2.3.44 Problems 4301 to 4400

Table 2.661: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4301	26042	\begin{align*} x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }&=2 x^{3}-x \\ \end{align*}	✓	✓	✓	✓	0.346
4302	27593	\begin{align*} y \left (y^{\prime }+2 x y^{\prime \prime }\right )&={y^{\prime }}^{2} x +1 \\ \end{align*}	✗	✓	✓	✗	0.346
4303	3562	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.347
4304	12514	\begin{align*} \left (-a^{2}+x^{2}\right ) y^{\prime \prime }+8 x y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.347
4305	16725	\begin{align*} y^{\prime \prime }-8 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.347
4306	17391	\begin{align*} 7 y^{\prime \prime }+4 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.347
4307	17731	\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.347
4308	19436	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.347
4309	20592	\begin{align*} x^{2} y^{\prime \prime \prime \prime }+1&=0 \\ \end{align*}	✓	✓	✓	✓	0.347
4310	20932	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.347
4311	27577	\begin{align*} x y y^{\prime \prime }&=y^{\prime } \left (y^{\prime }+y\right ) \\ \end{align*}	✗	✓	✓	✗	0.347
4312	310	\begin{align*} y^{\prime \prime }-i y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.348
4313	1085	\begin{align*} \left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y&=0 \\ y \left (3\right ) &= 2 \\ y^{\prime }\left (3\right ) &= 0 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	0.348
4314	9229	\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.348
4315	9339	\begin{align*} y^{\prime \prime }+y&=-8 \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.348
4316	10232	\begin{align*} y^{\prime \prime }+\left (x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.348
4317	10559	\begin{align*} 8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.348
4318	10716	\begin{align*} x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.348
4319	14955	\begin{align*} y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.348
4320	15767	\begin{align*} x^{\prime }&=-x+2 y \\ y^{\prime }&=-2 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.348
4321	16144	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&={\mathrm e}^{-2 t} \sin \left (4 t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.348
4322	16501	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.348
4323	19058	\begin{align*} x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= -5 \\ x_{2} \left (0\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	0.348
4324	19655	\begin{align*} x^{\prime }&=-4 x-y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.348
4325	19689	\begin{align*} x^{\prime \prime }-4 x^{\prime }+4 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.348
4326	20922	\begin{align*} x^{\prime }&=-4 x-y+{\mathrm e}^{-t} \\ y^{\prime }&=x-2 y+2 \,{\mathrm e}^{-3 t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.348
4327	22788	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+4 y^{\prime }&=12 \,{\mathrm e}^{2 x}+24 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.348
4328	23705	\begin{align*} y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.348
4329	23785	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=-x \\ \end{align*}	✓	✓	✓	✓	0.348
4330	26414	\begin{align*} y^{\prime \prime }-4 y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.348
4331	26957	\begin{align*} y^{\prime \prime }-2 \alpha y^{\prime }+\alpha ^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.348
4332	27069	\begin{align*} y^{\prime \prime }+y x&=\cos \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.348
4333	27767	\begin{align*} \left (x^{2}-x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.348
4334	240	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.349
4335	279	\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.349
4336	428	\begin{align*} y^{\prime \prime }+x y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.349
4337	965	\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.349
4338	1418	\begin{align*} x_{1}^{\prime }&=-\frac {3 x_{1}}{2}+x_{2} \\ x_{2}^{\prime }&=-\frac {x_{1}}{4}-\frac {x_{2}}{2} \\ \end{align*}	✓	✓	✓	✓	0.349
4339	2365	\begin{align*} y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.349
4340	3792	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=4 \,{\mathrm e}^{2 x} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.349
4341	4114	\begin{align*} x +\left (2-x +2 y\right ) y^{\prime }&=x y \left (y^{\prime }-1\right ) \\ \end{align*}	✓	✓	✓	✓	0.349
4342	7262	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.349
4343	9212	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.349
4344	10003	\begin{align*} \frac {{y^{\prime }}^{2}}{4}-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.349
4345	10075	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.349
4346	10583	\begin{align*} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.349
4347	15309	\begin{align*} x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.349
4348	17018	\begin{align*} y^{\prime \prime }-6 y^{\prime }+45 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.349
4349	19660	\begin{align*} x^{\prime }&=b \,{\mathrm e}^{t} \\ x \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.349
4350	20389	\begin{align*} {y^{\prime }}^{2} x +\left (-x +y\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.349
