2.3.29 Problems 2801 to 2900

Table 2.589: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2801	8269	\begin{align*} {y^{\prime }}^{2}&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.168
2802	9111	\begin{align*} y^{\prime }-2 y x&=6 x \,{\mathrm e}^{x^{2}} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.168
2803	10092	\begin{align*} y^{\prime \prime }-y^{\prime }-y x -x&=0 \\ \end{align*}	✓	✓	✓	✗	0.168
2804	10095	\begin{align*} y^{\prime \prime }-y^{\prime }-y x -x^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✗	0.168
2805	10575	\begin{align*} 6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.168
2806	10579	\begin{align*} 3 x^{2} \left (x +1\right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.168
2807	10755	\begin{align*} x \left (x +1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.168
2808	10758	\begin{align*} x \left (x -1\right )^{2} y^{\prime \prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.168
2809	10816	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.168
2810	10835	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.168
2811	10836	\begin{align*} 2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.168
2812	11015	\begin{align*} 2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.168
2813	11079	\begin{align*} y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1}&=0 \\ \end{align*}	✓	✓	✓	✗	0.168
2814	11123	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.168
2815	11156	\begin{align*} 4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.168
2816	11172	\begin{align*} 3 y^{\prime \prime } x -2 \left (3 x -1\right ) y^{\prime }+\left (3 x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.168
2817	14355	\begin{align*} x^{\prime \prime }-2 x^{\prime }+2 x&={\mathrm e}^{-t} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.168
2818	15219	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=t +2 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.168
2819	15314	\begin{align*} y^{\prime \prime } x +y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.168
2820	16672	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=3 \,{\mathrm e}^{x} \cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	0.168
2821	16766	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=t^{2} {\mathrm e}^{4 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.168
2822	17673	\begin{align*} x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+79 y^{\prime } x +125 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.168
2823	18884	\begin{align*} y^{\prime \prime }+2 y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.168
2824	19038	\begin{align*} x_{1}^{\prime }&=x_{2}-x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{3} \\ x_{3}^{\prime }&=x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.168
2825	19450	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.168
2826	20987	\begin{align*} y^{\prime }&=x^{3}+y^{3} \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.168
2827	25073	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=12 \,{\mathrm e}^{2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.168
2828	1682	\begin{align*} 14 x^{2} y^{3}+21 x^{2} y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.169
2829	2208	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{2 x} \left (-3 x^{2}-4 x +5\right ) \\ \end{align*}	✓	✓	✓	✓	0.169
2830	3126	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }-4 y&={\mathrm e}^{4 x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.169
2831	7221	\begin{align*} x y^{\prime } y-y x&=y \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.169
2832	12995	\begin{align*} y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}-a x -b&=0 \\ \end{align*}	✗	✗	✗	✗	0.169
2833	16789	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.169
2834	18910	\begin{align*} y_{1}^{\prime }&=-5 y_{1}+y_{2} \\ y_{2}^{\prime }&=-9 y_{1}+5 y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.169
2835	19448	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.169
2836	19565	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=9 x^{2}-2 x +1 \\ \end{align*}	✓	✓	✓	✓	0.169
2837	20389	\begin{align*} x {y^{\prime }}^{2}+\left (y-x \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.169
2838	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*}	✓	✓	✓	✓	0.169
2839	25747	\begin{align*} {y^{\prime }}^{2}&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.169
2840	1630	\begin{align*} 7 y^{\prime } x -2 y&=-\frac {x^{2}}{y^{6}} \\ \end{align*}	✓	✓	✓	✗	0.170
2841	2147	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=-{\mathrm e}^{x} \left (-24 x^{2}+76 x +4\right ) \\ \end{align*}	✓	✓	✓	✓	0.170
2842	5499	\begin{align*} x^{2} {y^{\prime }}^{2}-y^{\prime } x +y \left (1-y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.170
2843	7269	\begin{align*} y^{\prime \prime }+\left (1+2 i\right ) y^{\prime }+\left (-1+i\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.170
2844	7897	\begin{align*} 2 y-3 x +y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.170
2845	9444	\begin{align*} y^{\prime \prime }-y&=t^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.170
2846	9601	\begin{align*} y^{\prime }+6 y&={\mathrm e}^{4 t} \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.170
2847	9610	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.170
2848	11000	\begin{align*} 4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.170
2849	11122	\begin{align*} x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.170
2850	11175	\begin{align*} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.170
