2.3.119 Problems 11801 to 11900

Table 2.769: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
11801	1337	\begin{align*} y^{\prime \prime }+y&=\tan \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.855
11802	5536	\begin{align*} x^{4} {y^{\prime }}^{2}+y^{\prime } y^{2} x -y^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	1.855
11803	8686	\begin{align*} y^{\prime }&=\cos \left (x -y-1\right ) \\ \end{align*}	✓	✓	✓	✓	1.855
11804	19978	\begin{align*} 4 y&={y^{\prime }}^{2}+x^{2} \\ \end{align*}	✓	✓	✓	✗	1.855
11805	24977	\begin{align*} t y-\left (t +2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.855
11806	25730	\begin{align*} y^{\prime }&=x -2 y \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	1.855
11807	1341	\begin{align*} y^{\prime \prime }+y&=2 \sec \left (\frac {t}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	1.856
11808	17816	\begin{align*} x^{\prime \prime }+x&=\cos \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.856
11809	18521	\begin{align*} y+2 y^{\prime }&=3 t^{2} \\ \end{align*}	✓	✓	✓	✓	1.856
11810	5199	\begin{align*} 2 y y^{\prime } x^{3}+a +3 y^{2} x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.857
11811	15870	\begin{align*} y^{\prime }&=\cos \left (y\right ) \\ y \left (0\right ) &= -\frac {\pi }{2} \\ \end{align*}	✓	✓	✓	✗	1.858
11812	1126	\begin{align*} \frac {y}{4}+y^{\prime }&=3+2 \cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.859
11813	4767	\begin{align*} y^{\prime } x +x +\left (a x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.859
11814	5500	\begin{align*} x^{2} {y^{\prime }}^{2}+2 a x y^{\prime }+a^{2}+x^{2}-2 a y&=0 \\ \end{align*}	✓	✓	✓	✗	1.859
11815	15164	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.859
11816	16372	\begin{align*} 2 y+y^{\prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.859
11817	18877	\begin{align*} t^{2} y^{\prime \prime }-2 y&=3 t^{2}-1 \\ \end{align*}	✓	✓	✓	✓	1.859
11818	20228	\begin{align*} x^{2} y^{\prime }+y&=1 \\ \end{align*}	✓	✓	✓	✓	1.859
11819	14922	\begin{align*} \theta ^{\prime \prime }+4 \theta &=0 \\ \theta \left (0\right ) &= 0 \\ \theta ^{\prime }\left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	1.861
11820	19458	\begin{align*} y^{\prime \prime }-f \left (x \right ) y^{\prime }+\left (f \left (x \right )-1\right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	1.861
11821	19997	\begin{align*} a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	1.861
11822	1225	\begin{align*} y^{\prime } x +2 y&=\frac {\sin \left (x \right )}{x} \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.862
11823	14845	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.862
11824	22355	\begin{align*} y^{\prime }&=\sqrt {-x +y}+1 \\ \end{align*}	✓	✓	✓	✓	1.862
11825	3607	\begin{align*} y^{\prime }&=\frac {2 \sqrt {-1+y}}{3} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.863
11826	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*}	✓	✓	✓	✗	1.863
11827	15762	\begin{align*} y_{1}^{\prime }&=2 y_{1}+y_{2} \\ y_{2}^{\prime }&=-y_{1}+2 y_{2} \\ y_{3}^{\prime }&=3 y_{3}-4 y_{4} \\ y_{4}^{\prime }&=4 y_{3}+3 y_{4} \\ \end{align*}	✓	✓	✓	✓	1.863
11828	10032	\begin{align*} f^{\prime }&=\frac {1}{f} \\ \end{align*}	✓	✓	✓	✓	1.865
11829	167	\begin{align*} y^{\prime }+y^{2}&=x^{2}+1 \\ \end{align*}	✓	✓	✓	✗	1.866
11830	3291	\begin{align*} y^{2} {y^{\prime }}^{2}-2 y y^{\prime } x +2 y^{2}&=x^{2} \\ \end{align*}	✓	✓	✓	✗	1.866
11831	4194	\begin{align*} y^{\prime }+y \ln \left (x \right )&=x^{-x} \\ \end{align*}	✓	✓	✓	✓	1.867
11832	20276	\begin{align*} y^{\prime }+\frac {2 y}{x}&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.867
11833	21987	\begin{align*} y^{\prime }&=y x +1 \\ \end{align*}	✓	✓	✓	✓	1.867
11834	22325	\begin{align*} 1+{y^{\prime }}^{2}+2 y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.867
