2.3.46 Problems 4501 to 4600

Table 2.665: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4501	16735	\begin{align*} y^{\prime \prime }+20 y^{\prime }+100 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.361
4502	20840	\begin{align*} x^{\prime \prime }-x^{\prime }-6 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.361
4503	23272	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.361
4504	27119	\(\left [\begin {array}{cccc} -2 & 0 & 0 & 0 \\ -4 & -2 & 0 & 0 \\ 0 & 0 & -2 & 0 \\ 0 & 0 & 0 & -2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.361
4505	27184	\begin{align*} x_{1}^{\prime }&=-2 x_{1}+x_{2} \\ x_{2}^{\prime }&=2 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.361
4506	812	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.362
4507	863	\begin{align*} 3 x^{\prime \prime }+30 x^{\prime }+63 x&=0 \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.362
4508	1083	\begin{align*} y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.362
4509	1425	\begin{align*} x_{1}^{\prime }&=3 x_{1}+9 x_{2} \\ x_{2}^{\prime }&=-x_{1}-3 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.362
4510	2341	\begin{align*} 2 t y^{3}+3 t^{2} y^{2} y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.362
4511	9215	\begin{align*} 2 y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.362
4512	10564	\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.362
4513	12415	\begin{align*} x^{2} y^{\prime \prime }+\left (a x +b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.362
4514	16835	\begin{align*} y^{\prime \prime }-3 x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.362
4515	17008	\begin{align*} 16 y^{\prime \prime }+24 y^{\prime }+153 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.362
4516	17622	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.362
4517	19020	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }&=\frac {x_{1}}{2}-3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.362
4518	19579	\begin{align*} y^{\prime }+y&=1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.362
4519	19690	\begin{align*} x^{\prime \prime }-4 x^{\prime }+5 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.362
4520	20762	\begin{align*} \left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y&=\frac {2}{x^{3}} \\ \end{align*}	✓	✓	✓	✗	0.362
4521	21284	\begin{align*} x^{\prime \prime \prime \prime }+x^{\prime \prime }&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ x^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.362
4522	23588	\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.362
4523	23784	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x \\ \end{align*}	✓	✓	✓	✓	0.362
4524	23810	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.362
4525	25066	\begin{align*} y^{\prime \prime }+25 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.362
4526	430	\begin{align*} \left (x^{2}-3\right ) y^{\prime \prime }+2 x y^{\prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.363
4527	2235	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=F \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.363
4528	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.	✓	✓	✓	✓	0.363
4529	3542	\begin{align*} y^{\prime }+\frac {m}{x}&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.363
4530	3573	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.363
4531	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.	✓	✓	✓	✓	0.363
4532	10776	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.363
4533	16027	\begin{align*} x^{\prime }&=-2 x-y \\ y^{\prime }&=x-4 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.363
4534	21158	\begin{align*} x^{\prime \prime }+2 t^{3} x&=0 \\ \end{align*}	✓	✓	✓	✗	0.363
4535	23363	\begin{align*} 4 y^{\prime \prime }+8 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.363
4536	23769	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.363
4537	23770	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.363
4538	24845	\begin{align*} 6 {y^{\prime }}^{2} x -\left (3 x +2 y\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.363
4539	922	\begin{align*} x^{\prime }&=-3 y \\ y^{\prime }&=3 x \\ \end{align*}	✓	✓	✓	✓	0.364
4540	6652	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&=x \\ \end{align*}	✓	✓	✓	✓	0.364
4541	7263	\begin{align*} y^{\prime \prime }-2 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.364
4542	8186	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.364
4543	16458	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.364
4544	16505	\begin{align*} 9 y^{\prime \prime }+12 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.364
4545	19647	\begin{align*} x^{\prime }&=-4 x-y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.364
4546	23711	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+6 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.364
4547	24710	\begin{align*} y^{\prime }+y^{\prime \prime \prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.364
4548	25913	\begin{align*} 2 y^{\prime \prime }-9 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.364
4549	25967	\begin{align*} y^{\left (6\right )}+y^{\prime \prime \prime \prime }-y&=4 x^{5}-6 x^{2}+2 \\ \end{align*}	✓	✓	✓	✓	0.364
4550	27646	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=6 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.364
4551	241	\begin{align*} 9 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.365
