2.3.110 Problems 10901 to 11000

Table 2.751: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
10901	12948	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+a&=0 \\ \end{align*}	✓	✓	✓	✗	1.510
10902	18949	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{2}+y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.510
10903	18514	\begin{align*} -2 y+y^{\prime }&=3 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	1.511
10904	13206	\begin{align*} y^{\prime }&=f \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	1.512
10905	16278	\begin{align*} y^{\prime }+5 y&={\mathrm e}^{-3 x} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.512
10906	24970	\begin{align*} \left (1-t \right ) y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	1.512
10907	18630	\begin{align*} x^{\prime }&=x+2 y+\sin \left (t \right ) \\ y^{\prime }&=-x+y-\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.513
10908	16485	\begin{align*} y^{\prime \prime }+5 y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.515
10909	22059	\begin{align*} y^{\prime }+\frac {4 y}{x}&=x^{4} \\ \end{align*}	✓	✓	✓	✓	1.515
10910	2515	\begin{align*} 3 t^{2}+4 t y+\left (2 y+2 t^{2}\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.516
10911	5424	\begin{align*} {y^{\prime }}^{2}-y y^{\prime } x +y^{2} \ln \left (a y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	1.517
10912	6555	\begin{align*} \left (x +y\right ) \left (-y+y^{\prime } x \right )^{3}+x^{3} y^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	1.517
10913	9038	\begin{align*} y^{\prime \prime }&=y y^{\prime } \\ \end{align*}	✓	✓	✓	✗	1.517
10914	18716	\begin{align*} x^{\prime }&=\frac {x \sqrt {6 x-9}}{3} \\ x \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	1.517
10915	1796	\begin{align*} 6 y^{\prime }+6 y^{2}-y-1&=0 \\ \end{align*}	✓	✓	✓	✓	1.518
10916	10268	\begin{align*} y^{\prime }&=b y \\ \end{align*}	✓	✓	✓	✓	1.518
10917	24835	\begin{align*} 9 {y^{\prime }}^{2}+12 x y^{4} y^{\prime }+4 y^{5}&=0 \\ \end{align*}	✓	✓	✓	✗	1.518
10918	908	\begin{align*} x^{\prime \prime }+9 x&=10 \cos \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.519
10919	17379	\begin{align*} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.519
10920	22956	\begin{align*} \left (x^{2}-1\right ) y^{\prime }&=\left (-1+y\right ) x \\ \end{align*}	✓	✓	✓	✓	1.519
10921	8276	\begin{align*} y^{\prime }-2 y x&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.520
10922	14665	\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+4 y^{\prime \prime }+3 y^{\prime }+y&=x^{2} {\mathrm e}^{-x}+3 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	1.520
10923	18921	\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right . \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.520
10924	24587	\begin{align*} y^{\prime \prime }+y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.520
10925	18768	\begin{align*} y^{\prime \prime }+5 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.522
10926	18931	\begin{align*} y^{\prime \prime }+4 y&=\operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.522
10927	18953	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{10}+y&=k \delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.522
10928	104	\begin{align*} y^{\prime }+p \left (x \right ) y&=q \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.523
10929	575	\begin{align*} x^{\prime \prime }+4 x^{\prime }+8 x&=f \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.523
10930	3771	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.523
10931	7037	\begin{align*} \left (2 x y^{3}+y x +x^{2}\right ) y^{\prime }-y x +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.523
10932	9644	\begin{align*} y^{\prime \prime }+y&=\delta \left (t -\frac {\pi }{2}\right )+\delta \left (t -\frac {3 \pi }{2}\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.523
10933	11274	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +4 x^{4} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.523
