2.3.211 Problems 21001 to 21100

Table 2.995: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
21001	4309	\begin{align*} x \left (1+y^{2}\right )+\left (1+2 y\right ) {\mathrm e}^{-x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.253
21002	17122	\begin{align*} y^{\prime }&=\frac {3 y+1}{x +3} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.253
21003	16300	\begin{align*} y^{\prime }&=4+\frac {1}{\sin \left (4 x -y\right )} \\ \end{align*}	✓	✓	✓	✓	5.254
21004	14430	\begin{align*} y^{\prime }+y&=2 x \,{\mathrm e}^{-x} \\ y \left (-1\right ) &= {\mathrm e}+3 \\ \end{align*}	✓	✓	✓	✓	5.255
21005	22721	\begin{align*} y^{\prime \prime }+\omega ^{2} y&=t \left (\sin \left (\omega t \right )+\cos \left (\omega t \right )\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.255
21006	12970	\begin{align*} 12 y y^{\prime \prime }-15 {y^{\prime }}^{2}+8 y^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	5.256
21007	5384	\begin{align*} {y^{\prime }}^{2}+a y^{\prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✓	5.258
21008	15501	\begin{align*} x^{2} y^{\prime \prime }+6 x y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.258
21009	8693	\begin{align*} y-2 y x +x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.259
21010	6355	\begin{align*} g \left (x \right ) y^{\prime }+f \left (x \right ) {y^{\prime }}^{k}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.260
21011	10320	\begin{align*} y^{\prime }&=\left (1+6 x +y\right )^{{1}/{4}} \\ \end{align*}	✓	✓	✓	✓	5.260
21012	6129	\begin{align*} 2 y-\left (x +2\right ) y^{\prime }+\left (x +2\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.261
21013	4696	\begin{align*} y^{\prime }+y \left (1-x y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.262
21014	6063	\begin{align*} a^{2} y+x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.262
21015	14008	\begin{align*} y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.262
21016	24977	\begin{align*} y t -\left (t +2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.262
21017	3645	\begin{align*} x^{2} y^{\prime }&=y^{2}+3 y x +x^{2} \\ \end{align*}	✓	✓	✓	✓	5.263
21018	5311	\begin{align*} \left (5 x -y-7 x y^{3}\right ) y^{\prime }+5 y-y^{4}&=0 \\ \end{align*}	✓	✓	✓	✗	5.263
21019	16253	\begin{align*} x y^{\prime }&=y^{2}-y \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✗	✓	5.263
21020	25811	\begin{align*} y^{\prime }&=\left (y \,{\mathrm e}^{y}-9 y\right ) {\mathrm e}^{-y} \\ \end{align*}	✓	✓	✓	✓	5.263
21021	4225	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-2 y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.264
21022	14255	\begin{align*} x^{\prime }&=\left (a +\frac {b}{t}\right ) x \\ x \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.264
21023	17343	\begin{align*} y^{2}+\left (2 y t -2 \cos \left (y\right ) \sin \left (y\right )\right ) y^{\prime }&=0 \\ y \left (0\right ) &= \pi \\ \end{align*}	✓	✓	✓	✓	5.264
21024	210	\begin{align*} y^{\prime }&=x y^{3}-y x \\ \end{align*}	✓	✓	✓	✓	5.265
21025	12020	\begin{align*} y^{\prime }&=\frac {2 a}{-x^{2} y+2 a y^{4} x^{2}-16 a^{2} x y^{2}+32 a^{3}} \\ \end{align*}	✓	✓	✓	✗	5.268
21026	11783	\begin{align*} \left (-x +y\right )^{2} \left (1+{y^{\prime }}^{2}\right )-a^{2} \left (y^{\prime }+1\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.270
21027	5519	\begin{align*} \left (a^{2}+x^{2}\right ) {y^{\prime }}^{2}&=b^{2} \\ \end{align*}	✓	✓	✓	✓	5.271
21028	25856	\begin{align*} y+6 x y^{3}-4 y^{4}-\left (2 x +4 x y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.271
21029	11594	\begin{align*} 6 x y^{2} y^{\prime }+x +2 y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	5.272
21030	20234	\begin{align*} \left (1+{\mathrm e}^{x}\right ) y y^{\prime }&=\left (y+1\right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	5.272
21031	14690	\begin{align*} x^{2} y^{\prime \prime }-6 x y^{\prime }+10 y&=3 x^{4}+6 x^{3} \\ \end{align*}	✓	✓	✓	✓	5.273
21032	22026	\begin{align*} y^{\prime }&=-\frac {2 x y}{x^{2}+1} \\ y \left (2\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	5.274
