2.3.88 Problems 8701 to 8800

Table 2.749: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
8701	19993	\begin{align*} y&=y^{\prime } \left (x -b \right )+\frac {a}{y^{\prime }} \\ \end{align*}	✓	✓	✓	✗	1.133
8702	26935	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.133
8703	10099	\begin{align*} y^{\prime \prime }-2 y^{\prime }-y x -x^{3}-x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.134
8704	14122	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=2 x^{3}-x \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	1.134
8705	20930	\begin{align*} x^{\prime }&=3 x-y \\ y^{\prime }&=2 x-2 y \\ \end{align*}	✓	✓	✓	✓	1.134
8706	21233	\begin{align*} x^{\prime }&=2 x \\ y^{\prime }&=2 y+z \\ z^{\prime }&=-x-z \\ \end{align*}	✓	✓	✓	✓	1.134
8707	21524	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=3 \sin \left (x +\frac {\pi }{4}\right ) \\ \end{align*}	✓	✓	✓	✓	1.134
8708	23601	\begin{align*} x^{\prime }&=3 x-2 y \\ y^{\prime }&=2 x-y \\ \end{align*}	✓	✓	✓	✓	1.134
8709	2214	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y&={\mathrm e}^{x} \left (\left (2+6 x \right ) \cos \left (2 x \right )+3 \sin \left (2 x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	1.135
8710	9698	\begin{align*} x^{\prime }&=z \\ y^{\prime }&=y \\ z^{\prime }&=x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 2 \\ z \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	1.135
8711	13984	\begin{align*} y+2 x y^{2}-x^{2} y^{3}+2 x^{2} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.135
8712	15275	\begin{align*} 2 x^{\prime }-y^{\prime }&=t \\ 3 x^{\prime }+2 y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	1.135
8713	16640	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=100 \\ \end{align*}	✓	✓	✓	✓	1.135
8714	16648	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{-7 x}+2 \,{\mathrm e}^{-7 x} \\ \end{align*}	✓	✓	✓	✓	1.135
8715	18121	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=y^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✗	1.135
8716	25442	\begin{align*} y^{\prime }&=A \cos \left (\omega t \right )+B \sin \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	1.135
8717	26626	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }&=6 y \\ \end{align*}	✓	✓	✓	✓	1.135
8718	2542	\begin{align*} 2 t^{2} y^{\prime \prime }+3 y^{\prime } t -y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.136
8719	5582	\begin{align*} \left (a^{2}-y^{2}\right ) {y^{\prime }}^{2}&=y^{2} \\ \end{align*}	✓	✓	✓	✓	1.136
8720	7684	\begin{align*} x \left (x +1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (-1+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.136
8721	8294	\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	1.136
8722	16367	\begin{align*} x y^{2}+\left (x^{2} y+10 y^{4}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.136
8723	18117	\begin{align*} y y^{\prime \prime }&={y^{\prime }}^{2}+y^{\prime } \\ \end{align*}	✓	✓	✓	✗	1.136
8724	3352	\begin{align*} x^{2} \left (x +4\right ) y^{\prime \prime }+7 y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.137
8725	10139	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.137
8726	15277	\begin{align*} x^{\prime }-4 y^{\prime }&=0 \\ 2 x^{\prime }-3 y^{\prime }&=y+t \\ \end{align*}	✓	✓	✓	✓	1.137
8727	2090	\begin{align*} y^{\prime \prime } x -5 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.138
8728	3297	\begin{align*} y {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.138
8729	5872	\begin{align*} -\left (a^{2}+1\right ) y-2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.138
8730	6546	\begin{align*} 2 \left (1-y\right ) y y^{\prime \prime }&=4 y \left (f \left (x \right )+g \left (x \right ) y\right ) y^{\prime }+\left (1-3 y\right ) {y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	1.138
8731	10334	\begin{align*} y^{\prime } t +y&=0 \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.138
8732	14675	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right )^{3} \\ \end{align*}	✓	✓	✓	✓	1.138
8733	16824	\begin{align*} \left (x^{2}+1\right ) y^{\prime }-2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.138
8734	18272	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=2 \,{\mathrm e}^{x} x^{2} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	1.138
8735	19517	\begin{align*} y^{\prime \prime }+y&=\cot \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.138
8736	4438	\begin{align*} y^{\prime } \left (x -\ln \left (y^{\prime }\right )\right )&=1 \\ \end{align*}	✓	✓	✓	✓	1.139
8737	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*}	✓	✓	✓	✗	1.139
8738	16336	\begin{align*} x^{2} y^{\prime }-\sqrt {x}&=3 \\ \end{align*}	✓	✓	✓	✓	1.139
8739	17133	\begin{align*} y^{\prime }&=-y \\ \end{align*}	✓	✓	✓	✓	1.139
8740	1955	\begin{align*} \left (x +3\right ) x^{2} y^{\prime \prime }+x \left (5+4 x \right ) y^{\prime }-\left (1-2 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.140
8741	16111	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=5 \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.140
8742	2465	\begin{align*} 2 \sin \left (t \right ) y^{\prime \prime }+\left (1-t \right ) y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✗	1.141
8743	5913	\begin{align*} 2 \left (1-x \right ) y-\left (x +1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	1.141
8744	6148	\begin{align*} 4 y+2 \left (1-2 x \right ) y^{\prime }+\left (1-2 x \right ) \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.141
8745	10102	\begin{align*} y^{\prime \prime }-4 y^{\prime }-y x -x^{3}+2&=0 \\ \end{align*}	✓	✓	✓	✗	1.141
8746	16113	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=2 \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.141
8747	18036	\begin{align*} y^{2} {y^{\prime }}^{2}+y^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	1.141
8748	18395	\begin{align*} y^{\prime \prime }+\frac {5 y^{\prime }}{x}+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.141
8749	18727	\begin{align*} y^{\prime \prime }+y^{\prime }+16 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.141
