2.3.48 Problems 4701 to 4800

Table 2.639: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4701	23270	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.313
4702	24583	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.313
4703	25105	\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.313
4704	1450	\begin{align*} x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.314
4705	3116	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.314
4706	3172	\begin{align*} 4 y+y^{\prime \prime }&=2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.314
4707	6711	\begin{align*} -4 y-14 y^{\prime } x +\left (-8 x^{2}+3\right ) y^{\prime \prime }+x \left (-x^{2}+1\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.314
4708	9223	\begin{align*} 3 y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.314
4709	9712	\begin{align*} x^{2} {y^{\prime }}^{2}-5 y y^{\prime } x +6 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.314
4710	15245	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&={\mathrm e}^{-\frac {t}{2}} \delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.314
4711	15428	\begin{align*} s^{\prime \prime }-a^{2} s&=1+t \\ \end{align*}	✓	✓	✓	✓	0.314
4712	16719	\begin{align*} x^{2} y^{\prime \prime }+\frac {5 y}{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.314
4713	18888	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{t} t^{2}+7 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.314
4714	21536	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=3 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{-x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✓	0.314
4715	21962	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.314
4716	22889	\begin{align*} x^{\prime }+y^{\prime }+2 x-y&=-\sin \left (t \right ) \\ x^{\prime }-3 x+y^{\prime }+2 y&=4 \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✗	0.314
4717	23380	\begin{align*} x^{2} y^{\prime \prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.314
4718	25939	\begin{align*} y^{\prime \prime }-y&=5 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.314
4719	3985	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.315
4720	6875	\begin{align*} {y^{\prime }}^{2}-\frac {a^{2}}{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.315
4721	9713	\begin{align*} x^{2} {y^{\prime }}^{2}+y^{\prime } x -y^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.315
4722	16032	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.315
4723	18049	\begin{align*} x^{2}+y^{\prime } x&=3 x +y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.315
4724	18248	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{x} \sin \left (\frac {x}{2}\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.315
4725	18917	\begin{align*} y_{1}^{\prime }&=5 y_{1}-y_{2}+{\mathrm e}^{-t} \\ y_{2}^{\prime }&=y_{1}+3 y_{2}+2 \,{\mathrm e}^{t} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= -3 \\ y_{2} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.315
4726	21711	\begin{align*} y^{\prime }+2 y&={\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.315
4727	23009	\begin{align*} 3 y^{\prime \prime }+2 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.315
4728	25134	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 \\ \end{align*}	✓	✓	✓	✓	0.315
4729	25241	\begin{align*} t y^{\prime \prime }-4 y^{\prime }+t y&=0 \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.315
4730	365	\begin{align*} y^{\prime \prime }+y&=x \cos \left (x \right )^{3} \\ \end{align*}	✓	✓	✓	✓	0.316
4731	1012	\begin{align*} x_{1}^{\prime }&=7 x_{1}+x_{2} \\ x_{2}^{\prime }&=-4 x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.316
4732	1363	\begin{align*} y^{\prime \prime }+k^{2} x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.316
4733	3405	\begin{align*} y^{\prime }&={\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.316
4734	7958	\begin{align*} y^{2} {y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.316
4735	7999	\begin{align*} y^{\prime \prime }+y&=\csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.316
4736	8196	\begin{align*} {y^{\prime }}^{2}-2 y^{\prime }+4 y&=4 x -1 \\ \end{align*}	✓	✓	✓	✗	0.316
4737	9710	\begin{align*} -y^{2}+x^{2} {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.316
4738	14348	\begin{align*} x^{\prime \prime \prime }+x^{\prime \prime }&=2 \,{\mathrm e}^{t}+3 t^{2} \\ \end{align*}	✓	✓	✓	✓	0.316
4739	15075	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.316
4740	17740	\begin{align*} y^{\prime \prime }-10 y^{\prime }+34 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.316
4741	18299	\begin{align*} \left (2 x +1\right )^{2} y^{\prime \prime \prime }+2 \left (2 x +1\right ) y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.316
4742	19035	\begin{align*} x_{1}^{\prime }&=-4 x_{1}-x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.316
4743	20931	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=-5 x \\ \end{align*}	✓	✓	✓	✓	0.316
4744	20935	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.316
4745	21660	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.316
4746	22291	\begin{align*} y^{\prime \prime }-4 y^{\prime }-5 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.316
4747	22632	\begin{align*} i^{\prime \prime }-4 i^{\prime }+2 i&=0 \\ \end{align*}	✓	✓	✓	✓	0.316
4748	26131	\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=3 x-4 y \\ \end{align*}	✓	✓	✓	✓	0.316
4749	2204	\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+9 y^{\prime \prime }+7 y^{\prime }+2 y&={\mathrm e}^{-x} \left (30+24 x \right )-{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.317
