2.3.149 Problems 14801 to 14900

Table 2.841: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
14801	20417	\begin{align*} y&=y^{\prime } x +\sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	1.725
14802	5855	\begin{align*} \left (-a^{2}+b^{2}\right ) y+2 a \cot \left (a x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.726
14803	18474	\begin{align*} y^{\prime }&=\frac {x^{2} \left (x^{3}+1\right )}{y} \\ \end{align*}	✓	✓	✓	✓	1.727
14804	23544	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.728
14805	3390	\begin{align*} y^{\prime \prime } x -y^{\prime } x +y&=x^{3} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.729
14806	7215	\begin{align*} y^{\prime \prime } x +3 y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.729
14807	14308	\begin{align*} x^{\prime \prime }-x^{\prime }&=6+{\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	1.729
14808	16729	\begin{align*} 4 x^{2} y^{\prime \prime }+8 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.729
14809	21987	\begin{align*} y^{\prime }&=y x +1 \\ \end{align*}	✓	✓	✓	✓	1.729
14810	81	\begin{align*} -y+y^{\prime } x&=x \\ y \left (1\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	1.730
14811	12582	\begin{align*} -6 y x -y^{\prime }+x \left (x^{2}+2\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.730
14812	15785	\begin{align*} y^{\prime }&=\frac {1}{2 y+1} \\ \end{align*}	✓	✓	✓	✓	1.730
14813	20184	\begin{align*} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=x^{5} \\ \end{align*}	✓	✓	✓	✗	1.730
14814	11873	\begin{align*} y^{\prime }&=\frac {x}{-y+F \left (x^{2}+y^{2}\right )} \\ \end{align*}	✓	✓	✓	✗	1.732
14815	2633	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.734
14816	4305	\begin{align*} y^{2} y^{\prime }&=2+3 y^{6} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.734
14817	5556	\begin{align*} \left (2 x -y\right ) {y^{\prime }}^{2}-2 \left (1-x \right ) y^{\prime }+2-y&=0 \\ \end{align*}	✓	✓	✓	✗	1.734
14818	6291	\begin{align*} \left (-a^{2}+4 b \right ) y+12 x^{5} y^{\prime }+4 x^{6} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.734
14819	14750	\begin{align*} 2 x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}-3\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.734
14820	25231	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.734
14821	20328	\begin{align*} y^{\prime \prime }-n^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.735
14822	11871	\begin{align*} y^{\prime }&=\frac {x +F \left (-\left (x -y\right ) \left (x +y\right )\right )}{y} \\ \end{align*}	✓	✓	✓	✗	1.736
14823	13415	\begin{align*} y^{\prime }&=y^{2}+m y \cot \left (x \right )+b^{2} \sin \left (x \right )^{2 m} \\ \end{align*}	✓	✓	✓	✗	1.736
14824	14183	\begin{align*} \left (x^{2}-x \right ) y^{\prime \prime }+\left (2+4 x \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.736
14825	20	\begin{align*} y^{\prime }&=x +y \\ \end{align*}	✓	✓	✓	✓	1.737
14826	7670	\begin{align*} x^{\prime \prime }+2 \gamma x^{\prime }+\omega _{0} x&=F \cos \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	1.737
14827	8766	\begin{align*} y^{\prime \prime } x +y^{\prime } x -y&=x^{2}+2 x \\ \end{align*}	✓	✓	✓	✗	1.737
14828	12969	\begin{align*} 4 y y^{\prime \prime }-5 {y^{\prime }}^{2}+a y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.737
14829	14125	\begin{align*} y+3 y^{\prime } x +9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=\left (1+\ln \left (x \right )\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.738
14830	24253	\begin{align*} 2 y&=\left (x^{2}-1\right ) \left (1-y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	1.738
14831	25314	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=3 \delta \left (t -1\right ) \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.738
14832	5973	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=x^{2} \left (x +3\right ) \\ \end{align*}	✓	✓	✓	✓	1.739
14833	8887	\begin{align*} y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.739
