2.3.46 Problems 4501 to 4600

Table 2.641: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4501	16770	\begin{align*} y^{\prime \prime \prime }-27 y&={\mathrm e}^{-3 t} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ y^{\prime \prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.358
4502	17385	\begin{align*} 8 y^{\prime \prime }+6 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.358
4503	17597	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=\frac {{\mathrm e}^{t}}{t} \\ \end{align*}	✓	✓	✓	✓	0.358
4504	18766	\begin{align*} y^{\prime \prime }+2 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.358
4505	19853	\begin{align*} x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+8 y^{\prime } x&=\ln \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.358
4506	19856	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.358
4507	22110	\begin{align*} y^{\prime \prime }+y^{\prime }+\frac {y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.358
4508	449	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x +2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.359
4509	506	\begin{align*} y^{\prime \prime } x +y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.359
4510	971	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=6 x_{1}-5 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.359
4511	1315	\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+82 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.359
4512	10662	\begin{align*} 2 t y^{\prime \prime }+\left (1+t \right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.359
4513	11200	\begin{align*} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.359
4514	13169	\(\left [\begin {array}{cc} 0 & -4 \\ 36 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.359
4515	15204	\begin{align*} y^{\prime \prime }+6 y^{\prime }+34 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.359
4516	15321	\begin{align*} y^{\prime \prime }+9 y&=18 t \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.359
4517	16066	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.359
4518	16181	\begin{align*} y^{\prime }&=\sin \left (\frac {x}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.359
4519	22193	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.359
4520	22635	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.359
4521	22821	\begin{align*} y^{\prime }+y&=0 \\ y \left (0\right ) &= 4 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.359
4522	23358	\begin{align*} 5 y^{\prime \prime }+10 y^{\prime }+20 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.359
4523	23699	\begin{align*} y^{\prime \prime }-y x&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.359
4524	25193	\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } t +6 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.359
4525	868	\begin{align*} x^{\prime \prime }+10 x^{\prime }+125 x&=0 \\ x \left (0\right ) &= 6 \\ x^{\prime }\left (0\right ) &= 50 \\ \end{align*}	✓	✓	✓	✓	0.360
4526	1317	\begin{align*} 4 y^{\prime \prime }+12 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	0.360
4527	2423	\begin{align*} y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.360
4528	5891	\begin{align*} -\left (x +1\right ) y+y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.360
4529	12564	\begin{align*} \left (a \,x^{2}+b x \right ) y^{\prime \prime }+2 b y^{\prime }-2 a y&=0 \\ \end{align*}	✓	✓	✓	✗	0.360
4530	21121	\begin{align*} x^{\prime \prime }-2 x^{\prime }+2 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.360
4531	22842	\begin{align*} y^{\prime \prime }+y^{\prime } x -2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.360
4532	23791	\begin{align*} x^{\prime }&=5 x-6 y \\ y^{\prime }&=6 x-7 y \\ \end{align*}	✓	✓	✓	✓	0.360
4533	25109	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.360
4534	26015	\begin{align*} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.360
4535	589	\begin{align*} x^{\prime }&=-3 x+2 y \\ y^{\prime }&=-3 x+4 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.361
4536	7777	\begin{align*} y^{\prime \prime }+6 y^{\prime }+10 y&=50 x \\ \end{align*}	✓	✓	✓	✓	0.361
4537	7883	\begin{align*} x +\cos \left (x \right ) y+\sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.361
4538	9487	\begin{align*} y^{\prime }&=y^{2}-x \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.361
4539	10606	\begin{align*} 3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.361
4540	13663	\begin{align*} y^{\prime \prime }-\left (a x +b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.361
4541	14397	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=x+3 y \\ \end{align*}	✓	✓	✓	✓	0.361
4542	15496	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.361
4543	16501	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.361
4544	16516	\begin{align*} 9 y^{\prime \prime }+18 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.361
4545	23601	\begin{align*} x^{\prime }&=3 x-2 y \\ y^{\prime }&=2 x-y \\ \end{align*}	✓	✓	✓	✓	0.361
4546	23602	\begin{align*} x^{\prime }&=-4 x+y \\ y^{\prime }&=-x-2 y \\ \end{align*}	✓	✓	✓	✓	0.361
4547	23612	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.361
4548	24045	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{x} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.361
