2.3.213 Problems 21201 to 21300

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

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
21201	8369	\begin{align*} y^{\prime }&=y^{2} \sin \left (x^{2}\right ) \\ y \left (-2\right ) &= {\frac {1}{3}} \\ \end{align*}	✓	✓	✓	✓	4.195
21202	10063	\begin{align*} x^{\prime }&=4 A k \left (\frac {x}{A}\right )^{{3}/{4}}-3 k x \\ \end{align*}	✓	✓	✓	✗	4.196
21203	11348	\begin{align*} y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-a -1}&=0 \\ \end{align*}	✓	✓	✓	✗	4.196
21204	21401	\begin{align*} y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	4.196
21205	25782	\begin{align*} y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\ y \left (0\right ) &= -{\frac {5}{2}} \\ \end{align*}	✓	✓	✓	✓	4.196
21206	11318	\begin{align*} y^{\prime }+y^{2}+\left (y x -1\right ) f \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	4.198
21207	16355	\begin{align*} y^{\prime }&=\frac {x +2 y}{2 x -y} \\ \end{align*}	✓	✓	✓	✓	4.199
21208	13642	\begin{align*} y^{\prime }&=a y^{3}+3 a b x y^{2}-b -2 a \,b^{3} x^{3} \\ \end{align*}	✓	✓	✓	✗	4.201
21209	17211	\begin{align*} -\frac {1}{y}+\left (\frac {t}{y^{2}}+3 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.204
21210	114	\begin{align*} x y^{\prime } y&=x^{2}+3 y^{2} \\ \end{align*}	✓	✓	✓	✓	4.206
21211	14226	\begin{align*} x^{\prime }&=\left (4 t -x\right )^{2} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.206
21212	14546	\begin{align*} 4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.206
21213	93	\begin{align*} y^{\prime } x&=3 y+x^{4} \cos \left (x \right ) \\ y \left (2 \pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.207
21214	4312	\begin{align*} x y^{3}+\left (1+y\right ) {\mathrm e}^{-x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.207
21215	5764	\begin{align*} \left (a +b \sinh \left (x \right )^{2}\right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	4.207
21216	9976	\begin{align*} y^{\prime }+\frac {2 y}{x}&=6 x^{4} y^{2} \\ \end{align*}	✓	✓	✓	✓	4.208
21217	20226	\begin{align*} x \cos \left (y\right )^{2}&=y \cos \left (x \right )^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.209
21218	23953	\begin{align*} \left (x +\frac {x}{y^{2}+x^{2}}\right ) y^{\prime }+y-\frac {y}{y^{2}+x^{2}}&=0 \\ y \left (1\right ) &= \sqrt {3} \\ \end{align*}	✓	✓	✓	✗	4.209
21219	7421	\begin{align*} 3 t&={\mathrm e}^{t} y^{\prime }+y \ln \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	4.210
21220	9147	\begin{align*} x^{2} y^{\prime }-3 y x -2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.210
21221	8378	\begin{align*} y^{\prime }&=y^{2}-4 \\ y \left (\frac {1}{4}\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	4.212
21222	14168	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=x \\ \end{align*}	✓	✓	✓	✓	4.214
21223	19097	\begin{align*} \frac {y^{\prime } y+x}{\sqrt {1+x^{2}+y^{2}}}+\frac {y-y^{\prime } x}{y^{2}+x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	4.214
21224	3491	\begin{align*} \frac {y^{\prime \prime }}{y}-\frac {{y^{\prime }}^{2}}{y^{2}}+\frac {2 a \coth \left (2 a x \right ) y^{\prime }}{y}&=2 a^{2} \\ \end{align*}	✗	✓	✓	✗	4.215
21225	23135	\begin{align*} x^{2}+y^{2}-2 x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	4.216
21226	4691	\begin{align*} y^{\prime }&=\left (a \,{\mathrm e}^{x}+y\right ) y^{2} \\ \end{align*}	✗	✓	✓	✗	4.217
21227	1659	\begin{align*} y^{\prime }&=\frac {y}{y-2 x} \\ \end{align*}	✓	✓	✓	✓	4.218
21228	20920	\begin{align*} y^{\prime \prime }+6 y^{\prime }+18 y&=2 \operatorname {Heaviside}\left (\pi -t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.218
21229	19328	\begin{align*} y^{\prime } x&=x^{5}+x^{3} y^{2}+y \\ \end{align*}	✓	✓	✓	✓	4.220
21230	23876	\begin{align*} y^{\prime }&=1+\frac {3 y}{x} \\ \end{align*}	✓	✓	✓	✓	4.222
21231	8235	\begin{align*} y^{\prime }&=\sqrt {y^{2}-9} \\ y \left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	4.224
21232	13232	\begin{align*} y^{\prime }&=y^{2}+a \,x^{n} y-a b \,x^{n}-b^{2} \\ \end{align*}	✓	✓	✓	✗	4.224
