2.3.83 Problems 8201 to 8300

Table 2.715: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
8201	21518	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=x^{3}+3 \\ \end{align*}	✓	✓	✓	✓	0.602
8202	22693	\begin{align*} s^{\prime \prime }-3 s^{\prime }+2 s&=8 t^{2}+12 \,{\mathrm e}^{-t} \\ s \left (0\right ) &= 0 \\ s^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.602
8203	23533	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-2 x} \sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.602
8204	24750	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {1}{\sqrt {1+{\mathrm e}^{-2 x}}} \\ \end{align*}	✓	✓	✓	✓	0.602
8205	2401	\begin{align*} y^{\prime \prime }+y&=\sec \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.603
8206	7764	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=54 x +18 \\ \end{align*}	✓	✓	✓	✓	0.603
8207	8412	\begin{align*} 1+{x^{\prime }}^{2}&=\frac {a}{y} \\ \end{align*}	✓	✓	✓	✓	0.603
8208	9265	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {1}{1+{\mathrm e}^{-x}} \\ \end{align*}	✓	✓	✓	✗	0.603
8209	10387	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=x^{3}+x^{2}+x +1 \\ \end{align*}	✓	✓	✓	✓	0.603
8210	10475	\begin{align*} \left (1-t \right ) y^{\prime \prime }+y^{\prime } t -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.603
8211	18656	\begin{align*} x^{\prime }&=5 x-y \\ y^{\prime }&=3 x+y \\ \end{align*}	✓	✓	✓	✓	0.603
8212	18689	\begin{align*} x^{\prime }&=2 x+\frac {y}{2} \\ y^{\prime }&=-\frac {x}{2}+y \\ \end{align*}	✓	✓	✓	✓	0.603
8213	19498	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=20 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.603
8214	20921	\begin{align*} x^{\prime }&=2 x+3 y+2 \sin \left (2 t \right ) \\ y^{\prime }&=-3 x+2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.603
8215	23671	\begin{align*} \left (x -1\right )^{2} y^{\prime \prime }-\left (x^{2}-x \right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.603
8216	24067	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=12 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.603
8217	24083	\begin{align*} 4 \left (-x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x +3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.603
8218	24696	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=4 x^{2}-3 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.603
8219	25608	\begin{align*} y^{\prime \prime }+4 y&={\mathrm e}^{t} \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.603
8220	25943	\begin{align*} y^{\prime \prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.603
8221	1017	\begin{align*} x_{1}^{\prime }&=-13 x_{1}+40 x_{2}-48 x_{3} \\ x_{2}^{\prime }&=-8 x_{1}+23 x_{2}-24 x_{3} \\ x_{3}^{\prime }&=3 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.604
8222	1391	\begin{align*} \left (x^{2}-2 x -3\right ) y^{\prime \prime }+y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=-4\).	✓	✓	✓	✓	0.604
8223	2562	\begin{align*} 3 y^{\prime \prime }-2 y^{\prime }+4 y&=0 \\ y \left (2\right ) &= 1 \\ y^{\prime }\left (2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.604
8224	6853	\begin{align*} n \cos \left (x n +m y\right )-m \sin \left (x m +n y\right )+\left (m \cos \left (x n +m y\right )-n \sin \left (x m +n y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.604
8225	6938	\begin{align*} {\mathrm e}^{x}-\sin \left (y\right )+y^{\prime } \cos \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.604
8226	12363	\begin{align*} y^{\prime \prime } x -y^{\prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✓	0.604
8227	16701	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=12 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	0.604
8228	18884	\begin{align*} y^{\prime \prime }+2 y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.604
8229	20645	\begin{align*} y^{\prime \prime }-y&=\frac {2}{{\mathrm e}^{x}+1} \\ \end{align*}	✓	✓	✓	✓	0.604
8230	21215	\begin{align*} x^{\prime }&=2 x+6 y \\ y^{\prime }&=x+3 y \\ \end{align*}	✓	✓	✓	✓	0.604
8231	23508	\begin{align*} y^{\prime \prime }+y&=x +2 \,{\mathrm e}^{-x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.604
8232	23709	\begin{align*} y^{\prime \prime } x -2 y^{\prime }+y x&=0 \\ y \left (3\right ) &= 1 \\ y^{\prime }\left (3\right ) &= -2 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	0.604
8233	364	\begin{align*} y^{\prime \prime }+9 y&=\sin \left (x \right )^{4} \\ \end{align*}	✓	✓	✓	✓	0.605
8234	3733	\begin{align*} y^{\prime \prime }-16 y&=20 \cos \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.605
8235	3986	\begin{align*} y^{\prime \prime }+2 y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.605
8236	4135	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.605
8237	6523	\begin{align*} 2 x^{2} y y^{\prime \prime }&=-y^{2}+x^{2} {y^{\prime }}^{2} \\ \end{align*}	✗	✓	✓	✗	0.605
8238	7958	\begin{align*} y^{2} {y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.605
8239	9508	\begin{align*} \left (2+x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.605
8240	10240	\begin{align*} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=4 \sqrt {x}\, {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	0.605
8241	13882	\begin{align*} \left (a^{2}+x^{2}\right )^{2} y^{\prime \prime }+b^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.605
8242	14942	\begin{align*} x^{\prime \prime }+4 x^{\prime }+4 x&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.605
8243	15085	\begin{align*} y^{\prime \prime }+y&=1-\frac {1}{\sin \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	0.605
8244	17689	\begin{align*} \left (1+3 x \right ) y^{\prime \prime }-3 y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.605
8245	18231	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=4 x -2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.605
8246	19502	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=6 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.605
8247	21909	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.605
8248	22031	\begin{align*} 3 y^{2} x^{2}+\left (2 x^{3} y+4 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.605
