2.3.210 Problems 20901 to 21000

Table 2.993: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
20901	12045	\begin{align*} y^{\prime }&=\frac {\left (x \ln \left (y\right )+\ln \left (y\right )+x \right ) y}{x \left (x +1\right )} \\ \end{align*}	✓	✓	✓	✓	5.161
20902	19324	\begin{align*} y^{2}+y x +1+\left (x^{2}+y x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.161
20903	5396	\begin{align*} {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	5.163
20904	12496	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-v \left (v +1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✓	5.163
20905	7487	\begin{align*} 3+y+y x +\left (3+x +y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.165
20906	9203	\begin{align*} \csc \left (x \right ) y^{\prime }&=\csc \left (y\right ) \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	5.165
20907	13232	\begin{align*} y^{\prime }&=y^{2}+a \,x^{n} y-a b \,x^{n}-b^{2} \\ \end{align*}	✓	✓	✓	✗	5.165
20908	22950	\begin{align*} y^{\prime } \sin \left (y\right )&=\sec \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	5.165
20909	24255	\begin{align*} \left (1+\cos \left (x \right )\right ) y^{\prime }&=\sin \left (x \right ) \left (\sin \left (x \right )+\sin \left (x \right ) \cos \left (x \right )-y\right ) \\ \end{align*}	✓	✓	✓	✓	5.165
20910	18517	\begin{align*} 4 y t +\left (t^{2}+1\right ) y^{\prime }&=\frac {1}{\left (t^{2}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	5.166
20911	19749	\begin{align*} u \ln \left (u \right ) v^{\prime }+\sin \left (v\right )^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	5.167
20912	22008	\begin{align*} y^{\prime }&=\frac {x +y}{x} \\ \end{align*}	✓	✓	✓	✓	5.167
20913	4721	\begin{align*} y^{\prime }+\cot \left (x \right ) \cot \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.168
20914	13218	\begin{align*} x^{2} y^{\prime }&=a \,x^{2} y^{2}+b \\ \end{align*}	✓	✓	✓	✓	5.169
20915	20410	\begin{align*} x&=y+a \ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	5.169
20916	3528	\begin{align*} y^{\prime }&=y^{3} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.170
20917	21996	\begin{align*} x \cos \left (x \right )+\left (1-6 y^{5}\right ) y^{\prime }&=0 \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.171
20918	24265	\begin{align*} y^{\prime }&=4 x -2 y \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	5.171
20919	12606	\begin{align*} y^{\prime \prime }&=-\frac {\left (a \left (1-a \right ) x^{2}-b \left (x +b \right )\right ) y}{x^{4}} \\ \end{align*}	✗	✓	✓	✗	5.173
20920	17053	\begin{align*} t y^{\prime }+y&=t^{3} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.173
20921	3675	\begin{align*} y^{\prime }&=2 x \left (x +y\right )^{2}-1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.174
20922	9650	\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=\delta \left (t -\pi \right )+\delta \left (t -3 \pi \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	5.174
20923	3591	\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=x^{2} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.175
20924	23186	\begin{align*} y+\cos \left (x \right )+\left (x +\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.175
20925	18618	\begin{align*} y^{\prime }-4 y^{2} {\mathrm e}^{x}&=y \\ \end{align*}	✓	✓	✓	✓	5.176
20926	19316	\begin{align*} y x -1+\left (x^{2}-y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.176
20927	22040	\begin{align*} y^{\prime }&=\frac {-y+x y^{2}}{x} \\ \end{align*}	✓	✓	✓	✓	5.177
20928	24327	\begin{align*} y^{\prime }&=1+6 x \,{\mathrm e}^{x -y} \\ \end{align*}	✓	✓	✓	✓	5.177
20929	27208	\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}	✓	✓	✓	✓	5.177
20930	22071	\begin{align*} y^{\prime }-\frac {3 y}{x^{2}}&=\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.180
20931	1643	\begin{align*} y^{\prime }&=\frac {y^{2}+2 y x}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.181
20932	2843	\begin{align*} x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	5.181
20933	25845	\begin{align*} 2 x \cos \left (y\right )-{\mathrm e}^{x}-x^{2} \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.181
20934	17202	\begin{align*} t -\sin \left (t \right ) y+\left (y^{6}+\cos \left (t \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.183
