2.3.54 Problems 5301 to 5400

Table 2.681: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5301	9992	\begin{align*} y^{\prime }&=x +1 \\ \end{align*}	✓	✓	✓	✓	0.665
5302	17492	\begin{align*} y^{\prime \prime }+12 y^{\prime }+37 y&={\mathrm e}^{-6 t} \csc \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.665
5303	18661	\begin{align*} x^{\prime }&=5 x-y \\ y^{\prime }&=3 x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.665
5304	20042	\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.665
5305	20197	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x -a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.665
5306	24023	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=x^{2}-x \\ \end{align*}	✓	✓	✓	✓	0.665
5307	866	\begin{align*} 4 x^{\prime \prime }+20 x^{\prime }+169 x&=0 \\ x \left (0\right ) &= 4 \\ x^{\prime }\left (0\right ) &= 16 \\ \end{align*}	✓	✓	✓	✓	0.666
5308	4046	\begin{align*} 4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.666
5309	5639	\begin{align*} {y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+x y \left (x^{2}+y x +y^{2}\right ) y^{\prime }-x^{3} y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.666
5310	6724	\begin{align*} \sin \left (x \right )-\cos \left (x \right ) y-3 \sin \left (x \right ) y^{\prime }+3 \left (\cos \left (x \right )+1\right ) y^{\prime \prime }+\left (x +\sin \left (x \right )\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.666
5311	14523	\begin{align*} y^{2} {\mathrm e}^{2 x}+\left ({\mathrm e}^{2 x} y-2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.666
5312	15192	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.666
5313	17502	\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=\frac {{\mathrm e}^{-4 t}}{t^{4}} \\ \end{align*}	✓	✓	✓	✓	0.666
5314	1497	\begin{align*} y^{\prime \prime }+4 y&=\sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.667
5315	2698	\begin{align*} x^{\prime }&=-2 x+y+t \\ y^{\prime }&=-4 x+3 y-1 \\ \end{align*}	✓	✓	✓	✓	0.667
5316	2828	\begin{align*} x_{1}^{\prime }&=x_{1}-4 x_{2} \\ x_{2}^{\prime }&=-8 x_{1}+4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.667
5317	4049	\begin{align*} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.667
5318	9259	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.667
5319	9402	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.667
5320	24024	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }&={\mathrm e}^{-4 x} \\ \end{align*}	✓	✓	✓	✓	0.667
5321	486	\begin{align*} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.668
5322	1884	\begin{align*} \left (-x^{3}+1\right ) y^{\prime \prime }+15 x^{2} y^{\prime }-36 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.668
5323	5788	\begin{align*} -4 y-3 y^{\prime }+y^{\prime \prime }&=10 \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.668
5324	13165	\(\left [\begin {array}{cc} 0 & -6 \\ 6 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.668
5325	14406	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=-x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.668
5326	16489	\begin{align*} y^{\prime \prime }+2 y^{\prime }-24 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.668
5327	17503	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {{\mathrm e}^{-3 t}}{t} \\ \end{align*}	✓	✓	✓	✓	0.668
5328	18660	\begin{align*} x^{\prime }&=2 x-y \\ y^{\prime }&=3 x-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.668
5329	20395	\begin{align*} x^{2} {y^{\prime }}^{2}+y y^{\prime } x -6 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.668
5330	24865	\begin{align*} x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.668
5331	1421	\begin{align*} x_{1}^{\prime }&=x_{2}+x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{3} \\ x_{3}^{\prime }&=x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.669
5332	2275	\begin{align*} y_{1}^{\prime }&=-5 y_{1}-y_{2}+11 y_{3} \\ y_{2}^{\prime }&=-7 y_{1}+y_{2}+13 y_{3} \\ y_{3}^{\prime }&=-4 y_{1}+8 y_{3} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 0 \\ y_{2} \left (0\right ) &= 2 \\ y_{3} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.669