21033	24332	\begin{align*} k \,{\mathrm e}^{2 v}-u -2 \,{\mathrm e}^{2 v} \left ({\mathrm e}^{2 v}+k u \right ) v^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.274
21034	4854	\begin{align*} 2 x y^{\prime }&=\left (1+x -6 y^{2}\right ) y \\ \end{align*}	✓	✓	✓	✓	5.276
21035	4983	\begin{align*} x \left (-x^{2}+1\right ) y^{\prime }&=x^{3} \left (-x^{2}+1\right )+\left (-2 x^{2}+1\right ) y \\ \end{align*}	✓	✓	✓	✓	5.276
21036	14017	\begin{align*} y^{\prime }-x^{2} y&=x^{5} \\ \end{align*}	✓	✓	✓	✓	5.277
21037	25501	\begin{align*} y^{\prime }&={\mathrm e}^{t} y \\ \end{align*}	✓	✓	✓	✓	5.278
21038	5472	\begin{align*} {y^{\prime }}^{2} x -2 y y^{\prime }+x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.281
21039	13665	\begin{align*} y^{\prime \prime }-\left (a \,x^{2}+b \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	5.282
21040	7561	\begin{align*} \sqrt {y}+\left (x^{2}+4\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✗	5.286
21041	11455	\begin{align*} \left (x^{2}-1\right ) y^{\prime }-y \left (-x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.287
21042	6099	\begin{align*} 2 y-a y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.288
21043	15368	\begin{align*} s^{\prime }+s \cos \left (t \right )&=\frac {\sin \left (2 t \right )}{2} \\ \end{align*}	✓	✓	✓	✓	5.288
21044	14483	\begin{align*} y^{\prime }+3 y&=3 x^{2} {\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	5.289
21045	4999	\begin{align*} x \left (-2 x^{3}+1\right ) y^{\prime }&=2 \left (-x^{3}+1\right ) y \\ \end{align*}	✓	✓	✓	✓	5.292
21046	14420	\begin{align*} y^{\prime }+4 y x&=8 x \\ \end{align*}	✓	✓	✓	✓	5.292
21047	12089	\begin{align*} y^{\prime }&=-\frac {1}{-x -\textit {\_F1} \left (y-\ln \left (x \right )\right ) y \,{\mathrm e}^{y}} \\ \end{align*}	✗	✓	✓	✗	5.293
21048	27203	\begin{align*} y y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	5.293
21049	21350	\begin{align*} y^{\prime }&=\frac {x}{y^{3}} \\ \end{align*}	✓	✓	✓	✓	5.296
21050	25398	\begin{align*} y^{\prime }&=a \left (t \right ) y \\ \end{align*}	✓	✓	✓	✓	5.296
21051	4437	\begin{align*} y \left (6 y^{2}-x -1\right )+2 x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.297
21052	7017	\begin{align*} x y^{\prime }-y-x \sin \left (\frac {y}{x}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.299
21053	8417	\begin{align*} \left (2 y+2\right ) y^{\prime }-4 x^{3}-6 x&=0 \\ y \left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	5.300
21054	23948	\begin{align*} x \sqrt {a^{2}+x^{2}}&=y \sqrt {y^{2}-a^{2}}\, y^{\prime } \\ \end{align*}	✓	✓	✓	✓	5.300
21055	5509	\begin{align*} {y^{\prime }}^{2} x^{2}-3 x y y^{\prime }+x^{3}+2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	5.302
21056	10287	\begin{align*} y^{\prime }&=\cos \left (x \right )+\frac {y^{2}}{x} \\ \end{align*}	✗	✗	✗	✗	5.302
21057	21418	\begin{align*} 2 x^{2}+y+\left (x^{2} y-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.303
21058	21606	\begin{align*} y^{\prime }+x \left (-x +y\right )+x^{3} \left (-x +y\right )^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	5.305
21059	4755	\begin{align*} x y^{\prime }&=x^{m}+y \\ \end{align*}	✓	✓	✓	✓	5.307
21060	22979	\begin{align*} y^{\prime }+7 y&={\mathrm e}^{5 x} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.307
21061	12316	\begin{align*} y^{\prime \prime }+x y^{\prime }+\left (n +1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	5.309
21062	13270	\begin{align*} x \left (x^{2}+a \right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (b \,x^{2}+c \right ) y+s x&=0 \\ \end{align*}	✓	✓	✓	✗	5.309
21063	12037	\begin{align*} y^{\prime }&=\frac {y^{{3}/{2}}}{y^{{3}/{2}}+x^{2}-2 y x +y^{2}} \\ \end{align*}	✓	✓	✓	✗	5.310
21064	22630	\begin{align*} y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.311
21065	1220	\begin{align*} y^{\prime }&=\frac {2 x +y}{3-x +3 y^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.312
21066	4007	\begin{align*} \left (x -2\right )^{2} y^{\prime \prime }+\left (x -2\right ) {\mathrm e}^{x} y^{\prime }+\frac {4 y}{x}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.312
21067	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*}	✗	✓	✓	✗	5.312