4351	21536	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=3 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{-x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✓	0.349
4352	22181	\begin{align*} \left (x +1\right )^{3} y^{\prime \prime }+\left (x^{2}-1\right ) \left (x +1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=-1\).	✗	✗	✓	✗	0.349
4353	23688	\begin{align*} y^{\prime \prime }-2 x y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.349
4354	26039	\begin{align*} 3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x +1 \\ \end{align*}	✓	✓	✓	✓	0.349
4355	26073	\begin{align*} y^{\prime }&=3 y-4 z \\ z^{\prime }&=y-z \\ \end{align*}	✓	✓	✓	✓	0.349
4356	10345	\begin{align*} y^{\prime }+\left (a t +b t \right ) y&=0 \\ y \left (-3\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.350
4357	12548	\begin{align*} \left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y-3 x -1&=0 \\ \end{align*}	✓	✓	✓	✗	0.350
4358	12633	\begin{align*} y^{\prime \prime }&=-\frac {2 x y^{\prime }}{x^{2}-1}+\frac {a^{2} y}{\left (x^{2}-1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	0.350
4359	13663	\begin{align*} y^{\prime \prime }-\left (a x +b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.350
4360	13926	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{x}-b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.350
4361	15728	\begin{align*} 4 y+y^{\prime \prime }&=\cos \left (x \right ) \delta \left (x -\pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.350
4362	16758	\begin{align*} y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.350
4363	20116	\begin{align*} x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.350
4364	23327	\begin{align*} 4 y^{\prime \prime }-8 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.350
4365	26416	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.350
4366	275	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.351
4367	523	\begin{align*} 2 x^{2} y^{\prime \prime }-3 x y^{\prime }-2 \left (-x^{5}+14\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.351
4368	1012	\begin{align*} x_{1}^{\prime }&=7 x_{1}+x_{2} \\ x_{2}^{\prime }&=-4 x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.351
4369	1043	\begin{align*} y^{\prime }&=4 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.351
4370	2413	\begin{align*} y^{\prime \prime }-y t&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.351
4371	2415	\begin{align*} y^{\prime \prime }-t^{3} y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.351
4372	10011	\begin{align*} x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.351
4373	11147	\begin{align*} x^{2} \left (1-4 x \right ) y^{\prime \prime }+\left (-\frac {1}{4} x -x^{2}\right ) y^{\prime }-\frac {5 y x}{16}&=0 \\ \end{align*}	✓	✓	✓	✗	0.351
4374	13167	\(\left [\begin {array}{cc} 0 & -12 \\ 12 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.351
4375	18314	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-y&=1 \\ \end{align*}	✓	✓	✓	✗	0.351
4376	21913	\begin{align*} y^{\prime \prime }+n^{2} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= k \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.351
4377	22173	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.351
4378	25909	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.351
4379	27686	\begin{align*} y^{\prime \prime }-2 y&=2 x \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.351
4380	426	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.352
4381	2547	\begin{align*} 3 y^{\prime \prime }+6 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.352
4382	3695	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.352
4383	6911	\begin{align*} x +y+1+\left (2 x +2 y+2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.352
4384	7589	\begin{align*} z^{\prime \prime }+z^{\prime }-z&=0 \\ \end{align*}	✓	✓	✓	✓	0.352
4385	8122	\begin{align*} y^{\prime \prime }+4 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.352
4386	10050	\begin{align*} y^{2} y^{\prime \prime }&=x \\ \end{align*}	✗	✓	✗	✗	0.352
4387	10255	\begin{align*} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.352
4388	12413	\begin{align*} x^{2} y^{\prime \prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.352
4389	16503	\begin{align*} 25 y^{\prime \prime }-10 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.352
4390	19057	\begin{align*} x_{1}^{\prime }&=x_{1}-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1}-7 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 7 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.352
4391	19855	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.352
4392	20157	\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*}	✓	✓	✓	✗	0.352
4393	21981	\begin{align*} x y^{2}-x^{2} y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.352
4394	23012	\begin{align*} 2 y^{\prime \prime }-15 y^{\prime }+27 y&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.352
4395	23328	\begin{align*} 2 y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.352
4396	25075	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=4 \cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.352
4397	26043	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.352
4398	26067	\begin{align*} y_{1}^{\prime }&=y_{2} \\ y_{2}^{\prime }&=-y_{1}+2 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.352
4399	519	\begin{align*} 16 x^{2} y^{\prime \prime }+24 x y^{\prime }+\left (144 x^{3}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.353
4400	1274	\begin{align*} y^{\prime \prime }-2 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.353