2.3.26 Problems 2501 to 2600

Table 2.583: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2501	18279	\begin{align*} y^{\prime \prime \prime \prime }-y&=8 \,{\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= 4 \\ y^{\prime \prime \prime }\left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	0.152
2502	18457	\begin{align*} x^{\prime }-3 x&=3 t^{3}+3 t^{2}+2 t +1 \\ x \left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.152
2503	18718	\begin{align*} y^{\prime \prime }+t y&=0 \\ \end{align*}	✓	✓	✓	✓	0.152
2504	18914	\begin{align*} y_{1}^{\prime }&=-4 y_{1}-y_{2} \\ y_{2}^{\prime }&=y_{1}-2 y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.152
2505	20374	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y&=16 x^{2}+256 \\ \end{align*}	✓	✓	✓	✓	0.152
2506	22248	\begin{align*} y^{\prime \prime }+y&=\sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.152
2507	22905	\begin{align*} x^{\prime }-3 x-6 y&=27 t^{2} \\ x^{\prime }+y^{\prime }-3 y&=5 \,{\mathrm e}^{t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 5 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.152
2508	555	\begin{align*} t x^{\prime \prime }+\left (t -2\right ) x^{\prime }+x&=0 \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.153
2509	1714	\begin{align*} 2 y^{3}+3 y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.153
2510	2158	\begin{align*} 8 y^{\prime \prime \prime }-12 y^{\prime \prime }+6 y^{\prime }-y&={\mathrm e}^{\frac {x}{2}} \left (4 x +1\right ) \\ \end{align*}	✓	✓	✓	✓	0.153
2511	3695	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.153
2512	5750	\begin{align*} a \,x^{k} y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.153
2513	9611	\begin{align*} y^{\prime }+4 y&={\mathrm e}^{-4 t} \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.153
2514	9622	\begin{align*} y^{\prime \prime }+8 y^{\prime }+20 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.153
2515	10822	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.153
2516	11104	\begin{align*} y^{\prime \prime }+2 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.153
2517	15205	\begin{align*} y^{\prime \prime \prime }+8 y^{\prime \prime }+16 y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= -8 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.153
2518	15213	\begin{align*} 4 y^{\prime \prime }+16 y^{\prime }+17 y&=17 t -1 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.153
2519	16852	\begin{align*} y^{\prime \prime }-y^{2}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.153
2520	17626	\begin{align*} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }-46 y^{\prime } x +100 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.153
2521	17631	\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.153
2522	18261	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime }&=x +2 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.153
2523	23996	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }+2 y^{\prime }-y&=x^{4}-2 x +1 \\ \end{align*}	✓	✓	✓	✓	0.153
2524	24054	\begin{align*} y^{\prime \prime }+9 y&=3 x -6 \\ y \left (0\right ) &= {\frac {1}{3}} \\ y^{\prime }\left (0\right ) &= {\frac {4}{3}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.153
2525	3125	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-12 y&=x +{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.154
2526	3949	\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.	✓	✓	✓	✓	0.154
2527	5553	\begin{align*} y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.154
2528	6866	\begin{align*} 2 y x +\left (y^{2}-3 x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.154
2529	7270	\begin{align*} y^{\prime \prime }+\left (1+2 i\right ) y^{\prime }+\left (-1+i\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.154
2530	10003	\begin{align*} \frac {{y^{\prime }}^{2}}{4}-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.154
2531	10896	\begin{align*} x^{2} y^{\prime \prime }-x \left (2 x -1\right ) y^{\prime }+\left (x^{2}-x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.154
2532	10909	\begin{align*} y^{\prime \prime } x -\left (4 x +1\right ) y^{\prime }+\left (2+4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.154
2533	11185	\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*}	✓	✓	✓	✗	0.154
2534	11188	\begin{align*} x \left (x -1\right )^{2} y^{\prime \prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.154
2535	11255	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.154
2536	11256	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.154
2537	11261	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.154
2538	12843	\begin{align*} y^{\prime \prime }+d +b x y+c y+a y^{3}&=0 \\ \end{align*}	✗	✗	✗	✗	0.154
2539	15026	\begin{align*} {y^{\prime }}^{2}&=9 y^{4} \\ \end{align*}	✓	✓	✓	✓	0.154
2540	16755	\begin{align*} y^{\left (6\right )}-64 y&={\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.154
2541	16781	\begin{align*} y^{\prime \prime }-9 y&=24 \,{\mathrm e}^{-3 t} \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.154
2542	18904	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=\cos \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.154
2543	18911	\begin{align*} y_{1}^{\prime }&=5 y_{1}-2 y_{2} \\ y_{2}^{\prime }&=6 y_{1}-2 y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.154
2544	22255	\begin{align*} y^{\prime }+z&=t \\ z^{\prime }+4 y&=0 \\ \end{align*} With initial conditions \begin{align*} y \left (0\right ) &= 1 \\ z \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.154
2545	22335	\begin{align*} \left (y^{\prime }-2 x \right ) \left (y^{\prime }-3 x^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.154
2546	22486	\begin{align*} y^{\prime \prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.154
2547	23388	\begin{align*} x^{4} y^{\prime \prime \prime \prime }-5 x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-6 y^{\prime } x +6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.154
2548	23393	\begin{align*} x^{5} y^{\left (5\right )}+3 x^{3} y^{\prime \prime \prime }-9 x^{2} y^{\prime \prime }+18 y^{\prime } x -18 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.154
2549	24796	\begin{align*} {y^{\prime }}^{2}-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.154