21068	27329	\begin{align*} x \left (\ln \left (y\right )+2 \ln \left (x \right )-1\right ) y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	5.312
21069	3544	\begin{align*} y^{\prime }&=\frac {\left (x +y\right )^{2}}{2 x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.314
21070	2849	\begin{align*} y+3+\cot \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.315
21071	3605	\begin{align*} y^{\prime }&=1-\frac {\sin \left (x +y\right )}{\cos \left (x \right ) \sin \left (y\right )} \\ y \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✓	5.316
21072	5967	\begin{align*} x^{k} \left (a +b \,x^{k}\right ) y+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	5.316
21073	7145	\begin{align*} y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-a -1}&=0 \\ \end{align*}	✓	✓	✓	✗	5.317
21074	26175	\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}	✓	✓	✓	✓	5.317
21075	26398	\begin{align*} y^{\prime }&=\tan \left (a x +b y+c \right ) \\ \end{align*}	✓	✓	✓	✓	5.321
21076	27494	\begin{align*} y^{\prime }+\tan \left (y\right )&=x \sec \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	5.322
21077	5454	\begin{align*} {y^{\prime }}^{2} x +4 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	5.323
21078	6975	\begin{align*} y^{\prime }+\cos \left (x \right ) y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	5.326
21079	9821	\begin{align*} 9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-1&=0 \\ \end{align*}	✓	✓	✓	✗	5.327
21080	15071	\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=2 \\ \end{align*}	✓	✓	✓	✓	5.329
21081	15391	\begin{align*} y&=y {y^{\prime }}^{2}+2 x y^{\prime } \\ \end{align*}	✓	✓	✓	✓	5.329
21082	25488	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.330
21083	2845	\begin{align*} x y^{2}+x +\left (x^{2} y-y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.331
21084	24337	\begin{align*} x y^{\prime }-y&=x^{k} y \\ \end{align*}	✓	✓	✓	✓	5.331
21085	16695	\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.333
21086	3637	\begin{align*} y^{\prime }&=\frac {\left (x +y\right )^{2}}{2 x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.334
21087	12848	\begin{align*} y^{\prime \prime }-{\mathrm e}^{y}&=0 \\ \end{align*}	✓	✓	✓	✓	5.335
21088	26402	\begin{align*} y+x y^{2}-x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.335
21089	12312	\begin{align*} y^{\prime \prime }+a y^{\prime }-\left (b^{2} x^{2}+c \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	5.337
21090	22334	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.337
21091	11585	\begin{align*} \left (b \left (\beta y+\alpha x \right )^{2}-\beta \left (a x +b y\right )\right ) y^{\prime }+a \left (\beta y+\alpha x \right )^{2}-\alpha \left (a x +b y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	5.338
21092	1002	\begin{align*} x_{1}^{\prime }&=139 x_{1}-14 x_{2}-52 x_{3}-14 x_{4}+28 x_{5} \\ x_{2}^{\prime }&=-22 x_{1}+5 x_{2}+7 x_{3}+8 x_{4}-7 x_{5} \\ x_{3}^{\prime }&=370 x_{1}-38 x_{2}-139 x_{3}-38 x_{4}+76 x_{5} \\ x_{4}^{\prime }&=152 x_{1}-16 x_{2}-59 x_{3}-13 x_{4}+35 x_{5} \\ x_{5}^{\prime }&=95 x_{1}-10 x_{2}-38 x_{3}-7 x_{4}+23 x_{5} \\ \end{align*}	✓	✓	✓	✓	5.339
21093	18282	\begin{align*} y^{\prime \prime }-y&=1 \\ \end{align*}	✓	✓	✓	✓	5.342
21094	15799	\begin{align*} y^{\prime }&=-y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.343
21095	4233	\begin{align*} \left (x^{2}-1\right ) y^{\prime }&=\left (x^{2}+1\right ) y \\ \end{align*}	✓	✓	✓	✓	5.344
21096	4617	\begin{align*} y^{\prime }&=x^{2} \left (a \,x^{3}+b y\right ) \\ \end{align*}	✓	✓	✓	✓	5.345
21097	19384	\begin{align*} \cos \left (x +y\right )&=x \sin \left (x +y\right )+x \sin \left (x +y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	5.347
21098	5748	\begin{align*} \left (c \,x^{2}+b x +a \right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	5.348
21099	15329	\begin{align*} y {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	5.348
21100	12157	\begin{align*} y^{\prime }&=\frac {-2 y x +2 x^{3}-2 x -y^{3}+3 x^{2} y^{2}-3 x^{4} y+x^{6}}{-y+x^{2}-1} \\ \end{align*}	✓	✓	✓	✓	5.350