4750	3763	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=36 \,{\mathrm e}^{2 x} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.317
4751	7061	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.317
4752	7992	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.317
4753	8070	\begin{align*} y^{\prime }&=2 x^{2}+3 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.317
4754	14104	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&=x \\ \end{align*}	✓	✓	✓	✓	0.317
4755	14567	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }-3 \left (x +1\right ) y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.317
4756	14569	\begin{align*} \left (x^{2}-x +1\right ) y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.317
4757	16494	\begin{align*} y^{\prime \prime }-8 y^{\prime }+15 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.317
4758	17365	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.317
4759	22655	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.317
4760	24673	\begin{align*} y^{\prime \prime }-y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.317
4761	963	\begin{align*} x_{1}^{\prime }&=6 x_{1} \\ x_{2}^{\prime }&=-3 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.318
4762	1090	\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.318
4763	1489	\begin{align*} y^{\prime \prime \prime \prime }-4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.318
4764	12621	\begin{align*} y^{\prime \prime }&=\frac {\left (x^{2}-2\right ) y^{\prime }}{x \left (x^{2}-1\right )}-\frac {\left (x^{2}-2\right ) y}{x^{2} \left (x^{2}-1\right )} \\ \end{align*}	✓	✓	✓	✗	0.318
4765	14954	\begin{align*} \left (-t^{2}+t \right ) x^{\prime \prime }+\left (-t^{2}+2\right ) x^{\prime }+\left (2-t \right ) x&=0 \\ \end{align*}	✓	✓	✓	✗	0.318
4766	18005	\begin{align*} x {y^{\prime }}^{2}&={\mathrm e}^{\frac {1}{y^{\prime }}} \\ \end{align*}	✓	✓	✓	✗	0.318
4767	18959	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\cos \left (\alpha t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.318
4768	19692	\begin{align*} x^{\prime \prime }-3 x^{\prime }+2 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.318
4769	23024	\begin{align*} z^{\prime \prime }-7 z^{\prime }-13 z&=0 \\ \end{align*}	✓	✓	✓	✓	0.318
4770	23424	\begin{align*} y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.318
4771	333	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=2-\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.319
4772	578	\begin{align*} x^{\prime }&=-2 y \\ y^{\prime }&=2 x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.319
4773	1370	\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.319
4774	1425	\begin{align*} x_{1}^{\prime }&=3 x_{1}+9 x_{2} \\ x_{2}^{\prime }&=-x_{1}-3 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.319
4775	1525	\begin{align*} y^{\prime }&=-x \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.319
4776	1789	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=x^{2} \\ y \left (1\right ) &= {\frac {5}{4}} \\ y^{\prime }\left (1\right ) &= {\frac {3}{2}} \\ \end{align*}	✓	✓	✓	✓	0.319
4777	2379	\begin{align*} 4 y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.319
4778	3115	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.319
4779	8681	\begin{align*} x^{\prime }+t&=1 \\ \end{align*}	✓	✓	✓	✓	0.319
4780	12563	\begin{align*} \left (a^{2} x^{2}-1\right ) y^{\prime \prime }+2 a^{2} x y^{\prime }-2 a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.319
4781	16398	\begin{align*} x y^{\prime \prime \prime }+2 y^{\prime \prime }&=6 x \\ \end{align*}	✓	✓	✓	✓	0.319
4782	16413	\begin{align*} \left (y-3\right ) y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.319
4783	18160	\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&={\mathrm e}^{-3 x} \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.319
4784	18451	\begin{align*} x^{\prime }&=5 x+4 y \\ y^{\prime }&=x+2 y \\ \end{align*}	✓	✓	✓	✓	0.319
4785	18912	\begin{align*} y_{1}^{\prime }&=4 y_{1}-4 y_{2} \\ y_{2}^{\prime }&=5 y_{1}-4 y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.319
4786	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*}	✓	✓	✓	✓	0.319
4787	21209	\begin{align*} x^{\prime }&=x+3 y \\ y^{\prime }&=-3 x+y \\ \end{align*}	✓	✓	✓	✓	0.319
4788	24782	\begin{align*} y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.319
4789	25074	\begin{align*} y^{\prime \prime }-4 y^{\prime }-5 y&=150 t \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.319
4790	25747	\begin{align*} {y^{\prime }}^{2}&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.319
4791	1378	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.320
4792	3088	\begin{align*} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.320
4793	3335	\begin{align*} y^{\prime }&=y x -x^{2} \\ y \left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.320
4794	7453	\begin{align*} \theta r^{\prime }+3 r-\theta -1&=0 \\ \end{align*}	✓	✓	✓	✓	0.320
4795	10930	\begin{align*} x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.320
4796	11666	\begin{align*} {y^{\prime }}^{2}+a y^{\prime }+b x&=0 \\ \end{align*}	✓	✓	✓	✓	0.320
4797	12352	\begin{align*} 4 y^{\prime \prime }+9 y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.320
4798	13185	\(\left [\begin {array}{ccc} 2 & -2 & 1 \\ 2 & -2 & 1 \\ 2 & -2 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.320
4799	15303	\begin{align*} x^{2} y^{\prime \prime }+x \left (x -\frac {1}{2}\right ) y^{\prime }+\frac {y}{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.320
4800	16703	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.320