2.3.83 Problems 8201 to 8300

Table 2.697: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
8201	7098	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.411
8202	7522	\begin{align*} y^{\prime }&=-4 x-y \\ x^{\prime }&=2 x-y \\ \end{align*}	✓	✓	✓	✓	0.411
8203	8164	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.411
8204	8295	\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\ y \left (0\right ) &= -4 \\ \end{align*}	✗	✗	✗	✗	0.411
8205	9505	\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.411
8206	9822	\begin{align*} x^{2} {y^{\prime }}^{2}-\left (2 y x +1\right ) y^{\prime }+1+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.411
8207	10425	\begin{align*} y^{\prime \prime }-\frac {2 y}{x^{2}}&=x \,{\mathrm e}^{-\sqrt {x}} \\ \end{align*}	✓	✓	✓	✓	0.411
8208	13880	\begin{align*} \left (x^{2}+1\right )^{2} y^{\prime \prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✓	0.411
8209	16659	\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=3 x^{4} \\ \end{align*}	✓	✓	✓	✓	0.411
8210	18319	\begin{align*} y^{\prime \prime }-y^{\prime }+y \,{\mathrm e}^{2 x}&=x \,{\mathrm e}^{2 x}-1 \\ \end{align*}	✓	✓	✓	✗	0.411
8211	18937	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=\delta \left (t -\pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.411
8212	19208	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.411
8213	20347	\begin{align*} y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.411
8214	20933	\begin{align*} x^{\prime }&=2 x+3 y \\ y^{\prime }&=-3 x+2 y \\ \end{align*}	✓	✓	✓	✓	0.411
8215	21709	\begin{align*} y^{\prime }+2 y&=\cos \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.411
8216	22294	\begin{align*} x^{\prime \prime }-3 x&=\sin \left (y \right ) \\ \end{align*}	✓	✓	✓	✓	0.411
8217	24020	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime }-2 y&=2+x +x \,{\mathrm e}^{-x}+x^{2} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.411
8218	864	\begin{align*} x^{\prime \prime }+8 x^{\prime }+16 x&=0 \\ x \left (0\right ) &= 5 \\ x^{\prime }\left (0\right ) &= -10 \\ \end{align*}	✓	✓	✓	✓	0.412
8219	970	\begin{align*} x_{1}^{\prime }&=9 x_{1}+5 x_{2} \\ x_{2}^{\prime }&=-6 x_{1}-2 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.412
8220	1639	\begin{align*} y^{\prime }-4 y&=\frac {48 x}{y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.412
8221	3766	\begin{align*} y^{\prime \prime }-9 y&=F \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.412
8222	8294	\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	0.412
8223	9643	\begin{align*} y^{\prime \prime }+16 y&=\delta \left (t -2 \pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.412
8224	10157	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.412
8225	10238	\begin{align*} y^{\prime \prime }+2 \cot \left (x \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.412
8226	10644	\begin{align*} x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.412
8227	11730	\begin{align*} x^{2} {y^{\prime }}^{2}-4 x \left (y+2\right ) y^{\prime }+4 \left (y+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.412
8228	14299	\begin{align*} x^{\prime \prime }+x^{\prime }+x&=5 \sin \left (7 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.412
8229	15145	\begin{align*} y y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✗	0.412
8230	16934	\begin{align*} x^{\prime }&=5 x+4 y \\ y^{\prime }&=8 x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 9 \\ \end{align*}	✓	✓	✓	✓	0.412
8231	18025	\begin{align*} y^{2} \left (1+{y^{\prime }}^{2}\right )-4 y^{\prime } y-4 x&=0 \\ \end{align*}	✓	✓	✓	✗	0.412
8232	18262	\begin{align*} y^{\prime \prime }+y&=-2 x +2 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.412
8233	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*}	✓	✓	✓	✓	0.412
8234	20740	\begin{align*} {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.412
8235	21128	\begin{align*} x^{\prime \prime }-2 x^{\prime }+5 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (\theta \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.412
8236	21468	\begin{align*} \left (-y+y^{\prime } x \right )^{2}-{y^{\prime }}^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✗	0.412
8237	22163	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.412
8238	23499	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=2 x \,{\mathrm e}^{-x}+x^{2} \\ \end{align*}	✓	✓	✓	✓	0.412
8239	24738	\begin{align*} y^{\prime \prime }-y&=\frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	0.412
8240	1316	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ y \left (-1\right ) &= 2 \\ y^{\prime }\left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.413
8241	1335	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=3 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.413
8242	1443	\begin{align*} x_{1}^{\prime }&=5 x_{1}-x_{2} \\ x_{2}^{\prime }&=3 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.413
8243	2266	\begin{align*} y_{1}^{\prime }&=15 y_{1}-9 y_{2} \\ y_{2}^{\prime }&=16 y_{1}-9 y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 5 \\ y_{2} \left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	0.413
8244	5737	\begin{align*} y^{\prime \prime }&=a x +b y \\ \end{align*}	✓	✓	✓	✓	0.413
8245	7995	\begin{align*} y^{\prime \prime }-y&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.413
8246	16075	\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&={\mathrm e}^{-2 t} \\ \end{align*}	✓	✓	✓	✓	0.413
8247	16635	\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=6 \,{\mathrm e}^{-5 x} \\ \end{align*}	✓	✓	✓	✓	0.413
8248	18226	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=\left (1+\sin \left (x \right )\right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.413
8249	18259	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=x \,{\mathrm e}^{2 x}+\sin \left (x \right )+x^{2} \\ \end{align*}	✓	✓	✓	✓	0.413
