2.3.179 Problems 17801 to 17900

Table 2.907: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
17801	755	\begin{align*} 3 y^{\prime } y^{2} x&=3 x^{4}+y^{3} \\ \end{align*}	✓	✓	✓	✓	3.324
17802	3959	\begin{align*} 3 y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	3.324
17803	5045	\begin{align*} y y^{\prime }&=a x +b x y^{2} \\ \end{align*}	✓	✓	✓	✓	3.324
17804	2485	\begin{align*} t y+\left (t^{2}+1\right ) y^{\prime }&=\left (t^{2}+1\right )^{{5}/{2}} \\ \end{align*}	✓	✓	✓	✓	3.326
17805	10163	\begin{align*} v v^{\prime }&=\frac {2 v^{2}}{r^{3}}+\frac {\lambda r}{3} \\ \end{align*}	✓	✓	✓	✓	3.326
17806	23672	\begin{align*} x^{2} y^{\prime \prime }-\left (2+x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.326
17807	7793	\begin{align*} y^{\prime }-5 y&={\mathrm e}^{x} x^{2}-x \,{\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	3.327
17808	8181	\begin{align*} 2 y+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.327
17809	19723	\begin{align*} y^{\prime }+y x&=x \\ \end{align*}	✓	✓	✓	✓	3.327
17810	12432	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y-3 x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	3.332
17811	17765	\begin{align*} y^{\prime \prime }+25 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.332
17812	22562	\begin{align*} u v-2 v+\left (-u^{2}+u \right ) v^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.332
17813	11567	\begin{align*} 2 y x +\left (a +x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.333
17814	10310	\begin{align*} {y^{\prime }}^{2}&=\frac {y^{2}}{x} \\ \end{align*}	✓	✓	✓	✓	3.334
17815	23142	\begin{align*} y^{\prime }&=x -y x -y+1 \\ \end{align*}	✓	✓	✓	✓	3.335
17816	23896	\begin{align*} 2 \cos \left (x \right ) y-1+\sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.335
17817	7753	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=\cos \left (x \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.337
17818	10327	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{x +y}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.337
17819	13003	\begin{align*} 3 \left (1-y\right ) y y^{\prime \prime }-2 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	3.337
17820	25501	\begin{align*} y^{\prime }&={\mathrm e}^{t} y \\ \end{align*}	✓	✓	✓	✓	3.337
17821	14042	\begin{align*} x^{3} y^{4}+x^{2} y^{3}+x y^{2}+y+\left (y^{3} x^{4}-x^{3} y^{2}-x^{3} y+x \right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	3.338
17822	14198	\begin{align*} 2 t x^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	3.339
17823	14419	\begin{align*} y^{\prime }+3 y&=3 x^{2} {\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	3.339
17824	1003	\begin{align*} x_{1}^{\prime }&=9 x_{1}+13 x_{2}-13 x_{6} \\ x_{2}^{\prime }&=-14 x_{1}+19 x_{2}-10 x_{3}-20 x_{4}+10 x_{5}+4 x_{6} \\ x_{3}^{\prime }&=-30 x_{1}+12 x_{2}-7 x_{3}-30 x_{4}+12 x_{5}+18 x_{6} \\ x_{4}^{\prime }&=-12 x_{1}+10 x_{2}-10 x_{3}-9 x_{4}+10 x_{5}+2 x_{6} \\ x_{5}^{\prime }&=6 x_{1}+9 x_{2}+6 x_{4}+5 x_{5}-15 x_{6} \\ x_{6}^{\prime }&=-14 x_{1}+23 x_{2}-10 x_{3}-20 x_{4}+10 x_{5} \\ \end{align*}	✓	✓	✓	✓	3.340
17825	5588	\begin{align*} \left (x +y\right )^{2} {y^{\prime }}^{2}-\left (x^{2}-y x -2 y^{2}\right ) y^{\prime }-y \left (x -y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.340
17826	11440	\begin{align*} x^{2} \left (y^{\prime }+y^{2}\right )+a x y+b&=0 \\ \end{align*}	✓	✓	✓	✓	3.340
17827	16283	\begin{align*} y x +x^{2} y^{\prime }&=\sqrt {x}\, \sin \left (x \right ) \\ y \left (2\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	3.342
17828	5329	\begin{align*} x^{3} \left (1+5 x^{3} y^{7}\right ) y^{\prime }+\left (3 x^{5} y^{5}-1\right ) y^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	3.343
17829	15339	\begin{align*} y-a +x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.343
17830	20390	\begin{align*} {y^{\prime }}^{3}-x^{4} a&=0 \\ \end{align*}	✓	✓	✓	✓	3.343
17831	22059	\begin{align*} y^{\prime }+\frac {4 y}{x}&=x^{4} \\ \end{align*}	✓	✓	✓	✓	3.343
17832	3220	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	3.344
