2.3.60 Problems 5901 to 6000

Table 2.693: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5901	7	\begin{align*} y^{\prime }&=\frac {10}{x^{2}+1} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.458
5902	3276	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.458
5903	8358	\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ \end{align*}	✓	✓	✓	✓	0.458
5904	10028	\begin{align*} y^{\prime \prime }+y^{\prime }+4 y&=1 \\ \end{align*}	✓	✓	✓	✓	0.458
5905	10222	\begin{align*} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.458
5906	10347	\begin{align*} y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.458
5907	10383	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=1 \\ \end{align*}	✓	✓	✓	✓	0.458
5908	12742	\begin{align*} x^{2} y^{\prime \prime \prime }+3 x y^{\prime \prime }+\left (4 a^{2} x^{2 a}+1-4 \nu ^{2} a^{2}\right ) y^{\prime }&=4 a^{3} x^{2 a -1} y \\ \end{align*}	✓	✓	✓	✗	0.458
5909	16114	\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.458
5910	22628	\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.458
5911	23070	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.458
5912	23442	\begin{align*} y^{\prime \prime }+\cos \left (x \right ) y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.458
5913	4518	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=8 \sin \left (t \right ) {\mathrm e}^{-t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.459
5914	8567	\begin{align*} y^{\prime }&=-2 y x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.459
5915	9353	\begin{align*} y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.459
5916	10241	\begin{align*} x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y&=6 \,{\mathrm e}^{x} x^{3} \\ \end{align*}	✓	✓	✓	✗	0.459
5917	11094	\begin{align*} \left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.459
5918	14796	\(\left [\begin {array}{cc} 3 & 2 \\ 6 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.459
5919	18385	\begin{align*} y^{\prime }&={\mathrm e}^{y}+y x \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✗	✓	0.459
5920	20704	\begin{align*} y^{\prime \prime \prime }+a^{2} y^{\prime }&=\sin \left (a x \right ) \\ \end{align*}	✓	✓	✓	✓	0.459
5921	23035	\begin{align*} z^{\prime \prime }-3 z^{\prime }+2 z&=4 \sin \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.459
5922	23077	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=5 x^{3} \\ \end{align*}	✓	✓	✓	✓	0.459
5923	26984	\begin{align*} y^{\prime \prime }+4 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.459
5924	843	\begin{align*} y^{\prime \prime }+2 y&=6 x \\ \end{align*}	✓	✓	✓	✓	0.460
5925	3173	\begin{align*} y^{\prime \prime }+3 y&=3 \,{\mathrm e}^{-4 x} \\ \end{align*}	✓	✓	✓	✓	0.460
5926	3344	\begin{align*} y^{\prime \prime }-2 y&={\mathrm e}^{2 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.460
5927	7070	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.460
5928	7279	\begin{align*} y^{\prime \prime }+y&=2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.460
5929	7379	\begin{align*} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.460
5930	15192	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.460
5931	16650	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{-8 x} \\ \end{align*}	✓	✓	✓	✓	0.460
5932	17694	\begin{align*} y^{\prime \prime }-4 x^{2} y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.460
5933	19480	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.460
5934	19833	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=2 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.460
5935	20995	\begin{align*} x^{\prime }&=8 x+y \\ y^{\prime }&=-4 x+4 y \\ \end{align*}	✓	✓	✓	✓	0.460
5936	21219	\begin{align*} x^{\prime }&=3 x-y \\ y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.460
5937	21715	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{-t} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.460
5938	21931	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.460
5939	22280	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.460
5940	23041	\begin{align*} x^{\prime \prime }-9 x^{\prime }-10 x&=\cos \left (4 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.460
5941	23691	\begin{align*} \left (-x^{2}+4 x -3\right ) y^{\prime \prime }-2 \left (x -2\right ) y^{\prime }+6 y&=0 \\ y \left (2\right ) &= 1 \\ y^{\prime }\left (2\right ) &= 0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	0.460
5942	24503	\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+12 y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.460
5943	24590	\begin{align*} y^{\prime \prime }-y&=2 x -3 \\ \end{align*}	✓	✓	✓	✓	0.460
5944	24602	\begin{align*} 4 y^{\prime \prime }-y&=x \\ \end{align*}	✓	✓	✓	✓	0.460
5945	26453	\begin{align*} 4 y^{\prime }+{y^{\prime \prime }}^{2}&=4 x y^{\prime \prime } \\ \end{align*}	✓	✓	✓	✓	0.460
5946	27014	\begin{align*} y^{\prime }+4 y&=\cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.460
5947	8	\begin{align*} y^{\prime }&=\cos \left (2 x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.461
5948	1315	\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+82 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.461
5949	1334	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=2 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.461
5950	1866	\begin{align*} \left (8 x^{2}+1\right ) y^{\prime \prime }+2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.461
5951	1927	\begin{align*} 2 y^{\prime \prime }+5 x y^{\prime }+\left (2 x^{2}+4\right ) y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.461
