2.3.199 Problems 19801 to 19900

Table 2.929: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
19801	7245	\begin{align*} 3 y^{2} y^{\prime } x +3 y^{3}&=1 \\ \end{align*}	✓	✓	✓	✓	2.970
19802	18624	\begin{align*} \left (-x +2\right ) y^{\prime }&=y+2 \left (-x +2\right )^{5} \\ \end{align*}	✓	✓	✓	✓	2.970
19803	19994	\begin{align*} x y^{2} \left ({y^{\prime }}^{2}+2\right )&=2 y^{3} y^{\prime }+x^{3} \\ \end{align*}	✓	✓	✓	✓	2.971
19804	23890	\begin{align*} 3 x -2 y+2 y^{2}+\left (2 y x -x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.971
19805	19341	\begin{align*} y^{\prime }+y&=\frac {1}{{\mathrm e}^{2 x}+1} \\ \end{align*}	✓	✓	✓	✓	2.972
19806	162	\begin{align*} y^{\prime } x -4 x^{2} y+2 y \ln \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.974
19807	2930	\begin{align*} 2 y \sin \left (y x \right )+\left (2 x \sin \left (y x \right )+y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.975
19808	7249	\begin{align*} x^{2} y^{\prime }+y^{2}-y x&=0 \\ \end{align*}	✓	✓	✓	✓	2.976
19809	14269	\begin{align*} x^{\prime }&=-\frac {x}{t}+\frac {1}{t x^{2}} \\ \end{align*}	✓	✓	✓	✓	2.976
19810	23972	\begin{align*} y^{\prime }-y x&=-x^{5}+4 x^{3} \\ \end{align*}	✓	✓	✓	✓	2.976
19811	8359	\begin{align*} \left ({\mathrm e}^{x}+{\mathrm e}^{-x}\right ) y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	2.979
19812	14911	\begin{align*} {\mathrm e}^{-y} \sec \left (x \right )+2 \cos \left (x \right )-{\mathrm e}^{-y} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.979
19813	19423	\begin{align*} x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y x&=1 \\ \end{align*}	✓	✓	✓	✓	2.979
19814	9597	\begin{align*} \left ({\mathrm e}^{x}-1-x \right ) y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	2.981
19815	21612	\begin{align*} \left (2+x \right ) y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	2.981
19816	9935	\begin{align*} 9 x^{2} y^{\prime \prime }-15 y^{\prime } x +7 \left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.984
19817	8788	\begin{align*} y^{\prime }&=-\frac {y}{t}-1-y^{2} \\ \end{align*}	✓	✓	✓	✗	2.985
19818	25743	\begin{align*} 3 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.985
19819	17937	\begin{align*} x \ln \left (x \right ) y^{\prime }-y&=3 x^{3} \ln \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.986
19820	4434	\begin{align*} y^{\prime }-6 x \,{\mathrm e}^{x -y}-1&=0 \\ \end{align*}	✓	✓	✓	✓	2.987
19821	14456	\begin{align*} y+x \left (y^{2}+x^{2}\right )^{2}+\left (y \left (y^{2}+x^{2}\right )^{2}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.988
19822	22993	\begin{align*} \sin \left (x \right ) y^{\prime }+2 y \cos \left (x \right )&=4 \cos \left (x \right )^{3} \\ y \left (\frac {\pi }{4}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.988
19823	23177	\begin{align*} y^{\prime }&=\left (1-y\right ) \left (-\frac {1}{t \ln \left (t \right )}-\frac {3}{100}+\frac {3 y}{100}\right ) \\ \end{align*}	✓	✓	✓	✓	2.988
19824	8223	\begin{align*} y^{\prime } x&=2 y \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.990
19825	13208	\begin{align*} y^{\prime }&=y^{2}-a^{2} x^{2}+3 a \\ \end{align*}	✓	✓	✓	✗	2.990
19826	5421	\begin{align*} {y^{\prime }}^{2}+a y y^{\prime }-a x&=0 \\ \end{align*}	✓	✓	✓	✗	2.991
19827	17037	\begin{align*} y^{\prime }&=y^{{1}/{5}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.991
19828	25463	\begin{align*} y^{\prime }&=y+{\mathrm e}^{2 t} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.991
19829	24972	\begin{align*} y^{\prime }&=4 t y^{2} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.992
19830	4224	\begin{align*} \cot \left (x \right ) y^{\prime }&=y \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.993
19831	7557	\begin{align*} y^{\prime }-\frac {2 y}{x}&=x^{2} \cos \left (x \right ) \\ y \left (\pi \right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.993
19832	8429	\begin{align*} y^{\prime } x +2 y&=3 \\ \end{align*}	✓	✓	✓	✓	2.994
19833	22984	\begin{align*} y^{\prime }-\frac {3 y}{x}&=5 x \\ y \left ({\mathrm e}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.995
