2.3.27 Problems 2601 to 2700

Table 2.585: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2601	4495	\begin{align*} y^{\prime \prime \prime \prime }-18 y^{\prime \prime }+81 y&=72 \,{\mathrm e}^{3 x}+729 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.157
2602	5564	\begin{align*} x y {y^{\prime }}^{2}-\left (x^{2}-y^{2}\right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.157
2603	8507	\begin{align*} x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (x +5\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.157
2604	9181	\begin{align*} x y y^{\prime \prime }&=y^{\prime }+{y^{\prime }}^{3} \\ \end{align*}	✗	✗	✓	✗	0.157
2605	10804	\begin{align*} y^{\prime \prime } x +\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.157
2606	10898	\begin{align*} 2 y^{\prime \prime } x +\left (4 x +1\right ) y^{\prime }+\left (2 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.157
2607	11014	\begin{align*} 2 x^{2} \left (2+x \right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.157
2608	11145	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.157
2609	11202	\begin{align*} 2 y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.157
2610	20197	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x -a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.157
2611	20533	\begin{align*} y^{\prime \prime \prime }&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.157
2612	22502	\begin{align*} y&=y^{\prime } x +1+4 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.157
2613	23760	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.157
2614	934	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.158
2615	2638	\begin{align*} t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(t=2\).	✗	✗	✓	✗	0.158
2616	3152	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }&=\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.158
2617	3559	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.158
2618	3933	\begin{align*} y+y^{\prime }&=5 \,{\mathrm e}^{t} \sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.158
2619	3947	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=10 \cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.158
2620	3948	\begin{align*} y^{\prime \prime }+5 y^{\prime }+4 y&=20 \sin \left (2 t \right ) \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.158
2621	4117	\begin{align*} y^{\prime \prime }+8 y^{\prime }+15 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.158
2622	4159	\begin{align*} y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y&=\cos \left (2 x +3\right ) \\ \end{align*}	✓	✓	✓	✓	0.158
2623	4494	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y&=32 \,{\mathrm e}^{2 x}+16 x^{3} \\ \end{align*}	✓	✓	✓	✓	0.158
2624	6475	\begin{align*} 2 y y^{\prime \prime }&=y^{2} \left (a x +b y\right )+{y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	0.158
2625	6948	\begin{align*} {\mathrm e}^{x} \sin \left (y\right )+{\mathrm e}^{-y}-\left (x \,{\mathrm e}^{-y}-{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.158
2626	9026	\begin{align*} x^{2} y^{3}-x^{3} y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.158
2627	10353	\begin{align*} y^{\prime } x +y&=\frac {1}{x^{3}} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.158
2628	10574	\begin{align*} 2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.158
2629	10799	\begin{align*} y^{\prime \prime } x +\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.158
2630	11124	\begin{align*} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.158
2631	12842	\begin{align*} y^{\prime \prime }-2 a^{2} y^{3}+2 a b x y-b&=0 \\ \end{align*}	✗	✗	✗	✗	0.158
2632	13183	\(\left [\begin {array}{cc} 11 & 9 \\ -16 & -13 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.158
2633	16774	\begin{align*} y^{\prime \prime }+8 y^{\prime }+7 y&=165 \,{\mathrm e}^{4 t} \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.158
2634	17625	\begin{align*} x^{3} y^{\prime \prime \prime }+22 x^{2} y^{\prime \prime }+124 y^{\prime } x +140 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.158
2635	17659	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.158
2636	17706	\begin{align*} x \left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}+5 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.158
2637	18017	\begin{align*} y&=y^{\prime } x +{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.158
2638	18278	\begin{align*} y^{\prime \prime \prime }-y&=2 x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.158
2639	25679	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.158
2640	557	\begin{align*} t x^{\prime \prime }-\left (4 t +1\right ) x^{\prime }+2 \left (2 t +1\right ) x&=0 \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.159
2641	2293	\begin{align*} y^{\prime }+\sin \left (t \right ) y&=0 \\ y \left (0\right ) &= {\frac {3}{2}} \\ \end{align*}	✓	✓	✓	✓	0.159
2642	4465	\begin{align*} y^{\left (5\right )}-3 y^{\prime \prime \prime }+y&=9 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.159
2643	6636	\begin{align*} -3 y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=3 x^{2}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.159
2644	6961	\begin{align*} 2 y x +\left (a +x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.159
2645	11152	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4}&=0 \\ \end{align*}	✓	✓	✓	✗	0.159
2646	11729	\begin{align*} x^{2} {y^{\prime }}^{2}+4 x y^{\prime } y-5 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.159
2647	16759	\begin{align*} -2 y+y^{\prime }&=t^{3} \\ y \left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.159
2648	16761	\begin{align*} y^{\prime \prime }-4 y&=t^{3} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.159
2649	17576	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+30 y^{\prime \prime }-56 y^{\prime }+49 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ y^{\prime \prime \prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.159