4552	358	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=\sin \left (3 x \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.365
4553	438	\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.365
4554	811	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.365
4555	2222	\begin{align*} 4 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-5 x y^{\prime }+2 y&=30 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.365
4556	2552	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= v \\ \end{align*}	✓	✓	✓	✓	0.365
4557	7972	\begin{align*} -y+x y^{\prime }+x^{3} y^{\prime \prime \prime }&=3 x^{4} \\ \end{align*}	✓	✓	✓	✓	0.365
4558	7979	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.365
4559	8142	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.365
4560	11144	\begin{align*} \left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.365
4561	13187	\(\left [\begin {array}{ccc} 3 & -2 & 0 \\ 0 & 1 & 0 \\ -4 & 4 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.365
4562	14657	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }-4 y&=8 x^{2}+3-6 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 7 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.365
4563	14779	\begin{align*} x^{\prime }+y^{\prime }+2 y&=\sin \left (t \right ) \\ x^{\prime }+y^{\prime }-x-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.365
4564	16504	\begin{align*} 16 y^{\prime \prime }-24 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.365
4565	16709	\begin{align*} y^{\prime \prime }-12 y^{\prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.365
4566	17025	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.365
4567	21118	\begin{align*} x^{\prime \prime }+5 x^{\prime }+6 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.365
4568	21959	\begin{align*} {y^{\prime \prime }}^{{3}/{2}}+y&=x \\ \end{align*}	✗	✓	✓	✗	0.365
4569	23335	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.365
4570	27636	\begin{align*} y^{\prime \prime }-y&=2 \,{\mathrm e}^{x}-x^{2} \\ \end{align*}	✓	✓	✓	✓	0.365
4571	547	\begin{align*} x^{\prime \prime \prime \prime }+x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ x^{\prime \prime \prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.366
4572	585	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-9 x+6 y \\ \end{align*}	✓	✓	✓	✓	0.366
4573	870	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=3 x +4 \\ \end{align*}	✓	✓	✓	✓	0.366
4574	2254	\begin{align*} y_{1}^{\prime }&=-y_{2} \\ y_{2}^{\prime }&=y_{1}-2 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.366
4575	3398	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=6 \left (-x^{2}+1\right )^{2} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.366
4576	8125	\begin{align*} y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.366
4577	8628	\begin{align*} y^{\prime \prime }+7 y^{\prime }+12 y&=21 \,{\mathrm e}^{3 t} \\ y \left (0\right ) &= {\frac {7}{2}} \\ y^{\prime }\left (0\right ) &= -10 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.366
4578	16064	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-4 x-4 y \\ \end{align*}	✓	✓	✓	✓	0.366
4579	16428	\begin{align*} y^{\prime \prime }&=-2 {y^{\prime }}^{2} x \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.366
4580	18126	\begin{align*} 3 y^{\prime \prime }-2 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.366
4581	20520	\begin{align*} x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.366
4582	20912	\begin{align*} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.366
4583	23247	\begin{align*} x^{2} y^{\prime \prime }-{\mathrm e}^{x} y^{\prime }-2&=0 \\ \end{align*}	✓	✓	✓	✓	0.366
4584	23325	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.366
4585	24470	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.366
4586	26715	\begin{align*} y^{\prime }&={\mathrm e}^{y}+y x \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.366
4587	27016	\begin{align*} -2 y+y^{\prime }&=1-t \\ y \left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.366
4588	27585	\begin{align*} y y^{\prime }+x y y^{\prime \prime }-{y^{\prime }}^{2} x&=x^{3} \\ \end{align*}	✗	✓	✓	✗	0.366
4589	27594	\begin{align*} y^{\prime \prime }+2 y {y^{\prime }}^{2}&=\left (2 x +\frac {1}{x}\right ) y^{\prime } \\ \end{align*}	✗	✓	✓	✗	0.366
4590	7883	\begin{align*} x +\cos \left (x \right ) y+\sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.367
4591	7886	\begin{align*} 2 u^{2}+2 u v+\left (u^{2}+v^{2}\right ) v^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.367
4592	10589	\begin{align*} 16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.367
4593	18316	\begin{align*} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=\left (x -1\right )^{2} {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	0.367
4594	23437	\begin{align*} y^{\prime \prime }+\left (x +3\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.367
4595	24776	\begin{align*} {y^{\prime }}^{2} x -2 \left (2 x +y\right ) y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.367
4596	26008	\begin{align*} y^{\prime \prime }+x y^{\prime }+3 y&=x^{2} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.367
4597	420	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.368
4598	441	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.368
4599	587	\begin{align*} x^{\prime }&=-x+3 y \\ y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.368
4600	588	\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=2 x-3 y \\ \end{align*}	✓	✓	✓	✓	0.368