrt {3} \\ \end{align*}	✓	✓	✗	✓	7.213
21244	5764	\begin{align*} \left (a +b \sinh \left (x \right )^{2}\right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	7.217
21245	12400	\begin{align*} 4 y^{\prime \prime } x -\left (a +x \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	7.218
21246	17328	\begin{align*} t \ln \left (y\right )+\left (\frac {t^{2}}{2 y}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.224
21247	21303	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }&=x_{1}-2 x_{2}-x_{3} \\ x_{3}^{\prime }&=x_{2}-x_{3} \\ \end{align*}	✓	✓	✓	✗	7.231
21248	8822	\begin{align*} \left (y^{2} x^{2}+1\right ) y+\left (y^{2} x^{2}-1\right ) x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.237
21249	23396	\begin{align*} y^{\prime \prime }-\frac {5 y^{\prime }}{x}+\frac {5 y}{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	7.238
21250	7628	\begin{align*} \sin \left (x \right ) y^{\prime \prime }+\cos \left (x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	7.244
21251	13721	\begin{align*} y^{\prime \prime }+\left (a \,x^{n}+x^{m} b +c \right ) y^{\prime }+\left (x^{n +m} a b +x^{m} b c +x^{n -1} a n \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	7.246
21252	14078	\begin{align*} y&=y^{\prime } x +\frac {y {y^{\prime }}^{2}}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	7.248
21253	24191	\begin{align*} 1+y^{2}+x y^{2}+\left (x^{2} y+y+2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.248
21254	14259	\begin{align*} R^{\prime }&=\frac {R}{t}+t \,{\mathrm e}^{-t} \\ R \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.249
21255	14008	\begin{align*} y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.252
21256	5351	\begin{align*} \left (1-2 x -\ln \left (y\right )\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.254
21257	20300	\begin{align*} y^{\prime }&=\left (4 x +y+1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	7.255
21258	7525	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x +y}}{-1+y} \\ \end{align*}	✓	✓	✓	✓	7.256
21259	12175	\begin{align*} y^{\prime }&=\frac {\left (-256 a \,x^{2} y-32 a^{2} x^{6}-256 a \,x^{2}+512 y^{3}+192 x^{4} a y^{2}+24 y a^{2} x^{8}+a^{3} x^{12}\right ) x}{512 y+64 a \,x^{4}+512} \\ \end{align*}	✓	✓	✓	✓	7.261
21260	14211	\begin{align*} x^{\prime }&=\sqrt {x} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	7.265
21261	5341	\begin{align*} x \left (1-\sqrt {x^{2}-y^{2}}\right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✗	7.267
21262	11964	\begin{align*} y^{\prime }&=\frac {y+x^{3} b \ln \left (\frac {1}{x}\right )+b \,x^{4}+b \,x^{3}+x a y^{2} \ln \left (\frac {1}{x}\right )+a \,x^{2} y^{2}+a x y^{2}}{x} \\ \end{align*}	✓	✓	✓	✗	7.267
21263	17097	\begin{align*} y^{\prime }&=t^{2} y^{2}+y^{2}-t^{2}-1 \\ \end{align*}	✓	✓	✓	✗	7.268
21264	21157	\begin{align*} x^{\prime \prime }+\sqrt {t^{6}+3 t^{5}+1}\, x&=0 \\ \end{align*}	✗	✗	✗	✗	7.269
21265	12134	\begin{align*} y^{\prime }&=\frac {14 y x +12+2 x +x^{3} y^{3}+6 y^{2} x^{2}}{x^{2} \left (y x +2+x \right )} \\ \end{align*}	✓	✓	✓	✓	7.275
21266	6123	\begin{align*} 2 y-4 \left (1-x \right ) y^{\prime }+\left (1-x \right )^{2} y^{\prime \prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	7.276
21267	20799	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=4 \cos \left (\ln \left (x +1\right )\right ) \\ \end{align*}	✓	✓	✓	✗	7.283
21268	14419	\begin{align*} y^{\prime }+3 y&=3 x^{2} {\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	7.286
21269	17879	\begin{align*} 1+y^{2}&=y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	7.286
21270	8235	\begin{align*} y^{\prime }&=\sqrt {y^{2}-9} \\ y \left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	7.288
21271	15350	\begin{align*} x +y+\left (-x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.289