21233	24341	\begin{align*} 2 x y^{\prime } y&=y^{2}-2 x^{3} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.225
21234	11506	\begin{align*} y^{\prime } y+a y^{2}-b \cos \left (x +c \right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.226
21235	5405	\begin{align*} {y^{\prime }}^{2}+a x y^{\prime }+b \,x^{2}+c y&=0 \\ \end{align*}	✓	✗	✓	✗	4.230
21236	11594	\begin{align*} 6 y^{2} y^{\prime } x +x +2 y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	4.233
21237	9151	\begin{align*} x -y-\left (x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.237
21238	19077	\begin{align*} \left (x +y\right )^{2} y^{\prime }&=a^{2} \\ \end{align*}	✓	✓	✓	✓	4.238
21239	23238	\begin{align*} y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	4.238
21240	1644	\begin{align*} x y^{3} y^{\prime }&=y^{4}+x^{4} \\ \end{align*}	✓	✓	✓	✓	4.239
21241	6308	\begin{align*} y^{\prime \prime }&=\operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{3} \\ \end{align*}	✓	✓	✓	✗	4.241
21242	11559	\begin{align*} 2 x^{3}+y^{\prime } y+3 y^{2} x^{2}+7&=0 \\ \end{align*}	✓	✓	✓	✓	4.243
21243	19143	\begin{align*} y^{\prime \prime }&=\frac {1}{\sqrt {y}} \\ \end{align*}	✓	✓	✓	✗	4.243
21244	24329	\begin{align*} y^{\prime } x&=y-y^{3} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.243
21245	12443	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y-\frac {x^{2}}{\cos \left (x \right )}&=0 \\ \end{align*}	✓	✓	✓	✗	4.245
21246	16327	\begin{align*} 3 y+3 y^{2}+\left (2 x +4 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.245
21247	7891	\begin{align*} y \left (x -2 y\right )-x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.247
21248	12884	\begin{align*} y^{\prime \prime }-a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	4.248
21249	6819	\begin{align*} \frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}}&=0 \\ \end{align*}	✓	✓	✓	✗	4.249
21250	18014	\begin{align*} y&=x {y^{\prime }}^{2}-\frac {1}{y^{\prime }} \\ \end{align*}	✓	✓	✓	✗	4.249
21251	21352	\begin{align*} y^{\prime }&=2 y x \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	4.249
21252	12886	\begin{align*} y^{\prime \prime }+y^{3} y^{\prime }-y y^{\prime } \sqrt {y^{4}+4 y^{\prime }}&=0 \\ \end{align*}	✓	✓	✓	✗	4.250
21253	11416	\begin{align*} y^{\prime } x -{\mathrm e}^{\frac {y}{x}} x -y-x&=0 \\ \end{align*}	✓	✓	✓	✗	4.252
21254	109	\begin{align*} x \left (x +y\right ) y^{\prime }&=y \left (x -y\right ) \\ \end{align*}	✓	✓	✓	✓	4.256
21255	4722	\begin{align*} y^{\prime }&=\sin \left (x \right ) \left (\csc \left (y\right )-\cot \left (y\right )\right ) \\ \end{align*}	✓	✓	✓	✓	4.256
21256	3464	\begin{align*} \left (y^{3}+x \right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✗	4.257
21257	7413	\begin{align*} y^{\prime }&=x y^{3} \\ \end{align*}	✓	✓	✓	✓	4.257
21258	24121	\begin{align*} \sin \left (x \right ) \sin \left (y\right )+\cos \left (x \right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.259
21259	4259	\begin{align*} 1&=\frac {y}{1-y^{2} x^{2}}+\frac {x y^{\prime }}{1-y^{2} x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.260
21260	21568	\begin{align*} y^{\prime \prime }+k^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	4.260
21261	5064	\begin{align*} \left (2 x +y\right ) y^{\prime }+x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.261
21262	13218	\begin{align*} x^{2} y^{\prime }&=a \,x^{2} y^{2}+b \\ \end{align*}	✓	✓	✓	✓	4.262
21263	15915	\begin{align*} y^{\prime }&=-\frac {y}{t}+2 \\ \end{align*}	✓	✓	✓	✓	4.262
21264	118	\begin{align*} y^{\prime } y+x&=\sqrt {y^{2}+x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.263
21265	11476	\begin{align*} x^{2} \left (x -1\right ) y^{\prime }-y^{2}-x \left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	4.263
21266	15647	\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	4.263
21267	22470	\begin{align*} y-x \sqrt {y^{2}+x^{2}}+\left (x -y \sqrt {y^{2}+x^{2}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.263
21268	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*}	✓	✓	✓	✗	4.265
