2.3.73 Problems 7201 to 7300

Table 2.677: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
7201	7599	\begin{align*} z^{\prime \prime }-2 z^{\prime }-2 z&=0 \\ z \left (0\right ) &= 0 \\ z^{\prime }\left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	0.366
7202	8113	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}+\frac {9}{4}\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.366
7203	9589	\begin{align*} y x -x^{2} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.366
7204	10456	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-5\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.366
7205	11066	\begin{align*} x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.366
7206	12585	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+2 x \left (3 x +2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.366
7207	14203	\begin{align*} x^{\prime }&=t \cos \left (t^{2}\right ) \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.366
7208	14383	\begin{align*} x^{\prime }&=-3 y \\ y^{\prime }&=-2 x+y \\ \end{align*}	✓	✓	✓	✓	0.366
7209	14573	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=2-12 x +6 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.366
7210	16212	\begin{align*} y^{\prime }+4 y&=8 \\ \end{align*}	✓	✓	✓	✓	0.366
7211	16842	\begin{align*} y^{\prime \prime }-2 y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.366
7212	16895	\begin{align*} \left (x^{2}+4\right )^{2} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.366
7213	18212	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\left (x^{2}+x \right ) {\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.366
7214	18280	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.366
7215	18396	\begin{align*} y^{\prime \prime }+\frac {3 y^{\prime }}{x}+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.366
7216	18699	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=8 x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.366
7217	21639	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.366
7218	23979	\begin{align*} y^{\prime \prime }+k y^{\prime }+L y&=0 \\ \end{align*}	✓	✓	✓	✓	0.366
7219	24734	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\cos \left ({\mathrm e}^{-x}\right ) \\ \end{align*}	✓	✓	✓	✓	0.366
7220	24847	\begin{align*} 4 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.366
7221	25135	\begin{align*} y^{\prime \prime }+2 y^{\prime }-8 y&=6 \,{\mathrm e}^{-4 t} \\ \end{align*}	✓	✓	✓	✓	0.366
7222	3807	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.367
7223	5769	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\left (x -6\right ) x^{2} \\ \end{align*}	✓	✓	✓	✓	0.367
7224	7103	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.367
7225	7358	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=6 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.367
7226	10385	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=x +1 \\ \end{align*}	✓	✓	✓	✓	0.367
7227	14381	\begin{align*} x^{\prime }&=-x-2 y \\ y^{\prime }&=2 x-y \\ \end{align*}	✓	✓	✓	✓	0.367
7228	18664	\begin{align*} x^{\prime }&=-x-4 y \\ y^{\prime }&=x-y \\ \end{align*}	✓	✓	✓	✓	0.367
7229	18824	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=16 \,{\mathrm e}^{\frac {t}{2}} \\ \end{align*}	✓	✓	✓	✓	0.367
7230	20995	\begin{align*} x^{\prime }&=8 x+y \\ y^{\prime }&=-4 x+4 y \\ \end{align*}	✓	✓	✓	✓	0.367
7231	22733	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.367
7232	23669	\begin{align*} \left (1-x \right ) y^{\prime \prime }-y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.367
7233	23752	\begin{align*} \left (x^{2}-\frac {1}{4}\right ) y^{\prime \prime }+2 y^{\prime }-6 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.367
7234	24789	\begin{align*} x y \left (y^{2}+x^{2}\right ) \left (-1+{y^{\prime }}^{2}\right )&=y^{\prime } \left (x^{4}+y^{2} x^{2}+y^{4}\right ) \\ \end{align*}	✓	✓	✓	✓	0.367
7235	292	\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.368
7236	581	\begin{align*} x^{\prime }&=8 y \\ y^{\prime }&=-2 x \\ \end{align*}	✓	✓	✓	✓	0.368
7237	1461	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.368
7238	1737	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.368
7239	1864	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.368
7240	1928	\begin{align*} 3 y^{\prime \prime }+2 y^{\prime } x +\left (-x^{2}+4\right ) y&=0 \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.368
7241	2782	\begin{align*} x_{1}^{\prime }&=3 x_{1}-2 x_{2}+1-\operatorname {Heaviside}\left (t -\pi \right ) \\ x_{2}^{\prime }&=2 x_{1}-2 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.368
7242	7070	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.368
7243	7282	\begin{align*} y^{\prime \prime }-16 y&=40 \,{\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.368
7244	8576	\begin{align*} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.368
7245	9075	\begin{align*} \left (x^{2}-1\right ) y^{\prime }&=1 \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.368
7246	9378	\begin{align*} y^{\prime \prime }+y^{\prime }-y x&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.368
7247	9473	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=4 x+y \\ \end{align*}	✓	✓	✓	✓	0.368
7248	9489	\begin{align*} y^{\prime }-2 y&=x^{2} \\ y \left (1\right ) &= 1 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.368
7249	10543	\begin{align*} 3 x^{2} y^{\prime \prime }+2 x \left (-2 x^{2}+x +1\right ) y^{\prime }+\left (-8 x^{2}+2 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.368