5952	2243	\begin{align*} y_{1}^{\prime }&=4 y_{1}-3 y_{2} \\ y_{2}^{\prime }&=2 y_{1}-y_{2} \\ \end{align*}	✓	✓	✓	✓	0.461
5953	3147	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.461
5954	3420	\begin{align*} y^{\prime }&=\sin \left (t \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.461
5955	3826	\begin{align*} x_{1}^{\prime }&=3 x_{2} \\ x_{2}^{\prime }&=-3 x_{1} \\ \end{align*}	✓	✓	✓	✓	0.461
5956	7072	\begin{align*} y^{\prime \prime }-4 y^{\prime }+20 y&=0 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.461
5957	7758	\begin{align*} y^{\prime \prime }+25 y&=5 x^{2}+x \\ \end{align*}	✓	✓	✓	✓	0.461
5958	8894	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.461
5959	9606	\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.461
5960	10691	\begin{align*} 2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.461
5961	14559	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.461
5962	14575	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.461
5963	16738	\begin{align*} y^{\prime \prime }-9 y^{\prime }+14 y&=98 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.461
5964	18080	\begin{align*} x y^{\prime \prime \prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.461
5965	21645	\begin{align*} y^{\prime }&=y \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.461
5966	23071	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }-5 y&=2 \sin \left (2 x \right )+3 \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.461
5967	25062	\begin{align*} y^{\prime }+2 y&=3 \,{\mathrm e}^{t} \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.461
5968	26351	\begin{align*} {y^{\prime }}^{3}-y {y^{\prime }}^{2}-x^{2} y^{\prime }+x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.461
5969	3404	\begin{align*} y^{\prime }&=\frac {2}{\sqrt {-x^{2}+1}} \\ \end{align*}	✓	✓	✓	✓	0.462
5970	3933	\begin{align*} y+y^{\prime }&=5 \,{\mathrm e}^{t} \sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.462
5971	10336	\begin{align*} t y^{\prime }+y&=0 \\ y \left (x_{0} \right ) &= y_{0} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.462
5972	12736	\begin{align*} \left (x -2\right ) x y^{\prime \prime \prime }-x \left (x -2\right ) y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.462
5973	14576	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.462
5974	19498	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=20 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.462
5975	844	\begin{align*} y^{\prime \prime }+2 y&=6 x +4 \\ \end{align*}	✓	✓	✓	✓	0.463
5976	1285	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.463
5977	1928	\begin{align*} 3 y^{\prime \prime }+2 x y^{\prime }+\left (-x^{2}+4\right ) y&=0 \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.463
5978	2550	\begin{align*} 5 y^{\prime \prime }+5 y^{\prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.463
5979	3835	\begin{align*} x_{1}^{\prime }&=-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1} \\ \end{align*}	✓	✓	✓	✓	0.463
5980	8019	\begin{align*} y^{\prime \prime }-y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.463
5981	16651	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.463
5982	16951	\begin{align*} x^{\prime }&=3 x+y \\ y^{\prime }&=6 x+2 y \\ \end{align*}	✓	✓	✓	✓	0.463
5983	17117	\begin{align*} y^{\prime }&=\frac {1}{x^{2}+1} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.463
5984	18696	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.463
5985	18772	\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.463
5986	18781	\begin{align*} y^{\prime \prime }+4 y^{\prime }+\frac {25 y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.463
5987	21941	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=\frac {{\mathrm e}^{x}}{x^{3}} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.463
5988	22107	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.463
5989	24018	\begin{align*} y^{\prime \prime \prime }+3 k y^{\prime \prime }+3 k^{2} y^{\prime }+k^{3} y&={\mathrm e}^{-k x} f^{\prime \prime \prime }\left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.463
5990	27721	\begin{align*} x^{2} \left (2 x -1\right ) y^{\prime \prime \prime }+\left (4 x -3\right ) x y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.463
5991	2267	\begin{align*} y_{1}^{\prime }&=-3 y_{1}-4 y_{2} \\ y_{2}^{\prime }&=y_{1}-7 y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 2 \\ y_{2} \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.464
5992	3813	\begin{align*} x_{1}^{\prime }&=2 x_{2} \\ x_{2}^{\prime }&=-2 x_{1} \\ \end{align*}	✓	✓	✓	✓	0.464
5993	4166	\begin{align*} y_{1}^{\prime }&=y_{1}+y_{2} \\ y_{2}^{\prime }&=3 y_{2}-y_{1} \\ \end{align*}	✓	✓	✓	✓	0.464
5994	7756	\begin{align*} y^{\prime \prime }-4 y&=10 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.464
5995	8568	\begin{align*} x y^{\prime }-3 y&=k \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.464
5996	8609	\begin{align*} y^{\prime \prime }+k^{2} x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.464
5997	9476	\begin{align*} x^{\prime }&=3 x+2 y \\ y^{\prime }&=-2 x-y \\ \end{align*}	✓	✓	✓	✓	0.464
5998	10231	\begin{align*} y^{\prime \prime }&=\left (x^{2}+3\right ) y \\ \end{align*}	✓	✓	✓	✗	0.464
5999	14359	\begin{align*} x^{\prime \prime }-2 x&=1 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.464
6000	16607	\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=30 \,{\mathrm e}^{-4 x} \\ \end{align*}	✓	✓	✓	✓	0.464