8750	19457	\begin{align*} 3 y-\left (x +3\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	1.141
8751	23471	\begin{align*} y^{\prime \prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	1.141
8752	1804	\begin{align*} y^{\prime \prime }+9 y&=\tan \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.142
8753	1968	\begin{align*} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.142
8754	3280	\begin{align*} 2 y y^{\prime \prime }&=y^{3}+2 {y^{\prime }}^{2} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.142
8755	7406	\begin{align*} y^{\prime }&={\mathrm e}^{x^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.142
8756	14307	\begin{align*} x^{\prime \prime }+7 x&=t \,{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	1.142
8757	15996	\begin{align*} x^{\prime }&=-2 x-2 y \\ y^{\prime }&=-2 x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.142
8758	16115	\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=-4 \cos \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.142
8759	19167	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.142
8760	23602	\begin{align*} x^{\prime }&=-4 x+y \\ y^{\prime }&=-x-2 y \\ \end{align*}	✓	✓	✓	✓	1.142
8761	25180	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.142
8762	3512	\begin{align*} z y^{\prime \prime }+\left (1-z \right ) y^{\prime }+\lambda y&=0 \\ \end{align*} Series expansion around \(z=0\).	✓	✓	✓	✓	1.143
8763	6022	\begin{align*} \left (c \,x^{3}+b \right ) y+a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.143
8764	10097	\begin{align*} y^{\prime \prime }-4 y^{\prime }-y x -x^{2}-4&=0 \\ \end{align*}	✓	✓	✓	✗	1.143
8765	15994	\begin{align*} x^{\prime }&=-x-2 y \\ y^{\prime }&=x-4 y \\ \end{align*}	✓	✓	✓	✓	1.143
8766	16809	\begin{align*} y^{\prime \prime }+3 y^{\prime }&=\delta \left (t \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.143
8767	22184	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.143
8768	3771	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.144
8769	8296	\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\ y \left (8\right ) &= -4 \\ \end{align*}	✗	✗	✗	✗	1.144
8770	15513	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	1.144
8771	16413	\begin{align*} \left (y-3\right ) y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.144
8772	18218	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{-x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.144
8773	20996	\begin{align*} x^{\prime }&=x-y+2 z \\ y^{\prime }&=-x+y+2 z \\ z^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	1.144
8774	4140	\begin{align*} y^{\prime \prime }+2 n y^{\prime }+n^{2} y&=A \cos \left (p x \right ) \\ y \left (0\right ) &= 9 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.145
8775	4522	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=2 \sin \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.145
8776	4566	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2} \\ x_{2}^{\prime }&=x_{1}+3 x_{2}-x_{3} \\ x_{3}^{\prime }&=-x_{1}+2 x_{2}+3 x_{3} \\ \end{align*}	✓	✓	✓	✓	1.145
8777	9732	\begin{align*} {y^{\prime }}^{2}-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.145
8778	10105	\begin{align*} y^{\prime \prime }-y^{\prime }-y x -x^{4}+3&=0 \\ \end{align*}	✓	✓	✓	✗	1.145
8779	14858	\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=4 x+5 y \\ \end{align*}	✓	✓	✓	✓	1.145
8780	15766	\begin{align*} x^{\prime }&=-2 x+3 y \\ y^{\prime }&=-x+2 y \\ \end{align*}	✓	✓	✓	✓	1.145
8781	18269	\begin{align*} y^{\prime \prime }+y&=2 \cos \left (x \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.145
8782	9473	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=4 x+y \\ \end{align*}	✓	✓	✓	✓	1.146
8783	23029	\begin{align*} x^{\prime \prime }-2 x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	1.146
8784	1961	\begin{align*} 2 \left (x +3\right ) x^{2} y^{\prime \prime }+x \left (5 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.147
8785	12999	\begin{align*} \left (x^{2}+y^{2}\right ) y^{\prime \prime }-\left (1+{y^{\prime }}^{2}\right ) \left (-y+y^{\prime } x \right )&=0 \\ \end{align*}	✗	✓	✓	✗	1.147
8786	15459	\begin{align*} x^{\prime }&=-4 x-10 y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	1.147
8787	22747	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&={\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	1.147
8788	1188	\begin{align*} y^{\prime }&=y^{2} \left (y^{2}-1\right ) \\ \end{align*}	✓	✓	✓	✓	1.148
8789	2627	\begin{align*} t^{2} y^{\prime \prime }+5 y^{\prime } t -5 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.148
8790	3379	\begin{align*} x^{2} y^{\prime \prime }+x \left (2 x -1\right ) y^{\prime }+x \left (-1+x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.148
8791	15706	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=-x^{2}+1 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.148
8792	16013	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=-2 x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.148
8793	16071	\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=2 \,{\mathrm e}^{-3 t} \\ \end{align*}	✓	✓	✓	✓	1.148
8794	18835	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=4 \,{\mathrm e}^{-t} \cos \left (2 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.148
8795	19012	\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2}+4 x_{3} \\ x_{2}^{\prime }&=3 x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\ \end{align*}	✓	✓	✓	✓	1.148
8796	24440	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.148
8797	24728	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.148
8798	3973	\begin{align*} -2 y+y^{\prime }&=\delta \left (-2+t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.149
8799	6403	\begin{align*} -x^{2} y^{\prime }+x^{3} y^{\prime \prime }&=-x^{2}+3 \\ \end{align*}	✓	✓	✓	✓	1.149
8800	8295	\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\ y \left (0\right ) &= -4 \\ \end{align*}	✗	✗	✗	✗	1.149