2.3.160 Problems 15901 to 16000

Table 2.851: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
15901	20109	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{m} \\ \end{align*}	✓	✓	✓	✓	3.684
15902	24892	\begin{align*} {y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.684
15903	1522	\begin{align*} 2 y^{\prime }+x \left (-1+y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.685
15904	11582	\begin{align*} \left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }-3 x y^{2}+x&=0 \\ \end{align*}	✓	✓	✓	✗	3.685
15905	12258	\begin{align*} y^{\prime }&=\frac {y \left (y^{2}+y x +x^{2}+x \right )}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	3.686
15906	16349	\begin{align*} y^{\prime }&=\frac {3 y}{x +1}-y^{2} \\ \end{align*}	✓	✓	✓	✓	3.687
15907	9974	\begin{align*} t x^{\prime }+2 x&=4 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	3.688
15908	20092	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=2 \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.688
15909	20503	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=x \\ \end{align*}	✓	✓	✓	✓	3.688
15910	2386	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.689
15911	4822	\begin{align*} y^{\prime } x +\tan \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.689
15912	19411	\begin{align*} 3 y x +y^{2}+\left (3 y x +x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.689
15913	1672	\begin{align*} y^{\prime }&=y^{2} {\mathrm e}^{-x}+4 y+2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	3.690
15914	5339	\begin{align*} \left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	3.690
15915	12261	\begin{align*} y^{\prime }&=\frac {a^{3} x^{3} y^{3}+3 y^{2} a^{2} x^{2}+3 a x y+1+a^{2} x}{x^{3} a^{3}} \\ \end{align*}	✓	✓	✓	✓	3.690
15916	5087	\begin{align*} \left (3+2 x -2 y\right ) y^{\prime }&=1+6 x -2 y \\ \end{align*}	✓	✓	✓	✓	3.691
15917	5789	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.691
15918	17381	\begin{align*} y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.691
15919	2845	\begin{align*} x y^{2}+x +\left (x^{2} y-y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.692
15920	9121	\begin{align*} -y^{\prime } x +y&=y^{\prime } y^{2} {\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✓	3.692
15921	13218	\begin{align*} x^{2} y^{\prime }&=a \,x^{2} y^{2}+b \\ \end{align*}	✓	✓	✓	✓	3.692
15922	9629	\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.693
15923	2545	\begin{align*} 6 y^{\prime \prime }-7 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	3.694
15924	12380	\begin{align*} y^{\prime \prime } x -2 \left (x -1\right ) y^{\prime }-y&=0 \\ \end{align*}	✗	✓	✓	✗	3.696
15925	17084	\begin{align*} \sin \left (t \right )^{2}&=\cos \left (y\right )^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.696
15926	21802	\begin{align*} r^{\prime }&=r \tan \left (t \right ) \\ r \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.696
15927	15612	\begin{align*} y^{\prime }&=\frac {y}{-x^{2}+1}+\sqrt {x} \\ y \left (\frac {1}{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.697
15928	24110	\begin{align*} y^{\prime \prime } x +2 y^{\prime }-3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.697
15929	5949	\begin{align*} \left (b x +a \right ) y+8 y^{\prime }+16 y^{\prime \prime } x&=0 \\ \end{align*}	✗	✓	✓	✗	3.698
15930	19127	\begin{align*} y^{\prime }&=\sqrt {-x +y} \\ \end{align*}	✓	✓	✓	✓	3.699
15931	21049	\begin{align*} x^{\prime }&=x^{2}+1 \\ \end{align*}	✓	✓	✓	✓	3.699
15932	5058	\begin{align*} \left (x +y\right ) y^{\prime }+\tan \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.700
15933	19364	\begin{align*} y^{\prime \prime } x +y^{\prime }&=4 x \\ \end{align*}	✓	✓	✓	✓	3.701
15934	9207	\begin{align*} \frac {1}{y}-\frac {x y^{\prime }}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	3.702