10934	23840	\begin{align*} y^{\prime }&=y+t \\ \end{align*}	✓	✓	✓	✓	1.523
10935	1127	\begin{align*} -y+y^{\prime }&=1+3 \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.524
10936	1237	\begin{align*} y^{\prime }&={\mathrm e}^{x +y} \\ \end{align*}	✓	✓	✓	✓	1.524
10937	11242	\begin{align*} y^{\prime \prime } x +3 y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.524
10938	15657	\begin{align*} \sqrt {1-x}\, y^{\prime \prime }-4 y&=\sin \left (x \right ) \\ y \left (-2\right ) &= 3 \\ y^{\prime }\left (-2\right ) &= -1 \\ \end{align*}	✗	✓	✗	✗	1.524
10939	19691	\begin{align*} x^{\prime \prime }+3 x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.524
10940	2586	\begin{align*} 3 y^{\prime \prime }+4 y^{\prime }+y&=\sin \left (t \right ) {\mathrm e}^{-t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.525
10941	4571	\begin{align*} x_{1}^{\prime }&=-x_{1}+8 x_{2}+9 t \\ x_{2}^{\prime }&=x_{1}+x_{2}+3 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	1.525
10942	5957	\begin{align*} a y+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.525
10943	9912	\begin{align*} x \left (x +1\right ) y^{\prime \prime }+\left (x +5\right ) y^{\prime }-4 y&=0 \\ \end{align*} Series expansion around \(x=-1\).	✓	✓	✓	✗	1.525
10944	12296	\begin{align*} y^{\prime \prime }+\left (a \,x^{2 c}+b \,x^{c -1}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	1.525
10945	14765	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +8 \left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.525
10946	22133	\begin{align*} y^{\prime \prime }&=9 x^{2}+2 x -1 \\ \end{align*}	✓	✓	✓	✓	1.525
10947	1041	\begin{align*} x_{1}^{\prime }&=2 x_{1}-8 x_{3}-3 x_{4} \\ x_{2}^{\prime }&=-18 x_{1}-x_{2} \\ x_{3}^{\prime }&=-9 x_{1}-3 x_{2}-25 x_{3}-9 x_{4} \\ x_{4}^{\prime }&=33 x_{1}+10 x_{2}+90 x_{3}+32 x_{4} \\ \end{align*}	✓	✓	✓	✓	1.526
10948	11218	\begin{align*} y^{\prime \prime } x +3 y^{\prime }+x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.526
10949	18351	\begin{align*} x^{\prime \prime }+\left (2+x\right ) x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.526
10950	25424	\begin{align*} -y+y^{\prime }&=8 \,{\mathrm e}^{3 t} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.526
10951	5240	\begin{align*} \left (x^{2}-3 y^{2}\right ) y^{\prime }+1+2 y x&=0 \\ \end{align*}	✓	✓	✓	✗	1.527
10952	7006	\begin{align*} y^{\prime }&=\left (x +y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.527
10953	13777	\begin{align*} x^{2} y^{\prime \prime }-\left (a \,x^{3}+\frac {5}{16}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.527
10954	19561	\begin{align*} y^{\left (6\right )}-y&=x^{10} \\ \end{align*}	✓	✓	✓	✓	1.527
10955	25425	\begin{align*} y+y^{\prime }&=8 \,{\mathrm e}^{-3 t} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.527
10956	25479	\begin{align*} y^{\prime }&=y \left (1-y\right ) \left (2-y\right ) \\ \end{align*}	✓	✓	✓	✓	1.527
10957	1177	\begin{align*} y^{\prime }&=\frac {t^{2}}{\left (t^{3}+1\right ) y} \\ \end{align*}	✓	✓	✓	✓	1.528
10958	13106	\begin{align*} a x^{\prime }&=b c \left (y-z\right ) \\ b y^{\prime }&=c a \left (z-x\right ) \\ c z^{\prime }&=a b \left (x-y\right ) \\ \end{align*}	✓	✓	✓	✓	1.528
10959	19987	\begin{align*} x^{2} \left (-y^{\prime } x +y\right )&=y {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.528
10960	5760	\begin{align*} -\left (a^{2}-{\mathrm e}^{2 x}\right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.529
10961	15604	\begin{align*} y^{\prime } x +x^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.529
10962	19131	\begin{align*} y^{\prime }&=y \ln \left (y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.529
10963	19735	\begin{align*} y^{\prime }&=\left (x +y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.530
10964	22394	\begin{align*} y^{\prime }&=\left (x +y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.532
10965	8333	\begin{align*} y^{\prime }&=y \ln \left (y+2\right ) \\ \end{align*}	✓	✓	✓	✓	1.533
10966	20472	\begin{align*} \left (1-y^{\prime }\right )^{2}-{\mathrm e}^{-2 y}&={\mathrm e}^{-2 x} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.533