14834	17387	\begin{align*} y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.739
14835	25313	\begin{align*} y^{\prime \prime }+4 y&=\delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.739
14836	19471	\begin{align*} y^{\prime \prime }&=4 y \\ \end{align*}	✓	✓	✓	✓	1.740
14837	20567	\begin{align*} 1+{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.740
14838	13806	\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime } x +b \left (a \,x^{n}-1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.741
14839	11704	\begin{align*} x {y^{\prime }}^{2}+y y^{\prime }-y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	1.742
14840	8226	\begin{align*} y^{\prime } x&=y \\ \end{align*}	✓	✓	✓	✓	1.743
14841	21333	\begin{align*} y^{\prime }&=f \left (x \right ) g \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	1.743
14842	2580	\begin{align*} t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.744
14843	16681	\begin{align*} x^{2} y^{\prime \prime }-2 y&=15 \cos \left (3 \ln \left (x \right )\right )-10 \sin \left (3 \ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	1.744
14844	19003	\begin{align*} x_{1}^{\prime }&=-5 x_{1}-2 x_{2}-x_{3}+2 x_{4}+3 x_{5} \\ x_{2}^{\prime }&=-3 x_{2} \\ x_{3}^{\prime }&=x_{1}-x_{3}-x_{5} \\ x_{4}^{\prime }&=2 x_{1}+x_{2}-4 x_{4}-2 x_{5} \\ x_{5}^{\prime }&=-3 x_{1}-2 x_{2}-x_{3}+2 x_{4}+x_{5} \\ \end{align*}	✓	✓	✓	✓	1.744
14845	25220	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.744
14846	6760	\begin{align*} 2 y a^{2} b^{2}+2 \left (a^{2}+b^{2}\right ) y^{\prime \prime }+2 y^{\prime \prime \prime \prime }&=\cos \left (a x \right )+\cos \left (b x \right ) \\ \end{align*}	✓	✓	✓	✓	1.745
14847	771	\begin{align*} x^{3}+3 y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.747
14848	11706	\begin{align*} x {y^{\prime }}^{2}-y y^{\prime }+a&=0 \\ \end{align*}	✓	✓	✓	✗	1.748
14849	13057	\begin{align*} y^{\prime \prime }-f \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	1.748
14850	2564	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.749
14851	6274	\begin{align*} B y+\left (a -x \right ) \left (b -x \right ) \left (A +2 x \right ) y^{\prime }+\left (a -x \right )^{2} \left (b -x \right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.749
14852	8141	\begin{align*} y^{\prime \prime } x +y^{\prime } x -{\mathrm e}^{x} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.749
14853	24780	\begin{align*} \left (x +y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\ \end{align*}	✓	✓	✓	✓	1.749
14854	25423	\begin{align*} y^{\prime }&=-y+\operatorname {Heaviside}\left (t -3\right )+\delta \left (t -1\right ) \\ \end{align*}	✓	✓	✓	✓	1.749
14855	3387	\begin{align*} y^{\prime \prime } x +3 y^{\prime }-y&=x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.750
14856	7571	\begin{align*} m y^{\prime \prime }+b y^{\prime }+k y&=0 \\ \end{align*}	✓	✓	✓	✓	1.750
14857	8581	\begin{align*} y^{\prime \prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.750
14858	11882	\begin{align*} y^{\prime }&=\frac {-x +F \left (x^{2}+y^{2}\right )}{y} \\ \end{align*}	✓	✓	✓	✗	1.750
14859	14336	\begin{align*} x^{\prime \prime }+\frac {x^{\prime }}{t}&=a \\ \end{align*}	✓	✓	✓	✓	1.750
14860	14749	\begin{align*} 2 x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.750
14861	12913	\begin{align*} \left (-y+y^{\prime } x \right )^{3}+x^{4} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	1.751
14862	12615	\begin{align*} y^{\prime \prime }&=-\frac {2 \left (a +x \right ) y^{\prime }}{x^{2}}-\frac {b y}{x^{4}} \\ \end{align*}	✓	✓	✓	✗	1.752
14863	8620	\begin{align*} y^{\prime \prime }+\frac {y}{4 x}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.753
14864	17997	\begin{align*} {y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x}&=0 \\ \end{align*}	✓	✓	✓	✗	1.753
14865	18807	\begin{align*} 2 x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.753
14866	2581	\begin{align*} t^{2} y^{\prime \prime }-y^{\prime } t +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.754