4549	26556	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=x +1 \\ \end{align*}	✓	✓	✓	✓	0.361
4550	660	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-x} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.362
4551	855	\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.362
4552	1930	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.362
4553	2558	\begin{align*} 4 y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.362
4554	5750	\begin{align*} a \,x^{k} y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.362
4555	8610	\begin{align*} y^{\prime \prime }+k^{2} x^{4} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.362
4556	10591	\begin{align*} 36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (-9 x +1\right ) y^{\prime }+\left (1-70 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.362
4557	11163	\begin{align*} y^{\prime \prime }+n^{2} y&=\frac {6 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.362
4558	14837	\begin{align*} t^{3} x^{\prime \prime }+3 t^{2} x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.362
4559	16003	\begin{align*} x^{\prime }&=-4 x+y \\ y^{\prime }&=2 x-3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= -1 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.362
4560	16823	\begin{align*} \left (x -3\right ) y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.362
4561	16953	\begin{align*} x^{\prime }&=-x+2 y \\ y^{\prime }&=2 x-y \\ \end{align*}	✓	✓	✓	✓	0.362
4562	17722	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.362
4563	18744	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.362
4564	21627	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.362
4565	23416	\begin{align*} x \left (1-3 x \ln \left (x \right )\right ) y^{\prime \prime }+\left (1+9 \ln \left (x \right ) x^{2}\right ) y^{\prime }-\left (3+9 x \right ) y&=0 \\ \end{align*}	✓	✓	✗	✗	0.362
4566	25306	\begin{align*} y^{\prime }+2 y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.362
4567	614	\begin{align*} x_{1}^{\prime }&=4 x_{1}+x_{2} \\ x_{2}^{\prime }&=-2 x_{1}+x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 11 \\ x_{2} \left (0\right ) &= -7 \\ \end{align*}	✓	✓	✓	✓	0.363
4568	628	\begin{align*} x_{1}^{\prime }&=x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.363
4569	631	\begin{align*} x_{1}^{\prime }&=x_{1}-2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.363
4570	1526	\begin{align*} y^{\prime }&=x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.363
4571	2387	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.363
4572	5794	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.363
4573	6189	\begin{align*} -2 y+y^{\prime } x +x^{3} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.363
4574	9461	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.363
4575	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*}	✓	✓	✓	✗	0.363
4576	10571	\begin{align*} 9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.363
4577	14997	\(\left [\begin {array}{cc} 4 & -2 \\ 1 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.363
4578	16805	\begin{align*} y^{\prime }+2 y&=4 \delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.363
4579	16938	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=-2 x \\ \end{align*}	✓	✓	✓	✓	0.363
4580	18760	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.363
4581	20928	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.363
4582	23283	\begin{align*} 3 y^{\prime \prime }+48 y^{\prime }+192 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.363
4583	23653	\begin{align*} y^{\prime \prime }-10 y^{\prime }+21 y&=21 t^{2}+t +13 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.363
4584	25540	\begin{align*} y^{\prime \prime }&=2 a y^{\prime }-\left (a^{2}-\omega ^{2}\right ) y \\ \end{align*}	✓	✓	✓	✓	0.363
4585	3791	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=15 \,{\mathrm e}^{3 x} \sqrt {x} \\ \end{align*}	✓	✓	✓	✓	0.364
4586	5799	\begin{align*} 12 y-7 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.364
4587	8125	\begin{align*} y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.364
4588	19651	\begin{align*} x^{\prime }&=2 x \\ y^{\prime }&=3 y \\ \end{align*}	✓	✓	✓	✓	0.364
4589	20932	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.364
4590	21109	\begin{align*} x^{\prime \prime }+2 x^{\prime }+2 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.364
4591	22938	\begin{align*} x^{\prime }&=x+8 y \\ y^{\prime }&=-2 x-7 y \\ \end{align*}	✓	✓	✓	✓	0.364
4592	23025	\begin{align*} y^{\prime \prime }-3 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.364
4593	636	\begin{align*} x_{1}^{\prime }&=-50 x_{1}+20 x_{2} \\ x_{2}^{\prime }&=100 x_{1}-60 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.365
4594	3340	\begin{align*} y^{\prime }&=x^{2}+y^{2} \\ y \left (2\right ) &= 0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	0.365
4595	6300	\begin{align*} y^{\prime \prime }&=x +6 y^{2} \\ \end{align*}	✗	✗	✗	✗	0.365
4596	7782	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.365
4597	8483	\begin{align*} 2 y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.365
4598	8806	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=g \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.365
4599	9227	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.365
4600	10471	\begin{align*} \left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.365