8249	23366	\begin{align*} y^{\prime \prime }-2 r y^{\prime }+\left (r^{2}-\frac {\alpha ^{2}}{4}\right ) y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.605
8250	24781	\begin{align*} x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.605
8251	25930	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.605
8252	26456	\begin{align*} y^{\prime \prime }&=\frac {y^{\prime }}{x}+\frac {x^{2}}{y^{\prime }} \\ y \left (2\right ) &= 0 \\ y^{\prime }\left (2\right ) &= 4 \\ \end{align*}	✓	✓	✓	✗	0.605
8253	3301	\begin{align*} 2 x^{2} y+{y^{\prime }}^{2}&=x^{3} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.606
8254	5479	\begin{align*} x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.606
8255	7347	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.606
8256	9420	\begin{align*} y^{\prime \prime }-y^{\prime } x +y&=x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.606
8257	9516	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.606
8258	9803	\begin{align*} y^{\prime \prime }+y&=-\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.606
8259	10296	\begin{align*} y^{\prime } x&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.606
8260	10302	\begin{align*} x \sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.606
8261	13153	\(\left [\begin {array}{ccc} 1 & 0 & -1 \\ -2 & 3 & -1 \\ -6 & 6 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.606
8262	14604	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	0.606
8263	15984	\begin{align*} x^{\prime }&=1 \\ y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.606
8264	16166	\begin{align*} y^{\prime }&=x \cos \left (x^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.606
8265	17300	\begin{align*} y^{\prime } t -y-1&={y^{\prime }}^{2}-y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.606
8266	18793	\begin{align*} y^{\prime \prime }+6 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.606
8267	20215	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{r}&=0 \\ \end{align*}	✓	✓	✓	✓	0.606
8268	20850	\begin{align*} y^{\prime \prime }+5 y^{\prime }-6 y&=3 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.606
8269	21207	\begin{align*} x^{\prime }&=3 x-y \\ y^{\prime }&=x+3 y \\ \end{align*}	✓	✓	✓	✓	0.606
8270	21281	\begin{align*} x^{\prime }+x&=t \\ x \left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.606
8271	21666	\begin{align*} y^{\prime \prime }&=y^{2} {\mathrm e}^{x}-{y^{\prime }}^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.606
8272	23525	\begin{align*} y^{\prime \prime }+y&=\sin \left (a x \right ) \\ y \left (0\right ) &= y_{0} \\ y^{\prime }\left (0\right ) &= y_{1} \\ \end{align*}	✓	✓	✓	✓	0.606
8273	23822	\begin{align*} x^{\prime }&=-2 x-3 y \\ y^{\prime }&=-3 x+2 y \\ \end{align*}	✓	✓	✓	✓	0.606
8274	24544	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=6 x +6 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.606
8275	25309	\begin{align*} y+y^{\prime }&=\delta \left (t -1\right )-\delta \left (t -3\right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.606
8276	25417	\begin{align*} y^{\prime }&=\operatorname {Heaviside}\left (t -1\right )+\operatorname {Heaviside}\left (-2+t \right )+\operatorname {Heaviside}\left (t -3\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.606
8277	26060	\begin{align*} y&=y^{\prime } x +y^{\prime }-{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.606
8278	1934	\begin{align*} \left (x +1\right ) y^{\prime \prime }+\left (2 x^{2}-3 x +1\right ) y^{\prime }-\left (x -4\right ) y&=0 \\ y \left (1\right ) &= -2 \\ y^{\prime }\left (1\right ) &= 3 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.607
8279	2461	\begin{align*} t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.607
8280	14557	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{x} \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (1\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	0.607
8281	23079	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=5 \sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.607
8282	23834	\begin{align*} y^{\prime }&=\frac {t^{2}+1}{t \left (-2+t \right )} \\ \end{align*}	✓	✓	✓	✓	0.607
8283	24063	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=1+\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.607
8284	25339	\begin{align*} 2 t y^{\prime \prime }+y^{\prime }+t y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.607
8285	2743	\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2} \\ x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.608
8286	4136	\begin{align*} y^{\prime \prime }-y&=4 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.608
8287	5795	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.608
8288	5804	\begin{align*} 20 y-9 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.608
8289	6570	\begin{align*} X \left (x , y\right )^{3} y^{\prime \prime }&=1 \\ \end{align*}	✗	✗	✗	✗	0.608
8290	8396	\begin{align*} y^{\prime }&=\frac {1}{1+\sin \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	0.608
8291	9719	\begin{align*} y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.608
8292	10234	\begin{align*} y^{\prime \prime }+20 y^{\prime }+500 y&=100000 \cos \left (100 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.608
8293	14935	\begin{align*} x^{\prime \prime }+x^{\prime }-2 x&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.608
8294	15687	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+21 y^{\prime }-26 y&=36 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.608
8295	17807	\begin{align*} \frac {x^{\prime \prime }}{32}+2 x^{\prime }+x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.608
8296	18649	\begin{align*} x^{\prime }&=2 x-y \\ y^{\prime }&=3 x-2 y \\ \end{align*}	✓	✓	✓	✓	0.608
8297	18797	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ y \left (\frac {\pi }{4}\right ) &= 2 \\ y^{\prime }\left (\frac {\pi }{4}\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.608
8298	21137	\begin{align*} x^{\prime \prime }-3 x^{\prime }-x&=t^{2}+t \\ \end{align*}	✓	✓	✓	✓	0.608
8299	21572	\begin{align*} y^{\prime \prime }-y&=2 x +{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.608
8300	21906	\begin{align*} y^{\prime }-y^{2}-x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.608