2.3.50 Problems 4901 to 5000

Table 2.631: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4901	21855	\begin{align*} {y^{\prime }}^{2}-4 y^{\prime }+2&=0 \\ \end{align*}	✓	✓	✓	✓	0.383
4902	22865	\begin{align*} \left (1-x \right ) y^{\prime \prime }+\left (2-4 x \right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.383
4903	23588	\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.383
4904	5595	\begin{align*} \left (2-3 y\right )^{2} {y^{\prime }}^{2}&=4-4 y \\ \end{align*}	✓	✓	✓	✓	0.384
4905	6954	\begin{align*} \frac {y x +1}{y}+\frac {\left (-x +2 y\right ) y^{\prime }}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.384
4906	7657	\begin{align*} w^{\prime }+w x&={\mathrm e}^{x} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.384
4907	7841	\begin{align*} y^{\prime \prime }+2 x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.384
4908	9601	\begin{align*} y^{\prime }+6 y&={\mathrm e}^{4 t} \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.384
4909	16189	\begin{align*} y^{\prime }&=\frac {x}{\sqrt {x^{2}+5}} \\ y \left (2\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	0.384
4910	16825	\begin{align*} y^{\prime }+\frac {y}{x -1}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.384
4911	24045	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{x} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.384
4912	443	\begin{align*} y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.385
4913	2618	\begin{align*} y^{\prime \prime }-2 y^{\prime } t +\lambda y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.385
4914	3312	\begin{align*} x {y^{\prime }}^{3}&=y y^{\prime }+1 \\ \end{align*}	✓	✓	✓	✗	0.385
4915	3942	\begin{align*} y^{\prime \prime }+4 y&=10 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.385
4916	4650	\begin{align*} y^{\prime }&=f \left (x \right ) f^{\prime }\left (x \right )-y f^{\prime }\left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.385
4917	7458	\begin{align*} \frac {t y^{\prime }}{y}+1+\ln \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.385
4918	10060	\begin{align*} x^{\prime }&=7 x+y \\ y^{\prime }&=-4 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.385
4919	10349	\begin{align*} y^{\prime } x +y&=x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.385
4920	12889	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+a \,x^{v} y^{n}&=0 \\ \end{align*}	✗	✗	✗	✗	0.385
4921	13153	\(\left [\begin {array}{ccc} 1 & 0 & -1 \\ -2 & 3 & -1 \\ -6 & 6 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.385
4922	14066	\begin{align*} y&=2 y^{\prime } x +y^{2} {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.385
4923	15228	\begin{align*} y^{\prime \prime }+9 y&=24 \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.385
4924	15272	\begin{align*} x^{\prime }+y^{\prime }&=y \\ x^{\prime }-y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.385
4925	16822	\begin{align*} y^{\prime }+\frac {2 y}{2 x -1}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.385
4926	18669	\begin{align*} x^{\prime }&=-x-4 y \\ y^{\prime }&=x-y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	0.385
4927	20489	\begin{align*} y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}}&=1 \\ \end{align*}	✓	✓	✓	✓	0.385
4928	21470	\begin{align*} y&=y^{\prime } x +{y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.385
4929	23657	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=3 t^{3}-9 t^{2}-5 t +1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.385
4930	24065	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{x}+{\mathrm e}^{2 x}+{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.385
4931	25471	\begin{align*} y^{\prime }&=1+y \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.385
4932	7378	\begin{align*} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.386
4933	7656	\begin{align*} y^{\prime }-y x&=\sin \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.386
4934	11001	\begin{align*} x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.386
4935	16176	\begin{align*} y^{\prime }&=\frac {x -1}{x +1} \\ y \left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	0.386
4936	20102	\begin{align*} y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}}&=1 \\ \end{align*}	✓	✓	✓	✓	0.386
4937	23639	\begin{align*} y^{\prime \prime \prime }-27 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 6 \\ y^{\prime \prime }\left (0\right ) &= 18 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.386
4938	23694	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.386
4939	23833	\begin{align*} y^{\prime }&=t \ln \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.386
4940	3413	\begin{align*} {y^{\prime }}^{2}-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.387
4941	5466	\begin{align*} x {y^{\prime }}^{2}+\left (a +x -y\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.387
4942	7381	\begin{align*} y^{\prime }&=4 y^{2}-3 y+1 \\ \end{align*}	✓	✓	✓	✓	0.387
4943	7957	\begin{align*} y&=y^{\prime } x -2 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.387
4944	9368	\begin{align*} y^{\prime }&=x -y \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.387
4945	10976	\begin{align*} x^{2} \left (4 x +3\right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (4 x +3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.387
4946	12891	\begin{align*} b \,{\mathrm e}^{y} x +a y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✗	✗	✗	0.387
4947	18387	\begin{align*} \left (x +1\right ) y^{\prime }-n y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.387
4948	23786	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.387
4949	540	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=6 x+3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.388