8250	19240	\begin{align*} 1+y^{2}+y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.413
8251	24755	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right )^{2} \tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.413
8252	24835	\begin{align*} 9 {y^{\prime }}^{2}+12 x y^{4} y^{\prime }+4 y^{5}&=0 \\ \end{align*}	✓	✓	✓	✗	0.413
8253	25772	\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	0.413
8254	590	\begin{align*} x^{\prime }&=3 x-y \\ y^{\prime }&=5 x-3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.414
8255	3724	\begin{align*} y^{\prime \prime }-y&=9 x \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	0.414
8256	5535	\begin{align*} x^{4} {y^{\prime }}^{2}+2 x^{3} y y^{\prime }-4&=0 \\ \end{align*}	✓	✓	✓	✓	0.414
8257	5629	\begin{align*} {y^{\prime }}^{3}+{y^{\prime }}^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.414
8258	7578	\begin{align*} y^{\prime \prime }+2 y^{\prime }+4 y&=6 \cos \left (2 t \right )+8 \sin \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.414
8259	8809	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-4 y&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.414
8260	9574	\begin{align*} y^{\prime \prime } x -y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.414
8261	10566	\begin{align*} 2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.414
8262	10743	\begin{align*} y^{\prime \prime } x +3 y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.414
8263	11116	\begin{align*} 2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.414
8264	14218	\begin{align*} y^{\prime }&=r \left (a -y\right ) \\ \end{align*}	✓	✓	✓	✓	0.414
8265	14620	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=6 \sin \left (2 x \right )+7 \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.414
8266	14794	\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=7 x+4 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 6 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.414
8267	14925	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.414
8268	15999	\begin{align*} x^{\prime }&=3 x \\ y^{\prime }&=x-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.414
8269	16083	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&={\mathrm e}^{-2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.414
8270	16845	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +\lambda y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.414
8271	18136	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.414
8272	18228	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&={\mathrm e}^{2 x}+\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.414
8273	22699	\begin{align*} y^{\prime \prime }+y&=x^{2}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.414
8274	23592	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x \\ \end{align*}	✓	✓	✓	✓	0.414
8275	24501	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.414
8276	25189	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-5\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.414
8277	25521	\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{c t} \\ \end{align*}	✓	✓	✓	✓	0.414
8278	582	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=6 x-y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.415
8279	651	\begin{align*} y^{\prime }&=2 x +1 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.415
8280	1315	\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+82 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.415
8281	2398	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.415
8282	3734	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=50 \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.415
8283	4373	\begin{align*} y^{\prime }+y^{2}&=x^{2}+1 \\ \end{align*}	✓	✓	✓	✗	0.415
8284	4506	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	0.415
8285	5396	\begin{align*} {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.415
8286	5540	\begin{align*} x^{6} {y^{\prime }}^{2}-2 y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.415
8287	8296	\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\ y \left (8\right ) &= -4 \\ \end{align*}	✗	✗	✗	✗	0.415
8288	8906	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.415
8289	9185	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.415
8290	9247	\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=14 \,{\mathrm e}^{-5 x} \\ \end{align*}	✓	✓	✓	✓	0.415
8291	9421	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=x^{3}-x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.415
8292	9474	\begin{align*} x^{\prime }&=-3 x+\sqrt {2}\, y \\ y^{\prime }&=\sqrt {2}\, x-2 y \\ \end{align*}	✓	✓	✓	✓	0.415
8293	9765	\begin{align*} x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 y^{\prime } x&=0 \\ y \left (2\right ) &= 5 \\ y^{\prime }\left (2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.415
8294	11716	\begin{align*} \left (3 x +5\right ) {y^{\prime }}^{2}-\left (x +3 y\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.415
8295	11738	\begin{align*} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y^{\prime } y-x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.415
8296	14603	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 9 \\ \end{align*}	✓	✓	✓	✓	0.415
8297	14605	\begin{align*} 9 y^{\prime \prime }-6 y^{\prime }+y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.415
8298	14941	\begin{align*} x^{\prime \prime }+6 x^{\prime }+10 x&={\mathrm e}^{-2 t} \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.415
8299	15092	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{x} \cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	0.415
8300	16084	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&={\mathrm e}^{-4 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.415