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	4153	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{2}+\frac {y}{8}&=\frac {\sin \left (x \right )}{8}-\frac {\cos \left (x \right )}{4} \\ \end{align*}	✓	✓	✓	✓	0.545
4302	9217	\begin{align*} 20 y-9 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.545
4303	14189	\begin{align*} y^{\prime }+8 y^{\prime \prime } x +4 x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.545
4304	17445	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=25 \sin \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.545
4305	17787	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.545
4306	18345	\begin{align*} x^{\prime \prime }+2 x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.545
4307	20925	\begin{align*} x^{\prime }&=3 x \\ y^{\prime }&=-2 y \\ \end{align*}	✓	✓	✓	✓	0.545
4308	569	\begin{align*} x^{\prime \prime }+9 x&=\delta \left (t -3 \pi \right )+\cos \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.546
4309	976	\begin{align*} x_{1}^{\prime }&=x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.546
4310	1287	\begin{align*} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.546
4311	2038	\begin{align*} 9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.546
4312	2284	\begin{align*} y_{1}^{\prime }&=-3 y_{1}-y_{2} \\ y_{2}^{\prime }&=y_{1}-y_{2} \\ y_{3}^{\prime }&=-y_{1}-y_{2}-2 y_{3} \\ \end{align*}	✓	✓	✓	✓	0.546
4313	3801	\begin{align*} y^{\prime \prime }-4 y&=5 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.546
4314	3824	\begin{align*} x_{1}^{\prime }&=2 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}-3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.546
4315	9226	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.546
4316	10949	\begin{align*} \left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.546
4317	14199	\begin{align*} t^{2} x^{\prime \prime }-6 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.546
4318	18890	\begin{align*} y^{\prime \prime }+4 y&=3 \,{\mathrm e}^{-2 t} \sin \left (2 t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.546
4319	21867	\begin{align*} y y^{\prime }&=-x {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.546
4320	23407	\begin{align*} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.546
4321	24608	\begin{align*} y^{\prime \prime \prime }-y&=x^{2}+8 \\ \end{align*}	✓	✓	✓	✓	0.546
4322	1635	\begin{align*} y^{\prime }-2 y&=x y^{3} \\ y \left (0\right ) &= 2 \sqrt {2} \\ \end{align*}	✓	✓	✓	✓	0.547
4323	2641	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (1+t \right )}+y&=0 \\ \end{align*} Series expansion around \(t=-1\).	✗	✗	✓	✗	0.547
4324	12944	\begin{align*} 2 y^{\prime } \left (1+y^{\prime }\right )+\left (x -y\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.547
4325	16663	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=32 x \\ \end{align*}	✓	✓	✓	✓	0.547
4326	16954	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.547
4327	19486	\begin{align*} 4 x^{2} y^{\prime \prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.547
4328	2042	\begin{align*} x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-9 x^{2}+5\right ) y^{\prime }+\left (-3 x^{2}+4\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.548
4329	3813	\begin{align*} x_{1}^{\prime }&=2 x_{2} \\ x_{2}^{\prime }&=-2 x_{1} \\ \end{align*}	✓	✓	✓	✓	0.548
4330	6565	\begin{align*} a^{2} y+\left (x^{2}+y^{2}\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✗	✗	0.548
4331	13179	\(\left [\begin {array}{cc} 11 & -15 \\ 6 & -8 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.548
4332	18344	\begin{align*} x^{\prime \prime }+2 x^{\prime }+6 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.548
4333	18687	\begin{align*} x^{\prime }&=-3 x+\frac {5 y}{2} \\ y^{\prime }&=-\frac {5 x}{2}+2 y \\ \end{align*}	✓	✓	✓	✓	0.548
4334	3200	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }&={\mathrm e}^{-2 x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.549
4335	3809	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2} \\ x_{2}^{\prime }&=2 x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.549
4336	4131	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.549
4337	12812	\begin{align*} a y+12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.549
4338	12976	\begin{align*} f \left (x \right )+a y y^{\prime }+x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.549
4339	14559	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.549
4340	14799	\(\left [\begin {array}{cc} 3 & 4 \\ 5 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.549
4341	15476	\begin{align*} x^{\prime }&=0 \\ y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.549
4342	18694	\begin{align*} x^{\prime }&=-3 x+\frac {5 y}{2} \\ y^{\prime }&=-\frac {5 x}{2}+2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.549
4343	915	\begin{align*} 2 x^{\prime \prime }+2 x^{\prime }+x&=3 \sin \left (10 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.550
4344	5742	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.550
4345	5801	\begin{align*} 16 y+8 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.550
4346	12724	\begin{align*} y^{\prime \prime \prime }-\sin \left (x \right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y-\ln \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	0.550
4347	25153	\begin{align*} y^{\left (6\right )}+27 y^{\prime \prime \prime \prime }+243 y^{\prime \prime }+729 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.550
4348	25927	\begin{align*} y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }-4 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.550
4349	4650	\begin{align*} y^{\prime }&=f \left (x \right ) f^{\prime }\left (x \right )-y f^{\prime }\left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.551
4350	21168	\begin{align*} x x^{\prime \prime }-{x^{\prime }}^{2}+{\mathrm e}^{t} x^{2}&=0 \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✗	✓	✓	✗	0.551
4351	1406	\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2} \\ x_{2}^{\prime }&=-5 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.552