4950	580	\begin{align*} x^{\prime }&=\frac {y}{2} \\ y^{\prime }&=-8 x \\ \end{align*}	✓	✓	✓	✓	0.388
4951	2681	\begin{align*} y^{\prime \prime }-2 y^{\prime }+7 y&=\sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.388
4952	2774	\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2} \\ x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.388
4953	3881	\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2} \\ x_{2}^{\prime }&=-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.388
4954	5482	\begin{align*} \left (a -x \right ) {y^{\prime }}^{2}+y y^{\prime }-b&=0 \\ \end{align*}	✓	✓	✓	✗	0.388
4955	6432	\begin{align*} y y^{\prime \prime }&=-y^{2} x^{2}+\ln \left (y\right ) y^{2}+{y^{\prime }}^{2} \\ \end{align*}	✗	✓	✓	✗	0.388
4956	10591	\begin{align*} 36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.388
4957	15811	\begin{align*} y^{\prime }&=1-2 y \\ \end{align*}	✓	✓	✓	✓	0.388
4958	17025	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.388
4959	20936	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=-2 x+2 y \\ \end{align*}	✓	✓	✓	✓	0.388
4960	23814	\begin{align*} x^{\prime }&=2 x-y \\ y^{\prime }&=-x+2 y \\ \end{align*}	✓	✓	✓	✓	0.388
4961	445	\begin{align*} \left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y&=0 \\ y \left (3\right ) &= 2 \\ y^{\prime }\left (3\right ) &= 0 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	0.389
4962	467	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.389
4963	7034	\begin{align*} \left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (2 x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	0.389
4964	9064	\begin{align*} \left (x +1\right ) y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.389
4965	10614	\begin{align*} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.389
4966	11025	\begin{align*} 4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.389
4967	12897	\begin{align*} x^{2} y^{\prime \prime }&=a \left (y^{n}-y\right ) \\ \end{align*}	✗	✗	✗	✗	0.389
4968	13202	\begin{align*} y^{\prime }&=f \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	0.389
4969	14741	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.389
4970	16780	\begin{align*} y^{\prime \prime }-4 y^{\prime }+40 y&=122 \,{\mathrm e}^{-3 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.389
4971	16820	\begin{align*} y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.389
4972	16864	\begin{align*} y^{\prime }-{\mathrm e}^{x} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.389
4973	17661	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 y^{\prime } x&=-8 \\ \end{align*}	✓	✓	✓	✓	0.389
4974	22084	\begin{align*} y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.389
4975	432	\begin{align*} \left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.390
4976	572	\begin{align*} x^{\prime \prime }+4 x&=f \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.390
4977	625	\begin{align*} x_{1}^{\prime }&=6 x_{1}-7 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.390
4978	2416	\begin{align*} t \left (2-t \right ) y^{\prime \prime }-6 \left (t -1\right ) y^{\prime }-4 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*} Series expansion around \(t=1\).	✓	✓	✓	✓	0.390
4979	3406	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.390
4980	3419	\begin{align*} y^{\prime }&=\sin \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.390
4981	6502	\begin{align*} x y y^{\prime \prime }&=x y^{3}+a y y^{\prime }+x {y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	0.390
4982	8126	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +p^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.390
4983	10649	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.390
4984	10953	\begin{align*} x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.390
4985	17338	\begin{align*} y-y^{\prime } t&=-4 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.390
4986	17823	\begin{align*} x^{\prime }&=0 \\ y^{\prime }&=-2 y \\ \end{align*}	✓	✓	✓	✓	0.390
4987	19058	\begin{align*} x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= -5 \\ x_{2} \left (0\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	0.390
4988	19595	\begin{align*} y^{\prime \prime }+\sin \left (x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.390
4989	19637	\begin{align*} x^{\prime }&=x+3 y \\ y^{\prime }&=3 x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 5 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.390
4990	20453	\begin{align*} y^{2}-2 y y^{\prime } x +{y^{\prime }}^{2} \left (x^{2}-1\right )&=m \\ \end{align*}	✓	✓	✓	✗	0.390
4991	1867	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	0.391
4992	4556	\begin{align*} x^{\prime }-2 x-y&=2 \,{\mathrm e}^{t} \\ y^{\prime }-2 y-4 z&=4 \,{\mathrm e}^{2 t} \\ x-z^{\prime }-z&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 9 \\ y \left (0\right ) &= 3 \\ z \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.391
4993	9067	\begin{align*} y^{\prime } x&=1 \\ \end{align*}	✓	✓	✓	✓	0.391
4994	10350	\begin{align*} y^{\prime } x +y&=1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.391
4995	14057	\begin{align*} a^{2} y {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.391
4996	14276	\begin{align*} x+3 t x^{2} x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.391
4997	14407	\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=-2 x+4 y \\ \end{align*}	✓	✓	✓	✓	0.391
4998	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*}	✓	✓	✓	✓	0.391
4999	18700	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=8 x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	0.391
5000	22187	\begin{align*} y^{\prime \prime }+y^{\prime } x +\left (2 x -1\right ) y&=0 \\ y \left (-1\right ) &= 2 \\ y^{\prime }\left (-1\right ) &= -2 \\ \end{align*} Series expansion around \(x=-1\).	✓	✓	✓	✓	0.391