7250	10647	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.368
7251	14177	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=\ln \left (y\right ) y^{2}-y^{2} x^{2} \\ \end{align*}	✗	✓	✓	✗	0.368
7252	14400	\begin{align*} x^{\prime }&=2 x+2 y \\ y^{\prime }&=6 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.368
7253	14877	\begin{align*} y^{\prime }&=x -\frac {1}{3} x^{3} \\ y \left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.368
7254	16015	\begin{align*} x^{\prime }&=-3 x-5 y \\ y^{\prime }&=3 x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.368
7255	16808	\begin{align*} 3 y+y^{\prime }&=\delta \left (t -2\right ) \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.368
7256	17836	\begin{align*} x^{\prime \prime }+x&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.368
7257	18659	\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=3 x-4 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.368
7258	19651	\begin{align*} x^{\prime }&=2 x \\ y^{\prime }&=3 y \\ \end{align*}	✓	✓	✓	✓	0.368
7259	20051	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{\frac {5 x}{2}} \\ \end{align*}	✓	✓	✓	✓	0.368
7260	20205	\begin{align*} x^{\prime }+2 x+y^{\prime }+y&=0 \\ 5 x+y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.368
7261	21130	\begin{align*} x^{\prime \prime }-4 x&=t \\ \end{align*}	✓	✓	✓	✓	0.368
7262	24051	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-y^{\prime }+2 y&=-2 x^{4}+x^{2} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.368
7263	24758	\begin{align*} y^{\prime \prime }-y&=\frac {2}{{\mathrm e}^{x}+1} \\ \end{align*}	✓	✓	✓	✓	0.368
7264	25685	\begin{align*} \left (y-1\right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.368
7265	382	\begin{align*} y^{\prime \prime }+y&=2 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.369
7266	1369	\begin{align*} \left (-x^{2}+3\right ) y^{\prime \prime }-3 y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.369
7267	2560	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.369
7268	3146	\begin{align*} 4 y+y^{\prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.369
7269	4105	\begin{align*} y^{\prime }&={\mathrm e}^{x} \sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.369
7270	4562	\begin{align*} x_{1}^{\prime }&=x_{1}-3 x_{2} \\ x_{2}^{\prime }&=3 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.369
7271	5414	\begin{align*} {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.369
7272	5932	\begin{align*} a \,x^{2} \left (a \,x^{3}+1\right ) y-\left (-2 a \,x^{3}+1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.369
7273	6238	\begin{align*} -\left (2 x^{2}+1\right ) y+x^{4} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.369
7274	6464	\begin{align*} 2 y^{\prime } \left (1+y^{\prime }\right )+\left (x -y\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.369
7275	7699	\begin{align*} x^{2} y^{\prime }&=x^{3} \sin \left (3 x \right )+4 \\ \end{align*}	✓	✓	✓	✓	0.369
7276	8081	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.369
7277	8495	\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 \(x=0\).	✓	✓	✓	✓	0.369
7278	8574	\begin{align*} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.369
7279	8584	\begin{align*} y^{\prime \prime }+\left (x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.369
7280	9459	\begin{align*} x^{\prime }&=x+2 y \\ y^{\prime }&=3 x+2 y \\ \end{align*}	✓	✓	✓	✓	0.369
7281	9477	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=-x+y \\ \end{align*}	✓	✓	✓	✓	0.369
7282	9829	\begin{align*} x {y^{\prime }}^{2}+\left (k -x -y\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.369
7283	10509	\begin{align*} x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.369
7284	10553	\begin{align*} x^{2} \left (x +4\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.369
7285	14964	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.369
7286	15332	\begin{align*} y^{\prime \prime }-2 k y^{\prime }+k^{2} y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.369
7287	16073	\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&={\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.369
7288	16193	\begin{align*} y^{\prime } x&=\sin \left (x^{2}\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.369
7289	16617	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=18 x^{2}+3 x +4 \\ \end{align*}	✓	✓	✓	✓	0.369
7290	16951	\begin{align*} x^{\prime }&=3 x+y \\ y^{\prime }&=6 x+2 y \\ \end{align*}	✓	✓	✓	✓	0.369
7291	17439	\begin{align*} 16 y^{\prime \prime }-8 y^{\prime }-15 y&=75 t \\ \end{align*}	✓	✓	✓	✓	0.369
7292	18816	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=3 \sin \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.369
7293	21773	\begin{align*} x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✓	0.369
7294	22716	\begin{align*} y^{\prime \prime }-y&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.369
7295	23447	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.369
7296	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 \(x=3\).	✓	✓	✓	✓	0.369
7297	24060	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.369
7298	25677	\begin{align*} 2 y+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.369
7299	1365	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.370
7300	1873	\begin{align*} y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y&=0 \\ y \left (3\right ) &= -2 \\ y^{\prime }\left (3\right ) &= 3 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	0.370