17833	11431	\begin{align*} 3 y^{\prime } x -3 x y^{4} \ln \left (x \right )-y&=0 \\ \end{align*}	✓	✓	✓	✓	3.344
17834	2486	\begin{align*} 4 t y+\left (t^{2}+1\right ) y^{\prime }&=t \\ y \left (1\right ) &= {\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	3.345
17835	8455	\begin{align*} y^{\prime }+\tan \left (x \right ) y&=\cos \left (x \right )^{2} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.345
17836	19255	\begin{align*} y^{\prime }+\tan \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.345
17837	5650	\begin{align*} 4 {y^{\prime }}^{3} x -6 y {y^{\prime }}^{2}-x +3 y&=0 \\ \end{align*}	✓	✓	✓	✗	3.346
17838	16272	\begin{align*} y^{\prime } x&=\sqrt {x}+3 y \\ \end{align*}	✓	✓	✓	✓	3.346
17839	4192	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.347
17840	11320	\begin{align*} y^{\prime }-y^{2}-y x -x +1&=0 \\ \end{align*}	✓	✓	✓	✗	3.349
17841	16202	\begin{align*} y^{3}-25 y+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.349
17842	17156	\begin{align*} y^{\prime }-y x&=x \\ \end{align*}	✓	✓	✓	✓	3.349
17843	22378	\begin{align*} x^{2}+y \sin \left (y x \right )+x \sin \left (y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.349
17844	20861	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +3 y&=0 \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.350
17845	1853	\begin{align*} x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.351
17846	13935	\begin{align*} y^{\prime \prime }-y^{\prime }+\left (a \,{\mathrm e}^{3 \lambda x}+b \,{\mathrm e}^{2 \lambda x}+\frac {1}{4}-\frac {\lambda ^{2}}{4}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.351
17847	11322	\begin{align*} y^{\prime }-y^{2}+\left (x^{2}+1\right ) y-2 x&=0 \\ \end{align*}	✓	✓	✓	✗	3.352
17848	16685	\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=64 \ln \left (x \right ) x^{2} \\ \end{align*}	✓	✓	✓	✓	3.352
17849	19180	\begin{align*} \sin \left (x \right )^{2} y^{\prime \prime }+\cos \left (x \right ) \sin \left (x \right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✗	3.352
17850	23889	\begin{align*} \frac {y^{5} x^{2}+y^{2}+y}{1+x^{2} y^{4}}+\frac {\left (x^{3} y^{4}+2 y x +x \right ) y^{\prime }}{1+x^{2} y^{4}}&=0 \\ \end{align*}	✓	✓	✓	✗	3.352
17851	3643	\begin{align*} y^{\prime }&=\frac {y^{2}+2 y x -2 x^{2}}{x^{2}-y x +y^{2}} \\ \end{align*}	✓	✓	✓	✗	3.353
17852	8424	\begin{align*} y^{\prime }+3 x^{2} y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	3.353
17853	24110	\begin{align*} y^{\prime \prime } x +2 y^{\prime }-3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.353
17854	44	\begin{align*} \left (x +1\right ) y^{\prime }&=4 y \\ \end{align*}	✓	✓	✓	✓	3.355
17855	17945	\begin{align*} y^{\prime }-y&=-2 \,{\mathrm e}^{-x} \\ y \left (\infty \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.355
17856	26386	\begin{align*} 2 x y \,{\mathrm e}^{x^{2}}-x \sin \left (x \right )+{\mathrm e}^{x^{2}} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.355
17857	3780	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +5 y&=0 \\ y \left (1\right ) &= \sqrt {2} \\ y^{\prime }\left (1\right ) &= 3 \sqrt {2} \\ \end{align*}	✓	✓	✓	✓	3.356
17858	22055	\begin{align*} x^{3} y^{2}-y+\left (x^{2} y^{4}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.356
17859	7373	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.358
17860	7556	\begin{align*} t +x+3+x^{\prime }&=0 \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.358
17861	20458	\begin{align*} 3 y&=2 y^{\prime } x -\frac {2 {y^{\prime }}^{2}}{x} \\ \end{align*}	✓	✓	✓	✗	3.358
17862	25721	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.358
17863	4613	\begin{align*} y^{\prime }&=a \sin \left (b x +c \right )+k y \\ \end{align*}	✓	✓	✓	✓	3.359
17864	7128	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.360
17865	5253	\begin{align*} x \left (x^{2}+y^{2}\right ) y^{\prime }&=\left (x^{2}+x^{4}+y^{2}\right ) y \\ \end{align*}	✓	✓	✓	✗	3.361
17866	3984	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=4 \sin \left (t \right )+\delta \left (t -\frac {\pi }{6}\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.362
