2.3.28 Problems 2701 to 2800

Table 2.629: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2701	10549	\begin{align*} 3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.348
2702	10572	\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.348
2703	11008	\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.348
2704	12837	\begin{align*} y^{\prime \prime }-6 y^{2}-x&=0 \\ \end{align*}	✗	✗	✗	✗	0.348
2705	14952	\begin{align*} \left (-1+x \right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.348
2706	16720	\begin{align*} y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+13 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.348
2707	19591	\begin{align*} x^{3} \left (-1+x \right ) y^{\prime \prime }-2 \left (-1+x \right ) y^{\prime }+3 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.348
2708	519	\begin{align*} 16 x^{2} y^{\prime \prime }+24 y^{\prime } x +\left (144 x^{3}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.349
2709	829	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.349
2710	3589	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.349
2711	3722	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=2 \,{\mathrm e}^{-x}+3 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.349
2712	7169	\begin{align*} x^{4} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.349
2713	10570	\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.349
2714	10714	\begin{align*} 2 y^{\prime \prime } x +5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.349
2715	10808	\begin{align*} 3 t \left (1+t \right ) y^{\prime \prime }+y^{\prime } t -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.349
2716	14129	\begin{align*} -2 y+5 y^{\prime }-3 y^{\prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.349
2717	1758	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=x \\ \end{align*}	✓	✓	✓	✓	0.350
2718	3624	\begin{align*} y^{\prime }+\frac {2 y}{x}&=4 x \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.350
2719	7802	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x}+1 \\ \end{align*}	✓	✓	✓	✓	0.350
2720	18897	\begin{align*} y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.350
2721	1053	\begin{align*} y^{\prime \prime }&=4 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.351
2722	6705	\begin{align*} 8 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.351
2723	10494	\begin{align*} y^{\prime \prime } x -\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.351
2724	10750	\begin{align*} \left (2 x -3\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.351
2725	13087	\begin{align*} x^{\prime }-x+2 y&=0 \\ x^{\prime \prime }-2 y^{\prime }&=2 t -\cos \left (2 t \right ) \\ \end{align*}	✗	✓	✓	✗	0.351
2726	14629	\begin{align*} 4 y^{\prime \prime \prime }-4 y^{\prime \prime }-5 y^{\prime }+3 y&=3 x^{3}-8 x \\ \end{align*}	✓	✓	✓	✓	0.351
2727	17622	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.351
2728	851	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.352
2729	2616	\begin{align*} y^{\prime \prime }-y t^{3}&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.352
2730	2784	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{3}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }&=2 x_{2} \\ x_{3}^{\prime }&=3 x_{3}+{\mathrm e}^{2 t} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.352
2731	3065	\begin{align*} y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.352
2732	4063	\begin{align*} y^{\prime \prime }-x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.352
2733	6698	\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.352
2734	6703	\begin{align*} -8 y+7 y^{\prime } x -3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.352
2735	10598	\begin{align*} \left (1-x \right ) x^{2} y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.352
2736	10654	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.352
2737	11024	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.352
2738	12721	\begin{align*} y^{\prime \prime \prime }+\operatorname {a2} y^{\prime \prime }+\operatorname {a1} y^{\prime }+\operatorname {a0} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.352
2739	13125	\begin{align*} {x^{\prime }}^{2}+t x^{\prime }+a y^{\prime }-x&=0 \\ x^{\prime } y^{\prime }+y^{\prime } t -y&=0 \\ \end{align*}	✗	✓	✓	✓	0.352
2740	22641	\begin{align*} y^{\prime \prime \prime \prime }-20 y^{\prime \prime \prime }-16 y^{\prime \prime }+12 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.352
2741	2258	\begin{align*} y_{1}^{\prime }&=-10 y_{1}+9 y_{2} \\ y_{2}^{\prime }&=-4 y_{1}+2 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.353
2742	7991	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.353
2743	10662	\begin{align*} 2 t y^{\prime \prime }+\left (1+t \right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.353
2744	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*}	✓	✓	✓	✗	0.353
2745	14123	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=-3 \,{\mathrm e}^{2 x}+x^{2} \\ \end{align*}	✓	✓	✓	✓	0.353
2746	20072	\begin{align*} y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y&=\cos \left (x m \right ) \\ \end{align*}	✓	✓	✓	✓	0.353
2747	588	\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=2 x-3 y \\ \end{align*}	✓	✓	✓	✓	0.354
2748	1627	\begin{align*} x^{2} y^{\prime }&=y^{2}+y x -x^{2} \\ \end{align*}	✓	✓	✓	✓	0.354
2749	6301	\begin{align*} y^{\prime \prime }&=a +b x +c y^{2} \\ \end{align*}	✗	✗	✗	✗	0.354
2750	7717	\begin{align*} -y+y^{\prime } x&=x^{3}+3 x^{2}-2 x \\ \end{align*}	✓	✓	✓	✓	0.354
2751	10867	\begin{align*} \left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.354