5333	14992	\(\left [\begin {array}{cc} 7 & -2 \\ 26 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.669
5334	17461	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=3 t \\ y \left (0\right ) &= {\frac {23}{12}} \\ y^{\prime }\left (0\right ) &= -{\frac {3}{2}} \\ \end{align*}	✓	✓	✓	✓	0.669
5335	18860	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=2 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.669
5336	3911	\begin{align*} x_{1}^{\prime }&=-2 x_{1}-x_{3} \\ x_{2}^{\prime }&=-x_{2} \\ x_{3}^{\prime }&=x_{1} \\ \end{align*}	✓	✓	✓	✓	0.670
5337	7981	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.670
5338	14116	\begin{align*} -y+y^{\prime } x +x^{3} y^{\prime \prime \prime }&=x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.670
5339	18649	\begin{align*} x^{\prime }&=2 x-y \\ y^{\prime }&=3 x-2 y \\ \end{align*}	✓	✓	✓	✓	0.670
5340	23397	\begin{align*} x y^{\prime \prime \prime }-\frac {6 y}{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.670
5341	26803	\begin{align*} y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.670
5342	1881	\begin{align*} \left (-2 x^{3}+1\right ) y^{\prime \prime }-10 x^{2} y^{\prime }-8 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.671
5343	2380	\begin{align*} y^{\prime \prime }+y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.671
5344	3728	\begin{align*} y^{\prime \prime }-4 y^{\prime }+6 y&=7 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.671
5345	7583	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.671
5346	9384	\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 \(x=0\).	✗	✗	✓	✗	0.671
5347	12372	\begin{align*} y^{\prime \prime } x +a y^{\prime }+b \,x^{\operatorname {a1}} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.671
5348	12978	\begin{align*} x y y^{\prime \prime }-x {y^{\prime }}^{2}+a y y^{\prime }+y^{3} b x&=0 \\ \end{align*}	✗	✗	✗	✗	0.671
5349	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*}	✓	✓	✓	✓	0.671
5350	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*}	✓	✓	✓	✓	0.671
5351	15198	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.671
5352	17766	\begin{align*} y^{\prime \prime }-4 y&=t \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.671
5353	18183	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=-2 \\ \end{align*}	✓	✓	✓	✓	0.671
5354	18704	\begin{align*} x^{\prime }&=2 x-4 y \\ y^{\prime }&=2 x-2 y \\ \end{align*}	✓	✓	✓	✓	0.671
5355	18955	\begin{align*} y^{\prime \prime }+6 y^{\prime }+25 y&=\sin \left (\alpha t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.671
5356	26811	\begin{align*} y^{\left (5\right )}+2 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.671
5357	233	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.672
5358	1888	\begin{align*} \left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.672
5359	2280	\begin{align*} y_{1}^{\prime }&=-2 y_{1}-12 y_{2}+10 y_{3} \\ y_{2}^{\prime }&=2 y_{1}-24 y_{2}+11 y_{3} \\ y_{3}^{\prime }&=2 y_{1}-24 y_{2}+8 y_{3} \\ \end{align*}	✓	✓	✓	✓	0.672
5360	11288	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.672
5361	14353	\begin{align*} x^{\prime \prime }-x^{\prime }-6 x&=0 \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.672
5362	17033	\begin{align*} y^{\prime }&=\frac {4 x -9}{3 \left (x -3\right )^{{2}/{3}}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.672
5363	20748	\begin{align*} -2 y+2 y^{\prime } x -x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x^{2}+3 x \\ \end{align*}	✓	✓	✓	✓	0.672
5364	24845	\begin{align*} 6 x {y^{\prime }}^{2}-\left (3 x +2 y\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.672
5365	26788	\begin{align*} y^{\left (5\right )}+7 y^{\prime \prime \prime \prime }+33 y^{\prime \prime \prime }+88 y^{\prime \prime }+122 y^{\prime }+60 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.672
