2.3.54 Problems 5301 to 5400

Table 2.639: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5301	7347	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.280
5302	8808	\begin{align*} x x^{\prime \prime }-{x^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.280
5303	9067	\begin{align*} y^{\prime } x&=1 \\ \end{align*}	✓	✓	✓	✓	0.280
5304	9321	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.280
5305	10839	\begin{align*} y^{\prime \prime } x +\left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.280
5306	10897	\begin{align*} \left (1-2 x \right ) y^{\prime \prime }+2 y^{\prime }+\left (2 x -3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.280
5307	11034	\begin{align*} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.280
5308	17411	\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.280
5309	18385	\begin{align*} y^{\prime }&={\mathrm e}^{y}+y x \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✗	✓	0.280
5310	23055	\begin{align*} r^{\prime }&=-a \sin \left (\theta \right ) \\ r \left (0\right ) &= 2 a \\ \end{align*}	✓	✓	✓	✓	0.280
5311	23321	\begin{align*} y^{\prime \prime }+3 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.280
5312	23786	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.280
5313	23828	\begin{align*} y^{\prime }&=\frac {1}{t^{2}} \\ \end{align*}	✓	✓	✓	✓	0.280
5314	24679	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=x^{3}-4 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.280
5315	451	\begin{align*} \left (x^{3}+1\right ) y^{\prime \prime }+x^{4} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.281
5316	2557	\begin{align*} y^{\prime \prime }+2 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.281
5317	3812	\begin{align*} x_{1}^{\prime }&=2 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=-4 x_{1}-6 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.281
5318	3986	\begin{align*} y^{\prime \prime }+2 y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.281
5319	10340	\begin{align*} t y^{\prime }+y&=t \\ y \left (1\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.281
5320	10341	\begin{align*} t y^{\prime }+y&=t \\ y \left (1\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.281
5321	10516	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-10 y^{\prime } x +28 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.281
5322	10718	\begin{align*} x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.281
5323	14628	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }+3 y^{\prime }-5 y&=5 \sin \left (2 x \right )+10 x^{2}+3 x +7 \\ \end{align*}	✓	✓	✓	✓	0.281
5324	17393	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.281
5325	22880	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.281
5326	367	\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=3 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.282
5327	1070	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.282
5328	5406	\begin{align*} {y^{\prime }}^{2}+\left (b x +a \right ) y^{\prime }+c&=b y \\ \end{align*}	✓	✓	✓	✓	0.282
5329	6956	\begin{align*} \left (2 x +y+1\right ) y-x \left (x +2 y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.282
5330	7957	\begin{align*} y&=y^{\prime } x -2 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.282
5331	8968	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.282
5332	9493	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.282
5333	10074	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.282
5334	10465	\begin{align*} 3 y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.282
5335	10722	\begin{align*} x^{2} \left (1-4 x \right ) y^{\prime \prime }-\frac {y^{\prime } x}{2}-\frac {3 y x}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.282
5336	11161	\begin{align*} u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.282
5337	12514	\begin{align*} \left (-a^{2}+x^{2}\right ) y^{\prime \prime }+8 y^{\prime } x +12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.282
5338	12676	\begin{align*} y^{\prime \prime }&=\frac {y^{\prime }}{x \left (\ln \left (x \right )-1\right )}-\frac {y}{x^{2} \left (\ln \left (x \right )-1\right )} \\ \end{align*}	✓	✓	✓	✗	0.282
5339	15226	\begin{align*} y+y^{\prime }&=\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -2\right ) \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.282
5340	21205	\begin{align*} x^{\prime }&=a x \\ y^{\prime }&=a y \\ \end{align*}	✓	✓	✓	✓	0.282
5341	21703	\begin{align*} y^{\prime }-5 y&=0 \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.282
5342	22296	\begin{align*} y^{\prime \prime }+y x&=\sin \left (y^{\prime \prime }\right ) \\ \end{align*}	✗	✗	✗	✗	0.282
5343	22351	\begin{align*} y^{\prime }&=2 x \\ \end{align*}	✓	✓	✓	✓	0.282
5344	23505	\begin{align*} y^{\prime \prime }-7 y^{\prime }-8 y&={\mathrm e}^{x} \left (x^{2}+2\right ) \\ \end{align*}	✓	✓	✓	✓	0.282
5345	23810	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.282
5346	25598	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=t^{3} \\ \end{align*}	✓	✓	✓	✓	0.282
5347	550	\begin{align*} x^{\prime \prime \prime \prime }+2 x^{\prime \prime }+x&={\mathrm e}^{2 t} \\ 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 ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.283
5348	2784	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{3}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }&=2 x_{2} \\ x_{3}^{\prime }&=3 x_{3}+{\mathrm e}^{2 t} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.283
5349	3301	\begin{align*} 2 x^{2} y+{y^{\prime }}^{2}&=x^{3} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.283