11835	25778	\begin{align*} y^{\prime }&=-y x +1 \\ y \left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	1.867
11836	103	\begin{align*} y^{\prime }+p \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.868
11837	6039	\begin{align*} -2 y+a \,x^{2} y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.868
11838	19150	\begin{align*} x y y^{\prime \prime }+x {y^{\prime }}^{2}-y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.868
11839	2434	\begin{align*} t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.869
11840	8877	\begin{align*} y^{\prime } x +y&=3 x^{3}-1 \\ \end{align*}	✓	✓	✓	✓	1.869
11841	12354	\begin{align*} 4 y^{\prime \prime }+4 \tan \left (x \right ) y^{\prime }-\left (5 \tan \left (x \right )^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.869
11842	8344	\begin{align*} y^{\prime }&={\mathrm e}^{3 x +2 y} \\ \end{align*}	✓	✓	✓	✓	1.871
11843	9718	\begin{align*} \left (x +y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\ \end{align*}	✓	✓	✓	✓	1.871
11844	10373	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.871
11845	16723	\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	1.871
11846	20735	\begin{align*} y^{2} \left (1+{y^{\prime }}^{2}\right )&=r^{2} \\ \end{align*}	✓	✓	✓	✓	1.871
11847	25302	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ 6 & 1\le t <3 \\ 0 & 3\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	1.871
11848	25544	\begin{align*} y^{\prime \prime }&=\operatorname {Direct}_{t} \\ \end{align*}	✓	✓	✓	✓	1.871
11849	2966	\begin{align*} y^{2} x^{\prime }+\left (y^{2}+2 y \right ) x&=1 \\ \end{align*}	✓	✓	✓	✓	1.872
11850	8682	\begin{align*} y^{\prime }&=\cos \left (x -y\right ) \\ \end{align*}	✓	✓	✓	✓	1.872
11851	10421	\begin{align*} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.872
11852	13687	\begin{align*} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (a x +b -c \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.872
11853	25405	\begin{align*} y^{\prime }+9 y&=90 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.872
11854	15857	\begin{align*} y^{\prime }&=\frac {1}{\left (1+y\right ) \left (-2+t \right )} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.873
11855	15930	\begin{align*} y^{\prime }&=y+4 \cos \left (t^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	1.873
11856	3165	\begin{align*} y^{\prime \prime }+y&=\tan \left (\frac {x}{3}\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.874
11857	10231	\begin{align*} y^{\prime \prime }&=\left (x^{2}+3\right ) y \\ \end{align*}	✓	✓	✓	✗	1.874
11858	14239	\begin{align*} \frac {x^{\prime }+t x^{\prime \prime }}{t}&=-2 \\ \end{align*}	✓	✓	✓	✓	1.874
11859	5079	\begin{align*} 2 y y^{\prime }&=x y^{2}+x^{3} \\ \end{align*}	✓	✓	✓	✓	1.875
11860	15339	\begin{align*} y-a +x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.875
11861	1149	\begin{align*} y^{\prime }&=\frac {3 x^{2}+1}{-6 y+3 y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.876
11862	5578	\begin{align*} y^{2} {y^{\prime }}^{2}-2 y y^{\prime } x -x^{2}+2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.876
11863	609	\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=2 x_{3} \\ x_{3}^{\prime }&=3 x_{4} \\ x_{4}^{\prime }&=4 x_{1} \\ \end{align*}	✓	✓	✓	✓	1.877
11864	16157	\begin{align*} y^{\prime \prime }&=\frac {x +1}{x -1} \\ \end{align*}	✓	✓	✓	✓	1.877
11865	4123	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.878
11866	4741	\begin{align*} y^{\prime }&=f \left (x \right ) g \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	1.878
11867	6593	\begin{align*} \left (1+{y^{\prime }}^{2}+y y^{\prime \prime }\right )^{2}&=\left (1+{y^{\prime }}^{2}\right )^{3} \\ \end{align*}	✓	✓	✓	✗	1.878
11868	14900	\begin{align*} z^{\prime }&=z \tan \left (y \right )+\sin \left (y \right ) \\ \end{align*}	✓	✓	✓	✓	1.878