21272	16694	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	7.289
21273	23058	\begin{align*} \cot \left (\theta \right ) r^{\prime }&=r+b \\ \end{align*}	✓	✓	✓	✓	7.289
21274	24163	\begin{align*} x \csc \left (\frac {y}{x}\right )-y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	7.290
21275	5224	\begin{align*} \left (x +2 y+y^{2}\right ) y^{\prime }+y \left (1+y\right )+\left (x +y\right )^{2} y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	7.292
21276	14274	\begin{align*} t^{3}+\frac {x}{t}+\left (x^{2}+\ln \left (t \right )\right ) x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.295
21277	26236	\begin{align*} a^{2}+y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime }&=0 \\ y \left (a \right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	7.299
21278	5132	\begin{align*} y y^{\prime } x&=\left (x^{2}+1\right ) \left (1-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	7.302
21279	11920	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{-x^{2}} x}{y \,{\mathrm e}^{x^{2}}+1} \\ \end{align*}	✓	✓	✓	✗	7.302
21280	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*}	✓	✓	✓	✓	7.304
21281	8268	\begin{align*} y^{\prime }&=x^{2}+y^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	7.305
21282	22508	\begin{align*} \left (x^{2}+1\right ) \left (y^{3}-1\right )&=x^{2} y^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	7.306
21283	17327	\begin{align*} \tan \left (y\right )-t +\left (t \sec \left (y\right )^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.310
21284	5469	\begin{align*} x {y^{\prime }}^{2}-2 y y^{\prime }+a&=0 \\ \end{align*}	✓	✓	✓	✗	7.311
21285	21354	\begin{align*} y^{\prime }&=x^{2} y^{3} \\ \end{align*}	✓	✓	✓	✓	7.313
21286	5613	\begin{align*} {y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	7.318
21287	15352	\begin{align*} \left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.320
21288	17243	\begin{align*} 5 t y+4 y^{2}+1+\left (t^{2}+2 t y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.322
21289	4291	\begin{align*} {\mathrm e}^{x} \sin \left (y\right )-y \sin \left (y x \right )+\left ({\mathrm e}^{x} \cos \left (y\right )-x \sin \left (y x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.326
21290	14119	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y^{\prime }+6 y&=x \\ \end{align*}	✓	✓	✓	✗	7.328
21291	17256	\begin{align*} 3 y+y^{\prime }&=\sqrt {y}\, \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	7.329
21292	26208	\begin{align*} y^{\prime }&=\frac {y}{x +1}-y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.334
21293	12192	\begin{align*} y^{\prime }&=\frac {2 a x}{-x^{3} y+2 a \,x^{3}+2 a y^{4} x^{3}-16 y^{2} a^{2} x^{2}+32 a^{3} x +2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}} \\ \end{align*}	✓	✗	✓	✗	7.340
21294	11532	\begin{align*} \left (y x +a \right ) y^{\prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✓	7.341
21295	2512	\begin{align*} \frac {y^{2}}{2}-2 \,{\mathrm e}^{t} y+\left (-{\mathrm e}^{t}+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.343
21296	3456	\begin{align*} y^{\prime }-x y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	7.345
21297	13363	\begin{align*} y^{\prime } x&=a \,x^{2 n} \ln \left (x \right ) y^{2}+\left (b \,x^{n} \ln \left (x \right )-n \right ) y+c \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	7.346
21298	22464	\begin{align*} y+x^{3}+x y^{2}-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	7.352
21299	24784	\begin{align*} \left (4 x -y\right ) {y^{\prime }}^{2}+6 \left (x -y\right ) y^{\prime }+2 x -5 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.352
21300	6337	\begin{align*} b \sin \left (y\right )+a {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.355