14867	15938	\begin{align*} y^{\prime }&=3 y \\ \end{align*}	✓	✓	✓	✓	1.755
14868	16140	\begin{align*} y^{\prime \prime }+3 y&=5 \delta \left (-2+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.755
14869	18802	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +\frac {5 y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	1.755
14870	19785	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.755
14871	25812	\begin{align*} y^{\prime }&=\frac {2 y}{\pi }-\sin \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	1.755
14872	22066	\begin{align*} y^{\prime }-7 y&=14 x \\ \end{align*}	✓	✓	✓	✓	1.756
14873	65	\begin{align*} -y+y^{\prime } x&=2 x^{2} y \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.757
14874	11567	\begin{align*} 2 y x +\left (a +x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.757
14875	5444	\begin{align*} 5 {y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	1.758
14876	7579	\begin{align*} m y^{\prime \prime }+b y^{\prime }+k y&=\cos \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	1.758
14877	14621	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=10 \sin \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.758
14878	16764	\begin{align*} y^{\prime \prime }+4 y&=3 \operatorname {Heaviside}\left (-2+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.758
14879	17525	\begin{align*} y^{\prime \prime }+9 y&=\csc \left (3 t \right ) \\ y \left (\frac {\pi }{12}\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{12}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.758
14880	19685	\begin{align*} x^{\prime }&=-\lambda x \\ \end{align*}	✓	✓	✓	✓	1.758
14881	20603	\begin{align*} y x -x^{2} y^{\prime }+y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✗	1.758
14882	21431	\begin{align*} 2 y+y^{\prime }&=0 \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	1.758
14883	11358	\begin{align*} y^{\prime }-\sqrt {{| y|}}&=0 \\ \end{align*}	✓	✓	✓	✓	1.759
14884	5974	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=3 x^{3} \\ \end{align*}	✓	✓	✓	✓	1.760
14885	124	\begin{align*} y^{2} y^{\prime }+2 x y^{3}&=6 x \\ \end{align*}	✓	✓	✓	✓	1.761
14886	19416	\begin{align*} y^{\prime } x +y x +y-1&=0 \\ \end{align*}	✓	✓	✓	✓	1.761
14887	6127	\begin{align*} \left (1-x \right )^{2} y-2 \left (1-x \right )^{2} y^{\prime }+\left (1-x \right )^{2} y^{\prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	1.762
14888	21625	\begin{align*} y^{\prime }-k y&=A \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.762
14889	52	\begin{align*} y y^{\prime }&=x \left (1+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	1.763
14890	11600	\begin{align*} \left (y^{3}-x^{3}\right ) y^{\prime }-x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.763
14891	3779	\begin{align*} x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+m^{2} y&=x^{m} \ln \left (x \right )^{k} \\ \end{align*}	✓	✓	✓	✓	1.765
14892	19876	\begin{align*} x&={y^{\prime }}^{2}+y \\ \end{align*}	✓	✓	✓	✓	1.765
14893	91	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.766
14894	6537	\begin{align*} \left (1+y^{2}\right ) y^{\prime \prime }&=\left (a +3 y\right ) {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.766
14895	13696	\begin{align*} y^{\prime \prime }+\left (a \,x^{2}+2 b \right ) y^{\prime }+\left (a b \,x^{2}-a x +b^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.766
14896	16591	\begin{align*} 9 y+6 y^{\prime }+y^{\prime \prime }&=169 \sin \left (2 x \right ) \\ y \left (0\right ) &= -10 \\ y^{\prime }\left (0\right ) &= 9 \\ \end{align*}	✓	✓	✓	✓	1.766
14897	21181	\begin{align*} x^{\prime \prime \prime }-x^{\prime }&=0 \\ x \left (0\right ) &= 1 \\ x \left (\infty \right ) &= 0 \\ \end{align*}	✗	✓	✓	✓	1.766
14898	12502	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x -a&=0 \\ \end{align*}	✓	✓	✓	✓	1.767
14899	1235	\begin{align*} 2 y+y^{\prime }&={\mathrm e}^{-x^{2}-2 x} \\ \end{align*}	✓	✓	✓	✓	1.768
14900	9496	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.768