20935	51	\begin{align*} y^{\prime }&=x y^{3} \\ \end{align*}	✓	✓	✓	✓	5.185
20936	14665	\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+4 y^{\prime \prime }+3 y^{\prime }+y&=x^{2} {\mathrm e}^{-x}+3 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	5.185
20937	21579	\begin{align*} y^{\prime \prime }-2 a y^{\prime }+\left (a^{2}+b^{2}\right ) y&=f \left (x \right ) \\ y \left (x_{0} \right ) &= y_{0} \\ y^{\prime }\left (x_{0} \right ) &= y_{1} \\ \end{align*}	✓	✓	✓	✓	5.185
20938	2509	\begin{align*} 2 t \sin \left (y\right )+{\mathrm e}^{t} y^{3}+\left (\cos \left (y\right ) t^{2}+3 \,{\mathrm e}^{t} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.187
20939	36	\begin{align*} y^{\prime }&=x^{2}-y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✗	✓	✓	✗	5.189
20940	18617	\begin{align*} 1&=\left (3 \,{\mathrm e}^{y}-2 x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	5.189
20941	13451	\begin{align*} y^{\prime }&=f \left (x \right )+x f \left (x \right ) y+y^{2} \\ \end{align*}	✓	✓	✓	✗	5.190
20942	19927	\begin{align*} \cos \left (x \right )^{2} y^{\prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	5.191
20943	14513	\begin{align*} \cos \left (y\right ) y^{\prime }+\frac {\sin \left (y\right )}{x}&=1 \\ \end{align*}	✓	✓	✓	✓	5.192
20944	1156	\begin{align*} y^{\prime }&=\frac {t y \left (4-y\right )}{t +1} \\ \end{align*}	✓	✓	✓	✓	5.194
20945	3491	\begin{align*} -\frac {{y^{\prime }}^{2}}{y^{2}}+\frac {y^{\prime \prime }}{y}+\frac {2 a \coth \left (2 a x \right ) y^{\prime }}{y}&=2 a^{2} \\ \end{align*}	✗	✓	✓	✗	5.196
20946	5745	\begin{align*} \left (-x^{2}+a \right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	5.197
20947	11437	\begin{align*} x^{2} y^{\prime }-y^{2}-y x -x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.197
20948	15375	\begin{align*} 3 y^{2} y^{\prime }-a y^{3}-x -1&=0 \\ \end{align*}	✓	✓	✓	✓	5.197
20949	22037	\begin{align*} y-x y^{2}+\left (x^{2} y^{2}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.197
20950	15327	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\ \end{align*}	✓	✓	✓	✓	5.198
20951	21819	\begin{align*} y \,{\mathrm e}^{2 x}-3 x \,{\mathrm e}^{2 y}+\left (\frac {{\mathrm e}^{2 x}}{2}-3 x^{2} {\mathrm e}^{2 y}-{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.198
20952	24315	\begin{align*} y \left (x^{2} y^{2}+x^{2}+y^{2}\right )+x \left (x^{2}+y^{2}-x^{2} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.198
20953	16323	\begin{align*} 1+y^{4}+x y^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.201
20954	4524	\begin{align*} y^{\prime \prime }+4 y&=8 \left (t^{2}+t -1\right ) \operatorname {Heaviside}\left (t -2\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	5.202
20955	6894	\begin{align*} \frac {-x y^{\prime }+y}{y^{\prime }+y^{2}}&=\frac {-x y^{\prime }+y}{1+x^{2} y^{\prime }} \\ \end{align*}	✓	✓	✓	✓	5.202
20956	20240	\begin{align*} 3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.202
20957	14254	\begin{align*} x^{\prime }+\frac {5 x}{t}&=t +1 \\ x \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.203
20958	26288	\begin{align*} x \ln \left (x \right ) y^{\prime }-\left (1+\ln \left (x \right )\right ) y+\frac {\sqrt {x}\, \left (2+\ln \left (x \right )\right )}{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.204
20959	26325	\begin{align*} \sin \left (y\right )+y \sin \left (x \right )+\frac {1}{x}+\left (x \cos \left (y\right )-\cos \left (x \right )+\frac {1}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.205
20960	2853	\begin{align*} \sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.207
20961	9003	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.208
20962	17730	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (16 x^{2}-25\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	5.209
20963	9925	\begin{align*} 2 x y^{\prime \prime }+6 y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.211
20964	5350	\begin{align*} \left ({\mathrm e}^{x}+x \,{\mathrm e}^{y}\right ) y^{\prime }+y \,{\mathrm e}^{x}+{\mathrm e}^{y}&=0 \\ \end{align*}	✓	✓	✓	✗	5.217
20965	8342	\begin{align*} x y^{\prime }&=4 y \\ \end{align*}	✓	✓	✓	✓	5.218
20966	12180	\begin{align*} y^{\prime }&=\frac {2 a \left (-y^{2}+4 a x -1\right )}{-y^{3}+4 a x y-y-2 y^{6} a +24 y^{4} a^{2} x -96 y^{2} a^{3} x^{2}+128 a^{4} x^{3}} \\ \end{align*}	✓	✓	✓	✗	5.218
