2.3.58 Problems 5701 to 5800

Table 2.689: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5701	17632	\begin{align*} x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+7 x y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.444
5702	17763	\begin{align*} y^{\prime \prime }+10 y^{\prime }+16 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.444
5703	17994	\begin{align*} {y^{\prime }}^{2}-\left (2 x +y\right ) y^{\prime }+x^{2}+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.444
5704	19877	\begin{align*} y&=x y^{\prime }-{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.444
5705	20192	\begin{align*} y^{\prime \prime }+4 x y^{\prime }+4 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.444
5706	20886	\begin{align*} y^{\prime }&=-x +y \\ y \left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.444
5707	21097	\begin{align*} x&=x^{\prime } t -{x^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.444
5708	21646	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.444
5709	23454	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2}+3 \\ \end{align*}	✓	✓	✓	✓	0.444
5710	23789	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=5 x-y \\ \end{align*}	✓	✓	✓	✓	0.444
5711	25368	\begin{align*} y_{1}^{\prime }&=-y_{1} \\ y_{2}^{\prime }&=3 y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.444
5712	25636	\begin{align*} y^{\prime }-a y&=t \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.444
5713	27358	\begin{align*} {y^{\prime }}^{3}+y^{2}&=y y^{\prime } \left (y^{\prime }+1\right ) \\ \end{align*}	✓	✓	✓	✓	0.444
5714	818	\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.445
5715	1856	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.445
5716	1868	\begin{align*} y^{\prime \prime }-\left (x -3\right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	0.445
5717	3987	\begin{align*} y^{\prime \prime }-2 x y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.445
5718	4379	\begin{align*} 2 x^{3}-y^{4}+x y^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.445
5719	6695	\begin{align*} -2 y+2 x y^{\prime }-x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.445
5720	8826	\begin{align*} u^{\prime \prime }-\cot \left (\theta \right ) u^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.445
5721	8900	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.445
5722	11666	\begin{align*} {y^{\prime }}^{2}+a y^{\prime }+b x&=0 \\ \end{align*}	✓	✓	✓	✓	0.445
5723	16882	\begin{align*} \left (x -3\right )^{2} y^{\prime \prime }-2 \left (x -3\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.445
5724	19494	\begin{align*} y^{\prime \prime }+3 y^{\prime }-10 y&=6 \,{\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.445
5725	19638	\begin{align*} x^{\prime }&=x+2 y \\ y^{\prime }&=3 x+2 y \\ \end{align*}	✓	✓	✓	✓	0.445
5726	21727	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.445
5727	970	\begin{align*} x_{1}^{\prime }&=9 x_{1}+5 x_{2} \\ x_{2}^{\prime }&=-6 x_{1}-2 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.446
5728	4554	\begin{align*} x^{\prime }-2 x-y&=2 \,{\mathrm e}^{t} \\ x-y^{\prime }+2 y&=3 \,{\mathrm e}^{4 t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= x_{0} \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	0.446
5729	7969	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	0.446
5730	14396	\begin{align*} x^{\prime }&=-3 x+y \\ y^{\prime }&=-3 y \\ \end{align*}	✓	✓	✓	✓	0.446
5731	15147	\begin{align*} y^{\prime \prime }+4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.446
5732	17834	\begin{align*} x^{\prime \prime }+6 x^{\prime }+9 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.446
5733	20782	\begin{align*} x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.446
5734	23607	\begin{align*} x^{\prime }&=3 x-2 y \\ y^{\prime }&=12 x-7 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.446
5735	26156	\begin{align*} y^{\prime } \ln \left (\frac {y^{\prime }}{4}\right )&=4 x \\ \end{align*}	✓	✓	✓	✓	0.446
5736	10	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-x} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.447
5737	596	\begin{align*} x^{\prime }+2 y^{\prime }&=4 x+5 y \\ 2 x^{\prime }-y^{\prime }&=3 x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.447
5738	1925	\begin{align*} y^{\prime \prime }-2 x y^{\prime }-\left (3 x^{2}+2\right ) y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.447
5739	2423	\begin{align*} y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.447
5740	2674	\begin{align*} y^{\prime \prime }+3 y^{\prime }+7 y&=\cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.447
5741	3146	\begin{align*} 4 y+y^{\prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.447
5742	3415	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.447
5743	7761	\begin{align*} 3 y^{\prime \prime }-2 y^{\prime }-y&=2 x -3 \\ \end{align*}	✓	✓	✓	✓	0.447
5744	8131	\begin{align*} y^{\prime \prime }-y x&=\frac {1}{1-x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.447
5745	10156	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+y {y^{\prime }}^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	0.447
5746	23456	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.447
5747	24118	\begin{align*} y^{\prime }-y&=x^{2}+1 \\ y \left (0\right ) &= -3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.447
5748	25631	\begin{align*} y^{\prime }&={\mathrm e}^{a t} \\ y \left (0\right ) &= A \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.447
5749	25659	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.447