4352	3494	\begin{align*} \left (x -2\right ) y^{\prime \prime }+3 y^{\prime }+\frac {4 y}{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.552
4353	9711	\begin{align*} x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.552
4354	14575	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.552
4355	16539	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 13 \\ y^{\prime \prime }\left (0\right ) &= 86 \\ \end{align*}	✓	✓	✓	✓	0.552
4356	17751	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=3 \sin \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.552
4357	506	\begin{align*} y^{\prime \prime } x +y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.553
4358	629	\begin{align*} x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=4 x_{1}-2 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.553
4359	2282	\begin{align*} y_{1}^{\prime }&=-4 y_{1}-y_{3} \\ y_{2}^{\prime }&=-y_{1}-3 y_{2}-y_{3} \\ y_{3}^{\prime }&=y_{1}-2 y_{3} \\ \end{align*}	✓	✓	✓	✓	0.553
4360	3121	\begin{align*} -2 y^{\prime \prime }+3 y&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.553
4361	3835	\begin{align*} x_{1}^{\prime }&=-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1} \\ \end{align*}	✓	✓	✓	✓	0.553
4362	7453	\begin{align*} \theta r^{\prime }+3 r-\theta -1&=0 \\ \end{align*}	✓	✓	✓	✓	0.553
4363	9115	\begin{align*} y x +x^{2} y^{\prime }&=2 x \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.553
4364	12906	\begin{align*} 24+12 y x +x^{3} \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right )&=0 \\ \end{align*}	✗	✗	✓	✗	0.553
4365	14396	\begin{align*} x^{\prime }&=-3 x+y \\ y^{\prime }&=-3 y \\ \end{align*}	✓	✓	✓	✓	0.553
4366	14796	\(\left [\begin {array}{cc} 3 & 2 \\ 6 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.553
4367	15149	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.553
4368	16450	\begin{align*} y^{\prime \prime }-\left (4+\frac {2}{x}\right ) y^{\prime }+\left (4+\frac {4}{x}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.553
4369	16662	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=32 \,{\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.553
4370	17720	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.553
4371	17826	\begin{align*} x_{1}^{\prime }&=-x_{1}+1 \\ x_{2}^{\prime }&=x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.553
4372	18688	\begin{align*} x^{\prime }&=-x-\frac {y}{2} \\ y^{\prime }&=2 x-3 y \\ \end{align*}	✓	✓	✓	✓	0.553
4373	18777	\begin{align*} 9 y^{\prime \prime }-24 y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.553
4374	18902	\begin{align*} y^{\prime \prime }+4 y^{\prime }+29 y&={\mathrm e}^{-2 t} \sin \left (5 t \right ) \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.553
4375	18915	\begin{align*} y_{1}^{\prime }&=2 y_{1}-64 y_{2} \\ y_{2}^{\prime }&=y_{1}-14 y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 0 \\ y_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.553
4376	22791	\begin{align*} s^{\prime \prime \prime \prime }-2 s^{\prime \prime }+s&=100 \cos \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.553
4377	25914	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.553
4378	25929	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.553
4379	3233	\begin{align*} 3 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-10 y^{\prime } x +10 y&=\frac {4}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.554
4380	3834	\begin{align*} x_{1}^{\prime }&=-2 x_{1}-7 x_{2} \\ x_{2}^{\prime }&=-x_{1}+4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.554
4381	6765	\begin{align*} x^{2} y^{\prime \prime \prime \prime }&=2 y^{\prime \prime } \\ \end{align*}	✓	✓	✓	✓	0.554
4382	9827	\begin{align*} x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.554
4383	14999	\(\left [\begin {array}{cc} -7 & 6 \\ 12 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.554
4384	1846	\begin{align*} \left (-x +2\right ) y^{\prime \prime }+2 y&=0 \\ y \left (0\right ) &= a_{0} \\ y^{\prime }\left (0\right ) &= a_{1} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.555
4385	6507	\begin{align*} x y y^{\prime \prime }&=-\left (1+y\right ) y^{\prime }+2 x {y^{\prime }}^{2} \\ \end{align*}	✗	✓	✓	✗	0.555
4386	7943	\begin{align*} x {y^{\prime }}^{2}+\left (y-1-x^{2}\right ) y^{\prime }-\left (-1+y\right ) x&=0 \\ \end{align*}	✓	✓	✓	✓	0.555
4387	19050	\begin{align*} x_{1}^{\prime }&=3 x_{1}-9 x_{2} \\ x_{2}^{\prime }&=x_{1}-3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.555
4388	880	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.556
4389	900	\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.556
4390	1855	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.556
4391	2286	\begin{align*} y_{1}^{\prime }&=-11 y_{1}+4 y_{2} \\ y_{2}^{\prime }&=-26 y_{1}+9 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.556
4392	3989	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.556
4393	9229	\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.556
4394	16420	\begin{align*} y^{\prime \prime \prime }&=y^{\prime \prime } \\ y \left (0\right ) &= 10 \\ y^{\prime }\left (0\right ) &= 5 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.556
4395	17484	\begin{align*} y^{\prime \prime }+16 y&=2 \cos \left (4 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.556
4396	18914	\begin{align*} y_{1}^{\prime }&=-4 y_{1}-y_{2} \\ y_{2}^{\prime }&=y_{1}-2 y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.556
4397	2594	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=t \,{\mathrm e}^{\alpha t} \\ \end{align*}	✓	✓	✓	✓	0.557
4398	2744	\begin{align*} x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=4 x_{1}-x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.557
4399	2748	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2}+3 x_{3} \\ x_{2}^{\prime }&=2 x_{2}-x_{3} \\ x_{3}^{\prime }&=2 x_{3} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 2 \\ x_{3} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.557
4400	4496	\begin{align*} y^{\prime \prime }-y&=\frac {1}{x}-\frac {2}{x^{3}} \\ \end{align*}	✓	✓	✓	✓	0.557