19834	2944	\begin{align*} \left (x -x \sqrt {x^{2}-y^{2}}\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	2.996
19835	14463	\begin{align*} \left (x +4\right ) \left (1+y^{2}\right )+y \left (x^{2}+3 x +2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.996
19836	715	\begin{align*} y^{\prime } x +3 y&=2 x^{5} \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.997
19837	5917	\begin{align*} b y+\left (x +a \right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✓	✓	✗	2.997
19838	8304	\begin{align*} y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\ y \left (0\right ) &= -{\frac {5}{2}} \\ \end{align*}	✓	✓	✓	✓	2.998
19839	3455	\begin{align*} y^{\prime }&=-\cot \left (t \right ) y+6 \cos \left (t \right )^{2} \\ y \left (\frac {\pi }{4}\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.999
19840	20874	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=3 x^{2}-x \\ y \left (1\right ) &= \pi \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.999
19841	11436	\begin{align*} x^{2} y^{\prime }-y^{2}-y x&=0 \\ \end{align*}	✓	✓	✓	✓	3.000
19842	13991	\begin{align*} x^{2} y^{\prime }+\left (1-2 x \right ) y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	3.000
19843	19332	\begin{align*} -y+y^{\prime } x&=2 x^{2}-3 \\ \end{align*}	✓	✓	✓	✓	3.000
19844	17024	\begin{align*} y \cos \left (y x \right )+\sin \left (x \right )+x \cos \left (y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.001
19845	7157	\begin{align*} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.002
19846	8267	\begin{align*} y^{\prime } x +y&=2 x \\ y \left (x_{0} \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.002
19847	17980	\begin{align*} 1-x^{2} y+x^{2} \left (y-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.002
19848	21997	\begin{align*} y^{\prime } y+x&=0 \\ \end{align*}	✓	✓	✓	✓	3.002
19849	22395	\begin{align*} y^{\prime }&=\sqrt {2 x +3 y} \\ \end{align*}	✓	✓	✓	✓	3.002
19850	4663	\begin{align*} y^{\prime }&=f \left (x \right )+x f \left (x \right ) y+y^{2} \\ \end{align*}	✓	✓	✓	✗	3.003
19851	11401	\begin{align*} y^{\prime } x +x y^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✓	3.003
19852	11699	\begin{align*} x {y^{\prime }}^{2}+4 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	3.003
19853	12311	\begin{align*} y^{\prime \prime }+a y^{\prime }+b y-f \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.003
19854	25724	\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{6}\right ) &= -1 \\ \end{align*}	✓	✗	✗	✗	3.006
19855	8767	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2}+2 x \\ \end{align*}	✓	✓	✓	✓	3.007
19856	25049	\begin{align*} y^{\prime }&=\sqrt {y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.008
19857	12844	\begin{align*} y^{\prime \prime }+d +b y^{2}+c y+a y^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	3.010
19858	15797	\begin{align*} y^{\prime }&=-y^{2} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	3.010
19859	23968	\begin{align*} y^{\prime }-2 y&=x^{2}-1 \\ \end{align*}	✓	✓	✓	✓	3.010
19860	14011	\begin{align*} y^{\prime } x -y+2 x^{2} y-x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	3.011
19861	163	\begin{align*} y^{\prime }&=\frac {x -y-1}{x +y+3} \\ \end{align*}	✓	✓	✓	✓	3.012
19862	19724	\begin{align*} y^{\prime }+\frac {y}{x}&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.012
19863	14558	\begin{align*} y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✗	✓	✓	✗	3.013
19864	25719	\begin{align*} y^{\prime } x&=y \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.013
19865	11581	\begin{align*} \left (2 y-4 x +1\right )^{2} y^{\prime }-\left (y-2 x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.014
19866	12446	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (-v^{2}+x^{2}+1\right ) y-f \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	3.014
19867	7607	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 2 \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	3.016