5350	3347	\begin{align*} y^{\prime \prime }+\frac {{y^{\prime }}^{2}}{2}-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.283
5351	6676	\begin{align*} 2 y+4 y^{\prime } x -\left (-x^{2}+3\right ) y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.283
5352	6848	\begin{align*} 1+\frac {y^{2}}{x^{2}}-\frac {2 y y^{\prime }}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	0.283
5353	6935	\begin{align*} y^{2} {\mathrm e}^{x y^{2}}+4 x^{3}+\left (2 x y \,{\mathrm e}^{x y^{2}}-3 y^{2}\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.283
5354	6957	\begin{align*} y \left (2 x -y-1\right )+x \left (2 y-x -1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.283
5355	7263	\begin{align*} y^{\prime \prime }-2 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.283
5356	7645	\begin{align*} y^{\prime }+2 \left (x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.283
5357	8021	\begin{align*} y^{\prime \prime }-2 y^{\prime }-y&={\mathrm e}^{x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.283
5358	8894	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.283
5359	9315	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.283
5360	9608	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=\sin \left (3 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.283
5361	10532	\begin{align*} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.283
5362	10989	\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.283
5363	11009	\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*}	✓	✓	✓	✗	0.283
5364	13165	\(\left [\begin {array}{cc} 0 & -6 \\ 6 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.283
5365	13167	\(\left [\begin {array}{cc} 0 & -12 \\ 12 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.283
5366	16183	\begin{align*} y^{\prime }&=\sin \left (\frac {x}{2}\right ) \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.283
5367	16640	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=100 \\ \end{align*}	✓	✓	✓	✓	0.283
5368	17028	\begin{align*} y^{\prime }&=\frac {x^{2}}{\sqrt {x^{2}-1}} \\ \end{align*}	✓	✓	✓	✓	0.283
5369	17597	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=\frac {{\mathrm e}^{t}}{t} \\ \end{align*}	✓	✓	✓	✓	0.283
5370	17778	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.283
5371	19486	\begin{align*} 4 x^{2} y^{\prime \prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.283
5372	20768	\begin{align*} y+3 y^{\prime } x +2 y {y^{\prime }}^{2}+\left (x^{2}+2 y^{2} y^{\prime }\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.283
5373	22938	\begin{align*} x^{\prime }&=x+8 y \\ y^{\prime }&=-2 x-7 y \\ \end{align*}	✓	✓	✓	✓	0.283
5374	24549	\begin{align*} y^{\prime \prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.283
5375	24666	\begin{align*} 4 y^{\prime \prime }+y&=33 \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.283
5376	2176	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-4 y&={\mathrm e}^{-x} \left (\left (1-22 x \right ) \cos \left (2 x \right )-\left (1+6 x \right ) \sin \left (2 x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.284
5377	3895	\begin{align*} x_{1}^{\prime }&=-8 x_{1}+5 x_{2} \\ x_{2}^{\prime }&=-5 x_{1}+2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.284
5378	4170	\begin{align*} y_{1}^{\prime }&=y_{2} \\ y_{2}^{\prime }&=y_{1} \\ \end{align*}	✓	✓	✓	✓	0.284
5379	5592	\begin{align*} 4 y^{2} {y^{\prime }}^{2}+2 \left (1+3 x \right ) x y y^{\prime }+3 x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.284
5380	5904	\begin{align*} -y+2 n y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.284
5381	6373	\begin{align*} x y^{5}+2 y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✓	✓	✗	0.284
5382	6856	\begin{align*} \frac {1}{x}+\frac {y^{\prime }}{y}+\frac {2}{y}-\frac {2 y^{\prime }}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	0.284
5383	7062	\begin{align*} y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.284
5384	7852	\begin{align*} y^{\prime \prime }-y&=4-x \\ \end{align*}	✓	✓	✓	✓	0.284
5385	7915	\begin{align*} y \left (y^{2}-2 x^{2}\right )+x \left (2 y^{2}-x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.284
5386	9069	\begin{align*} \sin \left (x \right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.284
5387	9317	\begin{align*} y^{\prime \prime }-y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.284
5388	9742	\begin{align*} y&=y^{\prime } x +k {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.284
5389	10627	\begin{align*} x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.284
5390	10687	\begin{align*} y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.284
5391	10693	\begin{align*} x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.284
5392	10705	\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.284
5393	12763	\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+\left (a \,x^{3}-12\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.284
5394	16158	\begin{align*} x^{2} y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.284
5395	16831	\begin{align*} \left (x +1\right ) y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.284
5396	18782	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.284
5397	19591	\begin{align*} x^{3} \left (x -1\right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+3 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.284
5398	20342	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.284
5399	23551	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=\left (x^{2}+1\right )^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	0.284
5400	23768	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x \\ \end{align*}	✓	✓	✓	✓	0.284