15935	7203	\begin{align*} u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	3.703
15936	696	\begin{align*} 2 y y^{\prime }&=\frac {x}{\sqrt {x^{2}-16}} \\ y \left (5\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.704
15937	19251	\begin{align*} y^{\prime } x&=\left (-2 x^{2}+1\right ) \tan \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	3.704
15938	7926	\begin{align*} y \left (1+y^{2}\right )&=2 \left (1-2 x y^{2}\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.705
15939	14717	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -10 y&=0 \\ y \left (1\right ) &= 5 \\ y^{\prime }\left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	3.705
15940	19334	\begin{align*} y-x y^{2}+\left (y^{2} x^{2}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.705
15941	4765	\begin{align*} y^{\prime } x&=a +b \,x^{n}+c y \\ \end{align*}	✓	✓	✓	✗	3.707
15942	5652	\begin{align*} x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✗	3.707
15943	1214	\begin{align*} {\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 \csc \left (y\right ) y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.708
15944	5799	\begin{align*} 12 y-7 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.708
15945	20238	\begin{align*} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.708
15946	6790	\begin{align*} y^{\prime \prime \prime }&=y^{\prime } \left (1+y^{\prime }\right ) \\ \end{align*}	✓	✓	✗	✗	3.710
15947	13876	\begin{align*} x^{2} \left (x -a \right )^{2} y^{\prime \prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✗	3.710
15948	126	\begin{align*} x^{2} y^{\prime }+2 y x&=5 y^{4} \\ \end{align*}	✓	✓	✓	✓	3.711
15949	20187	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+n^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	3.711
15950	23940	\begin{align*} y^{\prime }&=f \left (x \right )+a y+b z \\ z^{\prime }&=g \left (x \right )+c y+d z \\ \end{align*}	✓	✓	✓	✓	3.711
15951	17739	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.712
15952	23253	\begin{align*} y^{\prime \prime }+5 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.712
15953	23720	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-4\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.712
15954	4442	\begin{align*} x y^{3}-1+x^{2} y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.713
15955	9049	\begin{align*} y^{\prime } x&=2 y \\ \end{align*}	✓	✓	✓	✓	3.713
15956	13697	\begin{align*} y^{\prime \prime }+\left (2 x^{2}+a \right ) y^{\prime }+\left (x^{4}+a \,x^{2}+b +2 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	3.713
15957	21601	\begin{align*} y^{\prime \prime }+2 y^{\prime }+\left (1-\frac {2}{\left (1+3 x \right )^{2}}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	3.713
15958	5883	\begin{align*} 4 y^{\prime \prime }&=\left (x^{2}+a \right ) y \\ \end{align*}	✗	✓	✓	✗	3.714
15959	11472	\begin{align*} x^{3} y^{\prime }-x^{6} y^{2}-\left (2 x -3\right ) x^{2} y+3&=0 \\ \end{align*}	✓	✓	✓	✓	3.716
15960	14933	\begin{align*} x^{\prime \prime }-4 x^{\prime }&=t^{2} \\ \end{align*}	✓	✓	✓	✓	3.716
15961	23230	\begin{align*} y^{\prime \prime } x +y^{\prime }&=3 \\ \end{align*}	✓	✓	✓	✓	3.716
15962	7829	\begin{align*} y^{\prime \prime }+5 y^{\prime }-3 y&=\operatorname {Heaviside}\left (x -4\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.717
15963	22093	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.717
15964	7941	\begin{align*} y+{\mathrm e}^{y}-{\mathrm e}^{-x}+\left (1+{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.718
15965	22370	\begin{align*} y+\left (x^{3}+x^{3} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.718
15966	4938	\begin{align*} x \left (1-x \right ) y^{\prime }&=a +2 \left (-x +2\right ) y \\ \end{align*}	✓	✓	✓	✓	3.719
15967	14017	\begin{align*} y^{\prime }-x^{2} y&=x^{5} \\ \end{align*}	✓	✓	✓	✓	3.719