10967	12434	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.534
10968	23380	\begin{align*} x^{2} y^{\prime \prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.534
10969	2757	\begin{align*} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=2 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }&=3 x_{1}+2 x_{2}+x_{3}+{\mathrm e}^{t} \cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.535
10970	5289	\begin{align*} \left (x^{3}-y^{3}\right ) y^{\prime }+x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.536
10971	9078	\begin{align*} y^{\prime }&=2 y x +1 \\ \end{align*}	✓	✓	✓	✓	1.537
10972	2435	\begin{align*} t^{2} y^{\prime \prime }-y^{\prime } t +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.539
10973	14763	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.539
10974	16419	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=8 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.539
10975	6380	\begin{align*} x {y^{\prime }}^{2}+y^{\prime \prime } x&=y^{\prime } \\ \end{align*}	✓	✓	✓	✓	1.540
10976	7257	\begin{align*} y^{\prime }&=\frac {2 y^{2}}{x}+\frac {y}{x}-2 x \\ \end{align*}	✓	✓	✓	✓	1.540
10977	10791	\begin{align*} 16 x^{2} y^{\prime \prime }+32 y^{\prime } x +\left (x^{4}-12\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.540
10978	12415	\begin{align*} x^{2} y^{\prime \prime }+\left (a x +b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.540
10979	15540	\begin{align*} y^{\prime }&=x^{3}+y^{3} \\ \end{align*}	✗	✗	✗	✗	1.540
10980	2077	\begin{align*} x^{2} y^{\prime \prime }+x \left (1-2 x \right ) y^{\prime }-\left (x +4\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.541
10981	7094	\begin{align*} y^{\prime \prime }-5 y^{\prime }-6 y&={\mathrm e}^{3 x} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.541
10982	11220	\begin{align*} 16 x^{2} y^{\prime \prime }+32 y^{\prime } x +\left (x^{4}-12\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.541
10983	8463	\begin{align*} y^{\prime }-2 y x&=-1 \\ y \left (0\right ) &= \frac {\sqrt {\pi }}{2} \\ \end{align*}	✓	✓	✓	✓	1.542
10984	10846	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +4 x^{4} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.542
10985	19130	\begin{align*} y^{\prime }&=y \ln \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	1.542
10986	21262	\begin{align*} x^{\prime \prime }+x+\frac {x^{2}}{3}&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	1.542
10987	7959	\begin{align*} 4 x -2 y y^{\prime }+x {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.543
10988	22660	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.544
10989	24561	\begin{align*} y^{\prime \prime }+y&=10 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.544
10990	1226	\begin{align*} y^{\prime }&=\frac {-1-2 y x}{x^{2}+2 y} \\ \end{align*}	✓	✓	✓	✗	1.545
10991	18365	\begin{align*} y^{\prime \prime }+\lambda ^{2} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.545
10992	2460	\begin{align*} t y^{\prime \prime }+y^{\prime } t +2 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	1.546
10993	8872	\begin{align*} L y^{\prime }+R y&=E \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.546
10994	10813	\begin{align*} y^{\prime \prime } x +3 y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.546
10995	17712	\begin{align*} 7 y^{\prime \prime } x +10 y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.546
10996	9648	\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=\delta \left (t -2 \pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.547
10997	7885	\begin{align*} 4 x^{3} y^{3}+\frac {1}{x}+\left (3 y^{2} x^{4}-\frac {1}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.548
10998	2301	\begin{align*} y+y^{\prime }&={\mathrm e}^{t} t \\ \end{align*}	✓	✓	✓	✓	1.549
10999	5559	\begin{align*} \left (1-a y\right ) {y^{\prime }}^{2}&=a y \\ \end{align*}	✓	✓	✓	✓	1.549
11000	15487	\begin{align*} x^{2} y^{\prime \prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.549