2.3.106 Problems 10501 to 10600

Table 2.785: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
10501	20528	\begin{align*} \sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 \sin \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.493
10502	20604	\begin{align*} 3 y-\left (x +3\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	1.493
10503	20838	\begin{align*} y^{\prime \prime }-3 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.493
10504	22165	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.493
10505	22197	\begin{align*} \left (x^{2}+4\right ) y^{\prime \prime }+y&=x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.493
10506	22798	\begin{align*} y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+\left (1+\sin \left (x \right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.493
10507	23530	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {{\mathrm e}^{-3 x}}{x^{3}} \\ \end{align*}	✓	✓	✓	✓	1.493
10508	24672	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.493
10509	25548	\begin{align*} 2 y^{\prime \prime }+4 y&={\mathrm e}^{i t} \\ \end{align*}	✓	✓	✓	✓	1.493
10510	8821	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	1.494
10511	14737	\begin{align*} y^{\prime \prime }-y^{\prime } x -y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.494
10512	17357	\begin{align*} t^{2} y^{\prime \prime }+7 y^{\prime } t -7 y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= -22 \\ \end{align*}	✓	✓	✓	✓	1.494
10513	18721	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (-\nu ^{2}+x^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.494
10514	19731	\begin{align*} 2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y&=0 \\ \end{align*}	✓	✓	✗	✓	1.494
10515	21920	\begin{align*} y^{\prime \prime }+4 y&=t \sin \left (t \right ) \\ y \left (0\right ) &= {\frac {7}{9}} \\ y^{\prime }\left (0\right ) &= -{\frac {5}{2}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.494
10516	24708	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=24 \,{\mathrm e}^{2 x} \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.494
10517	26364	\begin{align*} x&=\sin \left (y^{\prime }\right )+y^{\prime } \\ \end{align*}	✓	✓	✓	✗	1.494
10518	1095	\begin{align*} y^{\prime \prime } x +\sin \left (x \right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.495
10519	21698	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.495
10520	22937	\begin{align*} x^{\prime }+3 x-6 y&=0 \\ y^{\prime }&=x-3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.495
10521	6119	\begin{align*} x \left (7+6 x \right ) y+x \left (1-x \right ) y^{\prime }+\left (-x^{2}-x +2\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.496
10522	8490	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.496
10523	5571	\begin{align*} y^{2} {y^{\prime }}^{2}-a^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.497
10524	5625	\begin{align*} {y^{\prime }}^{3}-a x y y^{\prime }+2 a y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.497
10525	6987	\begin{align*} y^{\prime }&=2 \sec \left (x \right ) \tan \left (x \right )-\sin \left (x \right ) y^{2} \\ \end{align*}	✓	✓	✓	✗	1.497
10526	12962	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2} \left (1+{y^{\prime }}^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	1.497
10527	14127	\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.497
10528	18867	\begin{align*} 4 y^{\prime \prime }+y&=2 \sec \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.497
10529	21943	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x +20 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.497
10530	5841	\begin{align*} -a \,x^{-1+k} y+a \,x^{k} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.498
10531	6188	\begin{align*} -y+y^{\prime } x +x^{3} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.498
10532	3975	\begin{align*} y^{\prime }-5 y&=2 \,{\mathrm e}^{-t}+\delta \left (t -3\right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.499
10533	8416	\begin{align*} y^{\prime }&=-\frac {8 x +5}{3 y^{2}+1} \\ y \left (-1\right ) &= -3 \\ \end{align*}	✓	✓	✗	✗	1.499
10534	14061	\begin{align*} 4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 y^{\prime } x -1&=0 \\ \end{align*}	✓	✓	✓	✗	1.499
10535	14780	\begin{align*} x^{\prime }-y^{\prime }-2 x+4 y&=t \\ x^{\prime }+y^{\prime }-x-y&=1 \\ \end{align*}	✓	✓	✓	✓	1.499
10536	20622	\begin{align*} -\left (a^{2}+1\right ) y-2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.499
10537	7186	\begin{align*} y^{\prime \prime }+\frac {a y}{x^{{3}/{2}}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	1.500
10538	8890	\begin{align*} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.500
10539	9561	\begin{align*} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	1.500
10540	12366	\begin{align*} y^{\prime \prime } x +2 y^{\prime }-y x -{\mathrm e}^{x}&=0 \\ \end{align*}	✓	✓	✓	✗	1.500
10541	14959	\begin{align*} 4 y+y^{\prime \prime }&=\cot \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.500
10542	16187	\begin{align*} y^{\prime }&=3 \sqrt {x +3} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.500
10543	22734	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✓	1.500
10544	25983	\begin{align*} y^{\prime \prime }+y&=\csc \left (x \right ) \sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.500
10545	229	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ y \left (1\right ) &= 7 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.501
10546	15067	\begin{align*} y^{\prime \prime }-6 y^{\prime }+10 y&=100 \\ y \left (0\right ) &= 10 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	1.501
10547	18330	\begin{align*} y^{\prime \prime } x -\left (2 x^{2}+1\right ) y^{\prime }&=4 x^{3} {\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	1.501
10548	22270	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-9 x+6 y+t \\ \end{align*}	✓	✓	✓	✓	1.501
10549	24597	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=4-{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	1.501
10550	24695	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{-2 x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.501