15968	20627	\begin{align*} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-3\right ) y&={\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✗	3.719
15969	11391	\begin{align*} y^{\prime } x -y-\frac {x}{\ln \left (x \right )}&=0 \\ \end{align*}	✓	✓	✓	✓	3.720
15970	6840	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\ \end{align*}	✓	✓	✓	✓	3.721
15971	19319	\begin{align*} \left (2+x \right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.721
15972	21009	\begin{align*} x^{\prime }+\frac {x}{t^{2}-1}&=0 \\ x \left (-2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.721
15973	21973	\begin{align*} y^{\prime }&=x \sin \left (y\right )+{\mathrm e}^{x} \\ \end{align*}	✗	✗	✗	✗	3.722
15974	19390	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=4 x^{3} \\ \end{align*}	✓	✓	✓	✓	3.723
15975	24889	\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	3.723
15976	2834	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (L \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.724
15977	4645	\begin{align*} y^{\prime }&=2+2 \sec \left (2 x \right )+2 y \tan \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	3.724
15978	5070	\begin{align*} \left (2-3 x +y\right ) y^{\prime }+5-2 x -3 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.724
15979	7982	\begin{align*} y^{\prime \prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.724
15980	11583	\begin{align*} \left (6 y-x \right )^{2} y^{\prime }-6 y^{2}+2 y x +a&=0 \\ \end{align*}	✓	✓	✓	✓	3.724
15981	15252	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=12 \operatorname {Heaviside}\left (t \right )-12 \operatorname {Heaviside}\left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.724
15982	25092	\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.724
15983	25218	\begin{align*} \left (t -1\right ) y^{\prime \prime }-y^{\prime } t +y&=0 \\ \end{align*}	✓	✓	✓	✗	3.724
15984	5837	\begin{align*} -4 y x +x^{2} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.725
15985	13727	\begin{align*} y^{\prime \prime } x +\left (1-3 n \right ) y^{\prime }-a^{2} n^{2} x^{2 n -1} y&=0 \\ \end{align*}	✗	✓	✓	✗	3.725
15986	23375	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.725
15987	906	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.726
15988	21275	\begin{align*} t^{2} x^{\prime \prime }+t x^{\prime }+t^{2} x&=0 \\ x^{\prime }\left (0\right ) &= a \\ \end{align*}	✗	✗	✗	✓	3.726
15989	1251	\begin{align*} 6 y^{\prime \prime }-y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	3.727
15990	8267	\begin{align*} y^{\prime } x +y&=2 x \\ y \left (x_{0} \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.727
15991	7704	\begin{align*} y^{\prime } x -2 y&=\cos \left (x \right ) x^{3} \\ \end{align*}	✓	✓	✓	✓	3.728
15992	1669	\begin{align*} 3 y^{\prime } y^{2} x&=y^{3}+x \\ \end{align*}	✓	✓	✓	✓	3.731
15993	21980	\begin{align*} \sin \left (x \right )+y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.733
15994	4700	\begin{align*} y^{\prime }+\left (\tan \left (x \right )+y^{2} \sec \left (x \right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.734
15995	19414	\begin{align*} \frac {\cos \left (y\right )}{x +3}-\left (\sin \left (y\right ) \ln \left (5 x +15\right )-\frac {1}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.734
15996	725	\begin{align*} y^{\prime }&=2 y x +3 x^{2} {\mathrm e}^{x^{2}} \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	3.735
15997	4278	\begin{align*} x^{2} y^{3}+y&=\left (x^{3} y^{2}-x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.735
15998	4969	\begin{align*} x^{3} y^{\prime }&=x^{4}+y^{2} \\ \end{align*}	✓	✓	✓	✓	3.735
15999	17083	\begin{align*} y^{\prime }&={\mathrm e}^{3 y+2 t} \\ \end{align*}	✓	✓	✓	✓	3.735
16000	13989	\begin{align*} y^{\prime }-\frac {2 y}{x +1}&=\left (x +1\right )^{3} \\ \end{align*}	✓	✓	✓	✓	3.736