19868	11841	\begin{align*} \sqrt {1+{y^{\prime }}^{2}}+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	3.016
19869	13972	\begin{align*} \left (x +1\right ) y^{2}-x^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.016
19870	5907	\begin{align*} \left (\operatorname {b2} x +\operatorname {b1} \right ) y+a y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✓	✓	✗	3.017
19871	22463	\begin{align*} y+\left (y^{3}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.017
19872	25011	\begin{align*} -y+y^{\prime }&=t y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.018
19873	105	\begin{align*} \left (x +y\right ) y^{\prime }&=x -y \\ \end{align*}	✓	✓	✓	✓	3.019
19874	4836	\begin{align*} \left (x +1\right ) y^{\prime }&={\mathrm e}^{x} \left (x +1\right )^{n +1}+n y \\ \end{align*}	✓	✓	✓	✓	3.020
19875	7528	\begin{align*} y^{\prime }+\frac {3 y}{x}&=x^{2}-4 x +3 \\ \end{align*}	✓	✓	✓	✓	3.020
19876	5046	\begin{align*} y^{\prime } y&=\csc \left (x \right )^{2}-y^{2} \cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.021
19877	4334	\begin{align*} y \left (2 x -y+2\right )+2 \left (x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.022
19878	7809	\begin{align*} y^{\prime }+\frac {4 y}{x}&=x^{4} \\ \end{align*}	✓	✓	✓	✓	3.022
19879	17072	\begin{align*} \frac {6}{t^{9}}-\frac {6}{t^{3}}+t^{7}+\left (9+\frac {1}{s^{2}}-4 s^{8}\right ) s^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.023
19880	20678	\begin{align*} \cot \left (y\right )-\tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.023
19881	23909	\begin{align*} y^{\prime }+x^{2} y&=\left (x^{2}+1\right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	3.023
19882	23955	\begin{align*} y^{\prime }&=\frac {y}{y-y^{3}+2 x} \\ \end{align*}	✓	✓	✓	✓	3.023
19883	3023	\begin{align*} y^{\prime }&=\cos \left (y\right ) \cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	3.024
19884	18498	\begin{align*} 2 y^{\prime } y&=\frac {x}{\sqrt {x^{2}-4}} \\ y \left (3\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.024
19885	3444	\begin{align*} y^{\prime }&=\frac {2 t y}{t^{2}+1}+t +1 \\ \end{align*}	✓	✓	✓	✓	3.025
19886	21950	\begin{align*} t y^{\prime \prime }+t^{2} y^{\prime }-\sin \left (t \right ) \sqrt {t}&=t^{2}-t +1 \\ \end{align*}	✓	✓	✓	✗	3.025
19887	16236	\begin{align*} y^{\prime }&=3 y^{2}-\sin \left (x \right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	3.026
19888	18516	\begin{align*} 2 t y+y^{\prime }&=16 t \,{\mathrm e}^{-t^{2}} \\ \end{align*}	✓	✓	✓	✓	3.026
19889	2500	\begin{align*} y^{\prime }&=\frac {2 y}{t}+\frac {y^{2}}{t^{2}} \\ \end{align*}	✓	✓	✓	✓	3.027
19890	25736	\begin{align*} y^{\prime } x&=2 y \\ \end{align*}	✓	✓	✓	✓	3.027
19891	17109	\begin{align*} 1&=y^{\prime } \cos \left (y\right ) \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✓	3.028
19892	1503	\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=k \left (\operatorname {Heaviside}\left (t -\frac {3}{2}\right )-\operatorname {Heaviside}\left (t -\frac {5}{2}\right )\right ) \\ u \left (0\right ) &= 0 \\ u^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.029
19893	4899	\begin{align*} \left (x^{2}+1\right ) y^{\prime }-a -y x&=0 \\ \end{align*}	✓	✓	✓	✓	3.029
19894	13708	\begin{align*} y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (b \,x^{2 n}+c \,x^{n -1}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.029
19895	18010	\begin{align*} y&=\arcsin \left (y^{\prime }\right )+\ln \left (1+{y^{\prime }}^{2}\right ) \\ \end{align*}	✓	✓	✓	✗	3.029
19896	19090	\begin{align*} y^{\prime }&=y^{2}+\frac {1}{x^{4}} \\ \end{align*}	✓	✓	✓	✓	3.029
19897	19983	\begin{align*} y^{2}&=a^{2} \left (1+{y^{\prime }}^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	3.029
19898	5134	\begin{align*} x y^{\prime } y+x^{2} {\mathrm e}^{-\frac {2 y}{x}}-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.030
19899	14212	\begin{align*} x^{\prime }&={\mathrm e}^{-2 x} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.033
19900	17866	\begin{align*} y^{\prime }&=-\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	3.033