11869	48	\begin{align*} y^{\prime }&=2 x \sec \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	1.879
11870	23162	\begin{align*} y^{\prime }-\frac {x}{x^{2}+1}&=-\frac {x y}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	1.879
11871	31	\begin{align*} y^{\prime }&=\sqrt {x -y} \\ y \left (2\right ) &= 2 \\ \end{align*}	✓	✓	✗	✓	1.881
11872	4653	\begin{align*} y^{\prime }+f \left (x \right )^{2}&=f^{\prime }\left (x \right )+y^{2} \\ \end{align*}	✓	✓	✗	✗	1.881
11873	19055	\begin{align*} x_{1}^{\prime }&=-8 x_{1}-16 x_{2}-16 x_{3}-17 x_{4} \\ x_{2}^{\prime }&=-2 x_{1}-10 x_{2}-8 x_{3}-7 x_{4} \\ x_{3}^{\prime }&=-2 x_{1}-2 x_{3}-3 x_{4} \\ x_{4}^{\prime }&=6 x_{1}+14 x_{2}+14 x_{3}+14 x_{4} \\ \end{align*}	✓	✓	✓	✓	1.881
11874	7393	\begin{align*} x^{\prime }-x^{3}&=x \\ \end{align*}	✓	✓	✓	✓	1.882
11875	14033	\begin{align*} \left (1-x \right ) y-x \left (1+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.882
11876	15161	\begin{align*} y^{\prime \prime } x +\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✗	✗	1.882
11877	91	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.883
11878	7211	\begin{align*} y^{\prime \prime }+q y^{\prime }&=\frac {2 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	1.883
11879	12011	\begin{align*} y^{\prime }&=\frac {y \left (x -y\right )}{x \left (x -y^{3}\right )} \\ \end{align*}	✓	✓	✓	✗	1.883
11880	19758	\begin{align*} 5 x^{\prime }+x&=\sin \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.883
11881	23132	\begin{align*} y^{\prime }&=y x \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.883
11882	23200	\begin{align*} x^{2}-y^{2}+x +2 y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.883
11883	8464	\begin{align*} y^{\prime }+{\mathrm e}^{x} y&=1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.884
11884	11710	\begin{align*} x {y^{\prime }}^{2}-2 y y^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✓	1.884
11885	25212	\begin{align*} \sin \left (t \right ) y^{\prime \prime }+y&=\cos \left (t \right ) \\ y \left (\frac {\pi }{2}\right ) &= y_{1} \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= y_{1} \\ \end{align*}	✗	✗	✗	✗	1.884
11886	9814	\begin{align*} 4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9&=0 \\ \end{align*}	✓	✓	✓	✗	1.885
11887	13223	\begin{align*} a \,x^{2} \left (x -1\right )^{2} \left (y^{\prime }+\lambda y^{2}\right )+b \,x^{2}+c x +s&=0 \\ \end{align*}	✓	✓	✗	✗	1.885
11888	15035	\begin{align*} y^{\prime }-\frac {y}{x +1}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.885
11889	20494	\begin{align*} x^{2} y^{\prime \prime }+y&=3 x^{2} \\ \end{align*}	✓	✓	✓	✓	1.885
11890	24883	\begin{align*} y^{\prime \prime }-x {y^{\prime }}^{2}&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	1.886
11891	92	\begin{align*} y^{\prime }&=1+x +y+y x \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.887
11892	3329	\begin{align*} y&=y^{\prime } x -{y^{\prime }}^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✗	1.887
11893	23143	\begin{align*} \left (x^{2}+4\right ) y^{\prime }+3 y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.887
11894	15376	\begin{align*} \left (x^{2} y^{3}+y x \right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	1.888
11895	8318	\begin{align*} y^{\prime }&=y-\cos \left (\frac {\pi x}{2}\right ) \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.889
11896	8469	\begin{align*} y+\left (2 x +y x -3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.889
11897	8718	\begin{align*} y {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	1.889
11898	4897	\begin{align*} \left (x^{2}+1\right ) y^{\prime }-a +y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.890
11899	3583	\begin{align*} y^{\prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.891
11900	14886	\begin{align*} x^{\prime }&=t^{3} \left (1-x\right ) \\ x \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	1.891