17867	11782	\begin{align*} \left (\left (1-a \right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a x y y^{\prime }+x^{2}+\left (1-a \right ) y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.362
17868	14501	\begin{align*} {\mathrm e}^{x} \left (y-3 \left ({\mathrm e}^{x}+1\right )^{2}\right )+\left ({\mathrm e}^{x}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	3.362
17869	17155	\begin{align*} y^{\prime }+y x&=x^{3} \\ \end{align*}	✓	✓	✓	✓	3.362
17870	6481	\begin{align*} 2 y y^{\prime \prime }&=4 y^{2}+3 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	3.364
17871	8749	\begin{align*} x \left (2-9 x y^{2}\right )+y \left (4 y^{2}-6 x^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.364
17872	21624	\begin{align*} y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.364
17873	14430	\begin{align*} y^{\prime }+y&=2 x \,{\mathrm e}^{-x} \\ y \left (-1\right ) &= {\mathrm e}+3 \\ \end{align*}	✓	✓	✓	✓	3.365
17874	20446	\begin{align*} \left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }&=3 x y^{2}-x^{2} \\ \end{align*}	✓	✓	✓	✗	3.365
17875	20691	\begin{align*} a^{2}-2 y x -y^{2}-\left (x +y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.365
17876	4651	\begin{align*} y^{\prime }&=f \left (x \right )+g \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	3.366
17877	21918	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-2 y^{\prime }+y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= -3 \\ y^{\prime \prime \prime }\left (0\right ) &= -5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.366
17878	1669	\begin{align*} 3 y^{\prime } y^{2} x&=y^{3}+x \\ \end{align*}	✓	✓	✓	✓	3.367
17879	3539	\begin{align*} 1-\sin \left (x \right ) y-\cos \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.367
17880	14241	\begin{align*} y^{\prime }&=-y^{2} {\mathrm e}^{-t^{2}} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	3.367
17881	17063	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	3.369
17882	21970	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	3.370
17883	790	\begin{align*} y^{\prime } x +3 y&=\frac {3}{x^{{3}/{2}}} \\ \end{align*}	✓	✓	✓	✓	3.372
17884	8783	\begin{align*} 3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.372
17885	5864	\begin{align*} a \cos \left (x \right )^{2} y+\tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.373
17886	2836	\begin{align*} y^{\prime \prime }-\lambda y&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime }\left (L \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.375
17887	15927	\begin{align*} y^{\prime }&=\sin \left (t \right ) y+4 \\ \end{align*}	✓	✓	✓	✓	3.375
17888	18956	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+17 y&=g \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.375
17889	10319	\begin{align*} y^{\prime }&=\left (1+6 x +y\right )^{{1}/{3}} \\ \end{align*}	✓	✓	✓	✓	3.376
17890	11664	\begin{align*} {y^{\prime }}^{2}+a^{2} y^{2} \left (\ln \left (y\right )^{2}-1\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.376
17891	9195	\begin{align*} \sec \left (x \right ) y^{\prime }&=\sec \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	3.377
17892	15902	\begin{align*} y^{\prime }&=2 y+\sin \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	3.377
17893	16304	\begin{align*} y^{\prime }+\frac {y}{x}&=x^{2} y^{3} \\ \end{align*}	✓	✓	✓	✓	3.377
17894	22150	\begin{align*} y^{\prime }+\frac {4 y}{x}&=x^{4} \\ \end{align*}	✓	✓	✓	✓	3.379
17895	7325	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=2 x \\ \end{align*}	✓	✓	✓	✓	3.381
17896	23740	\begin{align*} \left (x -1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	3.381
17897	3223	\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +10 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.382
17898	14233	\begin{align*} x^{\prime }&=\frac {\left (4+2 t \right ) x}{\ln \left (x\right )} \\ x \left (0\right ) &= {\mathrm e} \\ \end{align*}	✓	✓	✓	✓	3.382
17899	26052	\begin{align*} {y^{\prime }}^{3}&=x^{4} a \\ \end{align*}	✓	✓	✓	✓	3.382
17900	737	\begin{align*} x^{2} y^{\prime }&=y x +y^{2} \\ \end{align*}	✓	✓	✓	✓	3.383