2851	12878	\begin{align*} y^{\prime \prime }-k \,x^{a} y^{b} {y^{\prime }}^{r}&=0 \\ \end{align*}	✗	✗	✗	✗	0.170
2852	15048	\begin{align*} y&=y^{\prime } x +{y^{\prime }}^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	0.170
2853	15210	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+10 y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 3 \\ y^{\prime \prime }\left (0\right ) &= 8 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.170
2854	15392	\begin{align*} y&=y^{\prime } y+y^{\prime }-{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.170
2855	20170	\begin{align*} y^{\prime \prime \prime }&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.170
2856	20382	\begin{align*} {y^{\prime }}^{2}-9 y^{\prime }+18&=0 \\ \end{align*}	✓	✓	✓	✓	0.170
2857	22052	\begin{align*} x y^{2}+\left (y^{2} x^{2}+x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.170
2858	22798	\begin{align*} y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+\left (1+\sin \left (x \right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.170
2859	22902	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.170
2860	23239	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.170
2861	24413	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.170
2862	560	\begin{align*} t x^{\prime \prime }+\left (4 t -2\right ) x^{\prime }+\left (13 t -4\right ) x&=0 \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.171
2863	1526	\begin{align*} y^{\prime }&=x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.171
2864	3128	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y&=x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.171
2865	3336	\begin{align*} y^{\prime }&=y^{2} x^{2} \\ y \left (1\right ) &= 0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.171
2866	3542	\begin{align*} y^{\prime }+\frac {m}{x}&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.171
2867	5799	\begin{align*} 12 y-7 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.171
2868	6474	\begin{align*} 2 y y^{\prime \prime }&=-1-2 x y^{2}+a y^{3}+{y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	0.171
2869	6482	\begin{align*} 2 y y^{\prime \prime }&=f \left (x \right ) y^{2}+3 {y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	0.171
2870	6947	\begin{align*} x -2 y x +{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.171
2871	7041	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.171
2872	9599	\begin{align*} -y+y^{\prime }&=1 \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.171
2873	10501	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (x^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.171
2874	10576	\begin{align*} 28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.171
2875	10620	\begin{align*} x^{2} \left (3 x +4\right ) y^{\prime \prime }-x \left (-3 x +4\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.171
2876	10621	\begin{align*} 4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (2 x +3\right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.171
2877	10977	\begin{align*} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.171
2878	11087	\begin{align*} t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.171
2879	11289	\begin{align*} \left (x^{2}-x \right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.171
2880	14812	\begin{align*} y+y^{\prime }&=2 \sin \left (t \right ) \\ y \left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.171
2881	16453	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.171
2882	16771	\begin{align*} t y^{\prime \prime }+y^{\prime }+t y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.171
2883	16773	\begin{align*} y^{\prime \prime }+9 y&=27 t^{3} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.171
2884	19451	\begin{align*} x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.171
2885	20039	\begin{align*} 9 y^{\prime \prime }+18 y^{\prime }-16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.171
2886	20381	\begin{align*} {y^{\prime }}^{2}-5 y^{\prime }+6&=0 \\ \end{align*}	✓	✓	✓	✓	0.171
2887	21201	\begin{align*} x^{\prime \prime \prime \prime }+x^{\prime \prime \prime }&=t \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.171
2888	21550	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.171
2889	22247	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=\sin \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.171
2890	22250	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=3 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.171
2891	23270	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.171
2892	24046	\begin{align*} y^{\prime \prime }+y&=x \sin \left (x \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.171
2893	24049	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=16 \,{\mathrm e}^{2 x} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.171
2894	2677	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{-t} \\ y \left (t_{0} \right ) &= 1 \\ y^{\prime }\left (t_{0} \right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.172
2895	4380	\begin{align*} y^{\prime }-\tan \left (x \right ) y+y^{2} \cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.172
2896	5794	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.172
2897	6763	\begin{align*} 5 y^{\prime \prime \prime }+x y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.172
2898	7453	\begin{align*} \theta r^{\prime }+3 r-\theta -1&=0 \\ \end{align*}	✓	✓	✓	✓	0.172
2899	9612	\begin{align*} -y+y^{\prime }&=1+{\mathrm e}^{t} t \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.172
2900	10779	\begin{align*} 2 y^{\prime \prime } x -y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.172