2752	12952	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}-4 y^{2} \left (x +2 y\right )&=0 \\ \end{align*}	✗	✗	✗	✗	0.354
2753	18329	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=\frac {-1+x}{x^{3}} \\ \end{align*}	✓	✓	✓	✓	0.354
2754	20094	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.354
2755	1061	\begin{align*} y^{\prime \prime }-4 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.355
2756	1079	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.355
2757	3936	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=4 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.355
2758	4062	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.355
2759	4666	\begin{align*} y^{\prime }&=3 a +3 b x +3 b y^{2} \\ \end{align*}	✓	✓	✓	✗	0.355
2760	6474	\begin{align*} 2 y y^{\prime \prime }&=-1-2 x y^{2}+a y^{3}+{y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	0.355
2761	7788	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=2 x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.355
2762	20170	\begin{align*} y^{\prime \prime \prime }&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.355
2763	20380	\begin{align*} {y^{\prime }}^{2}-7 y^{\prime }+12&=0 \\ \end{align*}	✓	✓	✓	✓	0.355
2764	20381	\begin{align*} {y^{\prime }}^{2}-5 y^{\prime }+6&=0 \\ \end{align*}	✓	✓	✓	✓	0.355
2765	22640	\begin{align*} y^{\prime \prime \prime \prime }-20 y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.355
2766	3064	\begin{align*} y^{\prime \prime }-2 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.356
2767	4528	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=10 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= -2 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.356
2768	4551	\begin{align*} x^{\prime }-x-2 y&=16 \,{\mathrm e}^{t} t \\ 2 x-y^{\prime }-2 y&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.356
2769	4553	\begin{align*} x^{\prime }-4 x+3 y&=\sin \left (t \right ) \\ 2 x+y^{\prime }-y&=2 \cos \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= x_{0} \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	0.356
2770	6410	\begin{align*} y^{b}+x^{a} y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.356
2771	6629	\begin{align*} 4 y+2 y^{\prime }+y^{\prime \prime }+y^{\prime \prime \prime }&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.356
2772	6697	\begin{align*} -8 y+3 y^{\prime } x +x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.356
2773	10603	\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+7 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.356
2774	12594	\begin{align*} y^{\prime \prime }&=\frac {\left (x -4\right ) y^{\prime }}{2 x \left (x -2\right )}-\frac {\left (x -3\right ) y}{2 x^{2} \left (x -2\right )} \\ \end{align*}	✓	✓	✓	✗	0.356
2775	15437	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&=2 x +3 \\ \end{align*}	✓	✓	✓	✓	0.356
2776	18463	\begin{align*} x^{\prime \prime }&=\cos \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.356
2777	20382	\begin{align*} {y^{\prime }}^{2}-9 y^{\prime }+18&=0 \\ \end{align*}	✓	✓	✓	✓	0.356
2778	10778	\begin{align*} x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.357
2779	10978	\begin{align*} x^{2} \left (2+x \right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.357
2780	14627	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-3 y^{\prime }-10 y&=8 \,{\mathrm e}^{-2 x} x \\ \end{align*}	✓	✓	✓	✓	0.357
2781	14697	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.357
2782	1043	\begin{align*} y^{\prime }&=4 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.358
2783	1757	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=\frac {4}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.358
2784	2257	\begin{align*} y_{1}^{\prime }&=4 y_{1}+12 y_{2} \\ y_{2}^{\prime }&=-3 y_{1}-8 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.358
2785	2294	\begin{align*} y^{\prime }+{\mathrm e}^{t^{2}} y&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.358
2786	3066	\begin{align*} 2 y^{\prime \prime }+2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.358
2787	3940	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=30 \,{\mathrm e}^{-3 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.358
2788	10561	\begin{align*} x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.358
2789	10655	\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.358
2790	11852	\begin{align*} \sin \left (y^{\prime }\right )+y^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✗	0.358
2791	14113	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=4+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.358
2792	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*}	✓	✓	✓	✗	0.358
2793	47	\begin{align*} y^{\prime }&=64^{{1}/{3}} \left (y x \right )^{{1}/{3}} \\ \end{align*}	✓	✓	✓	✗	0.359
2794	782	\begin{align*} 6 x y^{3}+2 y^{4}+\left (9 y^{2} x^{2}+8 x y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.359
2795	1044	\begin{align*} 2 y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.359
2796	5759	\begin{align*} -\left (a^{2}-b \,{\mathrm e}^{x}\right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.359
2797	8960	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.359
2798	9107	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=\cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.359
2799	10656	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +6 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.359
2800	16939	\begin{align*} x^{\prime }&=-2 y \\ y^{\prime }&=8 x \\ \end{align*}	✓	✓	✓	✓	0.359