10551	16060	\begin{align*} x^{\prime }&=-3 x+y \\ y^{\prime }&=-x \\ \end{align*}	✓	✓	✓	✓	1.502
10552	23037	\begin{align*} y^{\prime \prime }+3 y^{\prime }+5 y&=4 \,{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	1.502
10553	23632	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.502
10554	5722	\begin{align*} y^{\prime \prime }+y&=\sin \left (a x \right ) \sin \left (b x \right ) \\ \end{align*}	✓	✓	✓	✗	1.503
10555	6252	\begin{align*} \left (-x^{2}+2\right ) y-x \left (-x^{2}+2\right ) y^{\prime }+x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.503
10556	16186	\begin{align*} y^{\prime }&=3 \sqrt {x +3} \\ y \left (1\right ) &= 20 \\ \end{align*}	✓	✓	✓	✓	1.503
10557	16789	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.503
10558	17524	\begin{align*} y^{\prime \prime }+4 y&=\sec \left (2 t \right )+\tan \left (2 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.503
10559	21760	\begin{align*} y^{\prime }&=y^{\prime \prime } x +{y^{\prime \prime }}^{2} \\ y \left (-1\right ) &= 0 \\ y^{\prime }\left (-1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	1.503
10560	24539	\begin{align*} 4 y+y^{\prime \prime }&=15 \,{\mathrm e}^{x}-8 x \\ \end{align*}	✓	✓	✓	✓	1.503
10561	24671	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{x} \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.503
10562	12419	\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{2}-v \left (v -1\right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.504
10563	23595	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=-3 x+6 y \\ \end{align*}	✓	✓	✓	✓	1.504
10564	25984	\begin{align*} y^{\prime \prime }+y&=\csc \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.504
10565	2592	\begin{align*} y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1}&=t^{2}+1 \\ \end{align*}	✓	✓	✓	✗	1.505
10566	8483	\begin{align*} 2 y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.505
10567	13006	\begin{align*} a y \left (-1+y\right ) y^{\prime \prime }-\left (a -1\right ) \left (-1+2 y\right ) {y^{\prime }}^{2}+f y \left (-1+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.505
10568	6867	\begin{align*} y+\left (-x +2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.506
10569	7301	\begin{align*} y^{\prime \prime }+y&=x^{3}-1+2 \cos \left (x \right )+\left (2-4 x \right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.506
10570	9705	\begin{align*} x^{\prime }&=z \\ y^{\prime }&=-z \\ z^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	1.506
10571	17131	\begin{align*} y^{\prime }&=\left (3 y+1\right )^{4} \\ \end{align*}	✓	✓	✓	✓	1.506
10572	2687	\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ \cos \left (t \right ) & \pi \le t \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.507
10573	9232	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	1.507
10574	14279	\begin{align*} x^{\prime \prime }-4 x^{\prime }+4 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.507
10575	15296	\begin{align*} x^{\prime }&=9 x-3 y-6 t \\ y^{\prime }&=-x+11 y+10 t \\ \end{align*}	✓	✓	✓	✓	1.507
10576	18020	\begin{align*} x&=\frac {y}{y^{\prime }}+\frac {1}{{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	1.507
10577	18150	\begin{align*} y^{\prime \prime }+7 y^{\prime }&={\mathrm e}^{-7 x} \\ \end{align*}	✓	✓	✓	✓	1.507
10578	22261	\begin{align*} y^{\prime }-z&=0 \\ y-z^{\prime }&=0 \\ \end{align*} With initial conditions \begin{align*} y \left (0\right ) &= 1 \\ z \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.507
10579	23535	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 x}}{x^{4}} \\ \end{align*}	✓	✓	✓	✓	1.507
10580	24791	\begin{align*} x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.507
10581	25660	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.507
10582	27755	\begin{align*} y^{\prime }&=y+x \,{\mathrm e}^{y} \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.507
10583	14209	\begin{align*} x^{\prime }&=\frac {{\mathrm e}^{-t}}{\sqrt {t}} \\ x \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.508
10584	19613	\begin{align*} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.508
10585	10446	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.509
10586	22199	\begin{align*} y^{\prime \prime }-y^{\prime } x&={\mathrm e}^{-x} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.509
10587	3958	\begin{align*} y^{\prime }+2 y&=\operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right ) \\ y \left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.510
10588	1831	\begin{align*} \left (-1+x \right ) y^{\prime \prime }-y^{\prime } x +y&=2 \left (-1+x \right )^{2} {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	1.511
10589	7807	\begin{align*} x^{\prime \prime }+4 x&=\sin \left (2 t \right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.511
10590	19699	\begin{align*} x^{\prime \prime }-x^{\prime }+x&=\sin \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.511
10591	22701	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.511
10592	23563	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.511
10593	7185	\begin{align*} x \left (-x^{2}+1\right ) y^{\prime \prime }+\left (-3 x^{2}+1\right ) y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.512
10594	7773	\begin{align*} x^{\prime \prime }+4 x^{\prime }+3 x&={\mathrm e}^{-3 t} \\ x \left (0\right ) &= {\frac {1}{2}} \\ x^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	1.512
10595	17388	\begin{align*} y^{\prime \prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.512
10596	20793	\begin{align*} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-1\right ) y&=-3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✗	1.512
10597	21945	\begin{align*} y^{\prime \prime }+4 y&=2 t -8 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.512
10598	7641	\begin{align*} \left (x^{2}+x +1\right ) y^{\prime \prime }-3 y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	1.513
10599	8035	\begin{align*} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-10 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.513
10600	8498	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.513