2650	17628	\begin{align*} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+6 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.159
2651	18892	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= -2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.159
2652	3572	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.160
2653	6709	\begin{align*} 6 y+18 y^{\prime } x +9 x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.160
2654	10329	\begin{align*} x^{\prime }+y^{\prime }-x&=t +y \\ x^{\prime }+y^{\prime }&=2 x+3 y+{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✗	0.160
2655	14637	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&=3 \,{\mathrm e}^{x} x^{2}-7 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.160
2656	16779	\begin{align*} y^{\prime \prime }&={\mathrm e}^{t} \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.160
2657	20901	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=\infty \).	✗	✗	✓	✓	0.160
2658	22910	\begin{align*} x^{\prime }&=x+y+z \\ y^{\prime }&=2 x+5 y+3 z \\ z^{\prime }&=3 x+9 y+5 z \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= -2 \\ y \left (0\right ) &= -1 \\ z \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.160
2659	24010	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.160
2660	24034	\begin{align*} y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y&={\mathrm e}^{2 x} \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.160
2661	541	\begin{align*} x^{\prime \prime }+6 x^{\prime }+25 x&=0 \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.161
2662	2109	\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.161
2663	2156	\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+3 y^{\prime }+9 y&=2 \,{\mathrm e}^{3 x} \left (11-24 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.161
2664	2172	\begin{align*} 2 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }-y&={\mathrm e}^{x} \left (11+12 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.161
2665	3339	\begin{align*} y^{\prime }&=1+y^{2} \\ y \left (1\right ) &= -1 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.161
2666	3490	\begin{align*} y^{\prime \prime \prime }-12 y^{\prime }+16 y&=32 x -8 \\ \end{align*}	✓	✓	✓	✓	0.161
2667	3950	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=3 \cos \left (t \right )+\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.161
2668	4377	\begin{align*} \left (x +1\right ) \left (y^{\prime }+y^{2}\right )-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.161
2669	6413	\begin{align*} \sqrt {x}\, y^{\prime \prime }&=y^{{3}/{2}} \\ \end{align*}	✗	✗	✗	✗	0.161
2670	6541	\begin{align*} \left (y^{2}+x^{2}\right ) y^{\prime \prime }&=\left (1+y^{2}\right ) \left (-y+y^{\prime } x \right ) \\ \end{align*}	✗	✗	✗	✗	0.161
2671	6875	\begin{align*} {y^{\prime }}^{2}-\frac {a^{2}}{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.161
2672	7265	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.161
2673	7450	\begin{align*} y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.161
2674	9621	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.161
2675	9652	\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.161
2676	11192	\begin{align*} \left (-x +3\right ) y-x \left (4-x \right ) y^{\prime }+2 \left (-x +2\right ) x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.161
2677	12785	\begin{align*} y^{\prime \prime \prime \prime }-12 y^{\prime \prime }+12 y-16 x^{4} {\mathrm e}^{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.161
2678	12793	\begin{align*} x y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-24&=0 \\ \end{align*}	✓	✓	✓	✓	0.161
2679	12897	\begin{align*} x^{2} y^{\prime \prime }&=a \left (y^{n}-y\right ) \\ \end{align*}	✗	✗	✗	✗	0.161
2680	12920	\begin{align*} y y^{\prime \prime }+y^{2}-a x -b&=0 \\ \end{align*}	✗	✗	✓	✗	0.161
2681	14435	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=0 \\ y \left (2\right ) &= 0 \\ y^{\prime }\left (2\right ) &= 2 \\ y^{\prime \prime }\left (2\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	0.161
2682	16786	\begin{align*} y^{\prime \prime }+4 y&=\sin \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.161
2683	17586	\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-24 y^{\prime }+36 y&=108 t \\ \end{align*}	✓	✓	✓	✓	0.161
2684	18460	\begin{align*} x^{\prime }+x&=2 \sin \left (t \right ) \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.161
2685	21589	\begin{align*} y^{\prime \prime \prime \prime }-y&=\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.161
2686	22321	\begin{align*} x y {y^{\prime }}^{2}-\left (y^{2}+x^{2}\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.161
2687	22677	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.161
2688	24922	\begin{align*} y^{\prime }&=t +3 \\ \end{align*}	✓	✓	✓	✓	0.161
2689	25076	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=4 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.161
2690	234	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.162
2691	2108	\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.162
2692	3196	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=x^{2} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.162
2693	6472	\begin{align*} 2 y y^{\prime \prime }&=4 y^{2} \left (x +2 y\right )+{y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	0.162
2694	6847	\begin{align*} x^{3}+3 x y^{2}+\left (y^{3}+3 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.162
2695	9030	\begin{align*} 2 y^{3}+2+3 y^{2} y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.162
2696	9889	\begin{align*} 8 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.162
2697	10616	\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.162
2698	10905	\begin{align*} y^{\prime \prime } x -\left (4 x +1\right ) y^{\prime }+\left (2+4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.162
2699	10996	\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*}	✓	✓	✓	✗	0.162
2700	10997	\begin{align*} 8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.162