20967	18482	\begin{align*} y^{\prime }&=\frac {\sec \left (x \right )^{2}}{y^{3}+1} \\ \end{align*}	✓	✓	✓	✗	5.218
20968	8653	\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=\left (1-\operatorname {Heaviside}\left (t -10\right )\right ) {\mathrm e}^{t}-{\mathrm e}^{10} \delta \left (t -10\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✗	✓	5.219
20969	13992	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-2 \left (x +1\right ) y&=y^{{5}/{2}} \\ \end{align*}	✓	✓	✓	✗	5.220
20970	19852	\begin{align*} e y^{\prime \prime }&=P \left (a -y\right ) \\ \end{align*}	✓	✓	✓	✓	5.223
20971	11836	\begin{align*} {y^{\prime }}^{r}-a y^{s}-b \,x^{\frac {r s}{r -s}}&=0 \\ \end{align*}	✓	✓	✓	✗	5.224
20972	18931	\begin{align*} y^{\prime \prime }+4 y&=\operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	5.224
20973	17314	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{5 t}}{y^{4}} \\ \end{align*}	✓	✓	✓	✓	5.225
20974	18487	\begin{align*} x +y y^{\prime } {\mathrm e}^{-x}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.227
20975	20753	\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=\frac {1}{\left (1-x \right )^{2}} \\ \end{align*}	✓	✓	✓	✗	5.227
20976	27522	\begin{align*} \left (x +y\right ) \left (-y x +1\right )+\left (x +2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.228
20977	9121	\begin{align*} -x y^{\prime }+y&=y^{\prime } y^{2} {\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✓	5.229
20978	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*}	✓	✓	✓	✓	5.230
20979	4919	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=n \left (y^{2}-2 y x +1\right ) \\ \end{align*}	✗	✓	✓	✗	5.230
20980	19101	\begin{align*} y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.230
20981	17092	\begin{align*} \frac {x -2}{x^{2}-4 x +3}&=\frac {\left (1-\frac {1}{y}\right )^{2} y^{\prime }}{y^{2}} \\ \end{align*}	✓	✓	✓	✗	5.234
20982	23150	\begin{align*} y^{\prime }&=\frac {\left (-x +a \right ) y}{d \,x^{2}+c x +b} \\ \end{align*}	✓	✓	✓	✓	5.235
20983	5864	\begin{align*} a \cos \left (x \right )^{2} y+\tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.237
20984	21770	\begin{align*} {y^{\prime }}^{2} x -3 y y^{\prime }+9 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	5.237
20985	7228	\begin{align*} \left (y x +x \right ) y^{\prime }+y&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.238
20986	20275	\begin{align*} y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}&=1 \\ \end{align*}	✓	✓	✓	✓	5.238
20987	14035	\begin{align*} \left (x^{2}+y^{2}\right ) \left (y y^{\prime }+x \right )&=\left (x^{2}+y^{2}+x \right ) \left (x y^{\prime }-y\right ) \\ \end{align*}	✗	✓	✓	✗	5.239
20988	24976	\begin{align*} \frac {\left (u^{2}+1\right ) y^{\prime }}{y}&=u \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	5.239
20989	16358	\begin{align*} 1-\left (x +2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.242
20990	6510	\begin{align*} 4 y y^{\prime }-4 {y^{\prime }}^{2} x +x y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.243
20991	4768	\begin{align*} x y^{\prime }+\left (b x +a \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	5.244
20992	20239	\begin{align*} \left (\sin \left (y\right )+y \cos \left (y\right )\right ) y^{\prime }-\left (2 \ln \left (x \right )+1\right ) x&=0 \\ \end{align*}	✓	✓	✓	✓	5.245
20993	1175	\begin{align*} y^{\prime }&=2 t y^{2} \\ \end{align*}	✓	✓	✓	✓	5.247
20994	22002	\begin{align*} \sin \left (x \right )+y y^{\prime }&=0 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	5.247
20995	2862	\begin{align*} \sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.248
20996	4307	\begin{align*} y^{\prime }&=\frac {x^{3} {\mathrm e}^{x^{2}}}{\ln \left (y\right ) y} \\ \end{align*}	✓	✓	✓	✓	5.249
20997	19343	\begin{align*} y^{\prime }+y&=2 x \,{\mathrm e}^{-x}+x^{2} \\ \end{align*}	✓	✓	✓	✓	5.249
20998	25614	\begin{align*} y^{\prime }-a y&={\mathrm e}^{i \omega t} \\ \end{align*}	✓	✓	✓	✓	5.249
20999	20768	\begin{align*} y+3 x y^{\prime }+2 y {y^{\prime }}^{2}+\left (x^{2}+2 y^{2} y^{\prime }\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	5.251
21000	5280	\begin{align*} x^{2} \left (y+a \right )^{2} y^{\prime }&=\left (x^{2}+1\right ) \left (y^{2}+a^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	5.252