5366	876	\begin{align*} y^{\prime \prime }-4 y&=\cosh \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.673
5367	6879	\begin{align*} x&=a y^{\prime }+b {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.673
5368	15194	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.673
5369	17110	\begin{align*} \sin \left (y \right )^{2}&=x^{\prime } \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.673
5370	24059	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=x^{3}+{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.673
5371	454	\begin{align*} \cos \left (x \right ) y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.674
5372	1025	\begin{align*} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=x_{1}+3 x_{2}+x_{3} \\ x_{3}^{\prime }&=-2 x_{1}-4 x_{2}-x_{3} \\ \end{align*}	✓	✓	✓	✓	0.674
5373	1432	\begin{align*} x_{1}^{\prime }&=4 x_{1}-2 x_{2}+\frac {1}{t^{3}} \\ x_{2}^{\prime }&=8 x_{1}-4 x_{2}-\frac {1}{t^{2}} \\ \end{align*}	✓	✓	✓	✓	0.674
5374	2749	\begin{align*} x_{1}^{\prime }&=-x_{2}+x_{3} \\ x_{2}^{\prime }&=2 x_{1}-3 x_{2}+x_{3} \\ x_{3}^{\prime }&=x_{1}-x_{2}-x_{3} \\ \end{align*}	✓	✓	✓	✓	0.674
5375	3882	\begin{align*} x_{1}^{\prime }&=3 x_{1} \\ x_{2}^{\prime }&=3 x_{2}-x_{3} \\ x_{3}^{\prime }&=x_{2}+x_{3} \\ \end{align*}	✓	✓	✓	✓	0.674
5376	4016	\begin{align*} 2 y^{\prime \prime } x +y^{\prime }-2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.674
5377	13166	\(\left [\begin {array}{cc} 0 & -3 \\ 12 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.674
5378	15201	\begin{align*} 3 y^{\prime \prime }+8 y^{\prime }-3 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.674
5379	20886	\begin{align*} y^{\prime }&=-x +y \\ y \left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.674
5380	23481	\begin{align*} y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.674
5381	2584	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }+y&=\left (t^{2}+1\right ) {\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.675
5382	3127	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=x^{3} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.675
5383	3859	\begin{align*} x_{1}^{\prime }&=-2 x_{1} \\ x_{2}^{\prime }&=x_{1}-3 x_{2}-x_{3} \\ x_{3}^{\prime }&=-x_{1}+x_{2}-x_{3} \\ \end{align*}	✓	✓	✓	✓	0.675
5384	5792	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.675
5385	5795	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.675
5386	5804	\begin{align*} 20 y-9 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.675
5387	9315	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.675
5388	15199	\begin{align*} y^{\prime \prime }-20 y^{\prime }+51 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -14 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.675
5389	15524	\begin{align*} y^{\prime }&=1-x \\ \end{align*}	✓	✓	✓	✓	0.675
5390	17303	\begin{align*} y&=-y^{\prime } t +\frac {{y^{\prime }}^{5}}{5} \\ \end{align*}	✓	✓	✓	✗	0.675
5391	19246	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.675
5392	19644	\begin{align*} x^{\prime }&=5 x+4 y \\ y^{\prime }&=-x+y \\ \end{align*}	✓	✓	✓	✓	0.675
5393	27628	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.675
5394	1339	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{-2 t}}{t^{2}} \\ \end{align*}	✓	✓	✓	✓	0.676
5395	2261	\begin{align*} y_{1}^{\prime }&=\frac {y_{1}}{3}+\frac {y_{2}}{3}-y_{3} \\ y_{2}^{\prime }&=-\frac {4 y_{1}}{3}-\frac {4 y_{2}}{3}+y_{3} \\ y_{3}^{\prime }&=-\frac {2 y_{1}}{3}+\frac {y_{2}}{3} \\ \end{align*}	✓	✓	✓	✓	0.677
5396	3797	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=4 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.677
5397	7574	\begin{align*} y^{\prime \prime }+6 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.677
5398	7586	\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.677
5399	14378	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=x+2 y \\ \end{align*}	✓	✓	✓	✓	0.677
5400	17517	\begin{align*} y^{\prime \prime }+4 y&=\tan \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.677