2550	25058	\begin{align*} y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.154
2551	2678	\begin{align*} y^{\prime \prime }+y&=\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.155
2552	3686	\begin{align*} 2 x \,{\mathrm e}^{y}+\left (3 y^{2}+x^{2} {\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.155
2553	3689	\begin{align*} 4 \,{\mathrm e}^{2 x}+2 y x -y^{2}+\left (x -y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.155
2554	3696	\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.155
2555	3951	\begin{align*} y^{\prime \prime }+4 y&=9 \sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.155
2556	4118	\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.155
2557	4121	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.155
2558	6502	\begin{align*} x y y^{\prime \prime }&=x y^{3}+a y y^{\prime }+x {y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	0.155
2559	6704	\begin{align*} \left (-a^{2}+1\right ) x y^{\prime }+3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.155
2560	7451	\begin{align*} y^{2}+\left (2 y x +\cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.155
2561	11038	\begin{align*} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.155
2562	11146	\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.155
2563	11253	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.155
2564	12721	\begin{align*} y^{\prime \prime \prime }+\operatorname {a2} y^{\prime \prime }+\operatorname {a1} y^{\prime }+\operatorname {a0} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.155
2565	14044	\begin{align*} {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.155
2566	15324	\begin{align*} x^{\prime }+y^{\prime }+x&=0 \\ x^{\prime }-x+2 y^{\prime }&={\mathrm e}^{-t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.155
2567	16796	\begin{align*} y^{\prime \prime }&=\operatorname {Heaviside}\left (t -2\right ) \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.155
2568	16956	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+5 y^{\prime }+y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.155
2569	18260	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }&=x \,{\mathrm e}^{x}-1 \\ \end{align*}	✓	✓	✓	✓	0.155
2570	18915	\begin{align*} y_{1}^{\prime }&=2 y_{1}-64 y_{2} \\ y_{2}^{\prime }&=y_{1}-14 y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 0 \\ y_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.155
2571	22233	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=4 t^{2} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.155
2572	22909	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=x-y \\ z^{\prime }&=2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 0 \\ z \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.155
2573	23659	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=8 \,{\mathrm e}^{t}+5 t \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.155
2574	25535	\begin{align*} 2 y^{\prime \prime }+8 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.155
2575	531	\begin{align*} x^{\prime \prime }+9 x&=0 \\ x \left (0\right ) &= 3 \\ x^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.156
2576	2160	\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-2 y&=-3 \,{\mathrm e}^{2 x} \left (11+12 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.156
2577	2162	\begin{align*} 4 y^{\prime \prime \prime \prime }-11 y^{\prime \prime }-9 y^{\prime }-2 y&=-{\mathrm e}^{x} \left (1-6 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.156
2578	2171	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime }-y&={\mathrm e}^{x} \left (x +1\right ) \\ \end{align*}	✓	✓	✓	✓	0.156
2579	2207	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-2 y&=-{\mathrm e}^{3 x} \left (17 x^{2}+67 x +9\right ) \\ \end{align*}	✓	✓	✓	✓	0.156
2580	3946	\begin{align*} y^{\prime \prime }-y&=8 \sin \left (t \right )-6 \cos \left (t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.156
2581	5742	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.156
2582	7461	\begin{align*} \frac {1}{y}-\left (3 y-\frac {x}{y^{2}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.156
2583	8626	\begin{align*} y^{\prime \prime }-\frac {y}{4}&=0 \\ y \left (0\right ) &= 12 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.156
2584	10696	\begin{align*} x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.156
2585	10820	\begin{align*} y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (1+3 x \right )^{2}}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.156
2586	11041	\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*}	✓	✓	✓	✗	0.156
2587	11194	\begin{align*} 4 x \left (x^{2}+1\right ) y+\left (4 x^{2}+1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.156
2588	12761	\begin{align*} \left (-a^{2}+1\right ) x y^{\prime }+3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.156
2589	12888	\begin{align*} y^{\prime \prime } x +2 y^{\prime }-x y^{n}&=0 \\ \end{align*}	✗	✗	✗	✗	0.156
2590	13925	\begin{align*} y^{\prime \prime }+a \,{\mathrm e}^{\lambda x} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.156
2591	16134	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=2 \,{\mathrm e}^{t} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.156
2592	17993	\begin{align*} x^{2} {y^{\prime }}^{2}+3 x y^{\prime } y+2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.156
2593	22513	\begin{align*} y^{\prime }+2 x&=2 \\ \end{align*}	✓	✓	✓	✓	0.156
2594	22681	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.156
2595	274	\begin{align*} 2 y^{\prime \prime }-7 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.157
2596	1485	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.157
2597	2165	\begin{align*} 2 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-5 y^{\prime }-2 y&=18 \,{\mathrm e}^{x} \left (5+2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.157
2598	2296	\begin{align*} 2 t y+y^{\prime }&=t \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.157
2599	3191	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }-5 y^{\prime }&=x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.157
2600	3684	\begin{align*} \cos \left (y x \right )-x y \sin \left (y x \right )-x^{2} \sin \left (y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.157