21269	4858	\begin{align*} \left (2 x +1\right ) y^{\prime }&=4 \,{\mathrm e}^{-y}-2 \\ \end{align*}	✓	✓	✓	✓	4.266
21270	11420	\begin{align*} y^{\prime } x -\sin \left (x -y\right )&=0 \\ \end{align*}	✗	✗	✗	✗	4.266
21271	19394	\begin{align*} {\mathrm e}^{x} \left (x +1\right )&=\left (x \,{\mathrm e}^{x}-{\mathrm e}^{y} y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.267
21272	7438	\begin{align*} \cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=2 \cos \left (x \right )^{2} x \\ y \left (\frac {\pi }{4}\right ) &= -\frac {15 \sqrt {2}\, \pi ^{2}}{32} \\ \end{align*}	✓	✓	✓	✓	4.269
21273	14446	\begin{align*} \frac {\left (2 s-1\right ) s^{\prime }}{t}+\frac {s-s^{2}}{t^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	4.269
21274	16227	\begin{align*} y^{\prime } y&=3 \sqrt {x y^{2}+9 x} \\ y \left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✗	4.269
21275	24227	\begin{align*} y \left (x^{3} y^{3}+2 x^{2}-y\right )+x^{3} \left (x y^{3}-2\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	4.269
21276	2949	\begin{align*} \left (2 x +3 x^{2} y\right ) y^{\prime }+y+2 x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.270
21277	11839	\begin{align*} a {y^{\prime }}^{m}+b {y^{\prime }}^{n}-y&=0 \\ \end{align*}	✓	✓	✓	✗	4.270
21278	5127	\begin{align*} x y^{\prime } y&=a \,x^{3} \cos \left (x \right )+y^{2} \\ \end{align*}	✓	✓	✓	✓	4.272
21279	16299	\begin{align*} 3 y^{\prime }+\frac {2 y}{x}&=4 \sqrt {y} \\ \end{align*}	✓	✓	✓	✓	4.272
21280	5207	\begin{align*} \left (1+y\right ) y^{\prime } \sqrt {x^{2}+1}&=y^{3} \\ \end{align*}	✓	✓	✓	✓	4.273
21281	19735	\begin{align*} y^{\prime }&=\left (x +y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.274
21282	5213	\begin{align*} \left (y^{2}+x^{2}\right ) y^{\prime }&=y x \\ \end{align*}	✓	✓	✓	✓	4.276
21283	6839	\begin{align*} y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}}&=\frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	4.276
21284	20812	\begin{align*} y^{\prime }&=y^{2} \left (t^{2}+1\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.276
21285	13760	\begin{align*} y^{\prime \prime } x +\left (a \,x^{n}+b \right ) y^{\prime }+\left (c \,x^{2 n -1}+d \,x^{n -1}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	4.278
21286	15547	\begin{align*} y^{\prime }&=\frac {x y}{y^{2}+x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.278
21287	11422	\begin{align*} y^{\prime } x -y-x \sin \left (\frac {y}{x}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.280
21288	23118	\begin{align*} y^{\prime }&=\frac {y^{2}+x^{2}}{2 y x} \\ \end{align*}	✓	✓	✓	✓	4.281
21289	9190	\begin{align*} y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	4.282
21290	25714	\begin{align*} \left (y-x \right ) y^{\prime }&=x +y \\ \end{align*}	✓	✓	✓	✓	4.286
21291	4240	\begin{align*} x^{2}-y^{2}+x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	4.287
21292	4819	\begin{align*} y^{\prime } x&=y+x \sec \left (\frac {y}{x}\right )^{2} \\ \end{align*}	✓	✓	✓	✗	4.289
21293	13729	\begin{align*} y^{\prime \prime } x +a y^{\prime }+b \,x^{n} \left (-b \,x^{n +1}+a +n \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	4.289
21294	17940	\begin{align*} y^{\prime }&=\frac {y}{2 y \ln \left (y\right )+y-x} \\ \end{align*}	✓	✓	✓	✓	4.289
21295	20731	\begin{align*} \left (y^{\prime } y+n x \right )^{2}&=\left (y^{2}+n \,x^{2}\right ) \left (1+{y^{\prime }}^{2}\right ) \\ \end{align*}	✓	✓	✗	✓	4.289
21296	6492	\begin{align*} 12 y y^{\prime \prime }&=-8 y^{3}+15 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	4.290
21297	22033	\begin{align*} \left (x +y\right ) y^{\prime }+x -y&=0 \\ \end{align*}	✓	✓	✓	✓	4.290
21298	10450	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=2 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.291
21299	23919	\begin{align*} y^{\prime }+y x&=x y^{5} \\ \end{align*}	✓	✓	✓	✓	4.291
21300	20794	\begin{align*} y^{\prime \prime }-\left (8 \,{\mathrm e}^{2 x}+2\right ) y^{\prime }+4 \,{\mathrm e}^{4 x} y&={\mathrm e}^{6 x} \\ \end{align*}	✓	✓	✓	✗	4.292