5750	27138	\(\left [\begin {array}{ccc} 3 i & 0 & 0 \\ -1 & 0 & 0 \\ -i & 0 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.447
5751	816	\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 13 \\ \end{align*}	✓	✓	✓	✓	0.448
5752	1527	\begin{align*} y^{\prime }&=-x \,{\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.448
5753	1923	\begin{align*} y^{\prime \prime }-3 x y^{\prime }+\left (2 x^{2}+5\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.448
5754	3333	\begin{align*} y^{2}-2 x y y^{\prime }+{y^{\prime }}^{2} \left (x^{2}-1\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.448
5755	3419	\begin{align*} y^{\prime }&=\sin \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.448
5756	3422	\begin{align*} y^{\prime }&=\ln \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.448
5757	4666	\begin{align*} y^{\prime }&=3 a +3 b x +3 b y^{2} \\ \end{align*}	✓	✓	✓	✗	0.448
5758	6698	\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.448
5759	8895	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.448
5760	10029	\begin{align*} y^{\prime \prime }+y^{\prime }+4 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.448
5761	14799	\(\left [\begin {array}{cc} 3 & 4 \\ 5 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.448
5762	15983	\begin{align*} x^{\prime }&=2 x+3 y \\ y^{\prime }&=x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.448
5763	16649	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.448
5764	16769	\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=4 t +2 \,{\mathrm e}^{2 t} \sin \left (3 t \right ) \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.448
5765	17351	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.448
5766	18698	\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 ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.448
5767	19213	\begin{align*} y^{\prime }&=-z \\ z^{\prime }&=y \\ \end{align*} With initial conditions \begin{align*} y \left (0\right ) &= 1 \\ z \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.448
5768	19481	\begin{align*} y^{\prime \prime }+4 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2+3 \sqrt {2} \\ \end{align*}	✓	✓	✓	✓	0.448
5769	20936	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=-2 x+2 y \\ \end{align*}	✓	✓	✓	✓	0.448
5770	21121	\begin{align*} x^{\prime \prime }-2 x^{\prime }+2 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.448
5771	22105	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.448
5772	23513	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.448
5773	26556	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=x +1 \\ \end{align*}	✓	✓	✓	✓	0.448
5774	1737	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.449
5775	1846	\begin{align*} \left (2-x \right ) y^{\prime \prime }+2 y&=0 \\ y \left (0\right ) &= a_{0} \\ y^{\prime }\left (0\right ) &= a_{1} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.449
5776	3335	\begin{align*} y^{\prime }&=y x -x^{2} \\ y \left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.449
5777	3932	\begin{align*} -y+y^{\prime }&=5 \sin \left (2 t \right ) \\ y \left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.449
5778	7276	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=16 \\ \end{align*}	✓	✓	✓	✓	0.449
5779	7636	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.449
5780	12845	\begin{align*} y^{\prime \prime }+a \,x^{r} y^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	0.449
5781	22103	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.449
5782	22335	\begin{align*} \left (y^{\prime }-2 x \right ) \left (y^{\prime }-3 x^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.449
5783	25242	\begin{align*} t y^{\prime \prime }+\left (2 t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.449
5784	611	\begin{align*} x_{1}^{\prime }&=4 x_{1}+2 x_{2} \\ x_{2}^{\prime }&=-3 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.450
5785	1314	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.450
5786	1449	\begin{align*} x_{1}^{\prime }&=-x_{1}-x_{2} \\ x_{2}^{\prime }&=-\frac {5 x_{2}}{2} \\ \end{align*}	✓	✓	✓	✓	0.450
5787	1790	\begin{align*} \left (x^{2}-4\right ) y^{\prime \prime }+4 x y^{\prime }+2 y&=x +2 \\ y \left (0\right ) &= -{\frac {1}{3}} \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	0.450
5788	5380	\begin{align*} {y^{\prime }}^{2}-5 y^{\prime }+6&=0 \\ \end{align*}	✓	✓	✓	✓	0.450
5789	6647	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=x \left (1-{\mathrm e}^{x} x^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.450
5790	7634	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.450
5791	12859	\begin{align*} y^{\prime \prime }+a y^{\prime }+b \,x^{v} y^{n}&=0 \\ \end{align*}	✗	✗	✗	✗	0.450
5792	15190	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.450
5793	15996	\begin{align*} x^{\prime }&=-2 x-2 y \\ y^{\prime }&=-2 x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.450
5794	17044	\begin{align*} y^{\prime }&=\frac {1}{t^{2}+1} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.450
5795	17806	\begin{align*} x^{\prime \prime }+4 x^{\prime }+3 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	0.450
5796	18343	\begin{align*} x^{\prime \prime }+x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.450
5797	19241	\begin{align*} y^{\prime }&={\mathrm e}^{3 x}-x \\ \end{align*}	✓	✓	✓	✓	0.450
5798	19648	\begin{align*} x^{\prime }&=7 x+6 y \\ y^{\prime }&=2 x+6 y \\ \end{align*}	✓	✓	✓	✓	0.450
5799	19982	\begin{align*} x^{2}&=a^{2} \left (1+{y^{\prime }}^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.450
5800	23000	\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.450