2.3.98 Problems 9701 to 9800

Table 2.727: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
9701	271	\begin{align*} y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.107
9702	14159	\begin{align*} y^{\prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.107
9703	21592	\begin{align*} 2 x^{\prime }-3 x-2 y^{\prime }&=t \\ 2 x^{\prime }+3 x+2 y^{\prime }+8 y&=2 \\ \end{align*}	✓	✓	✓	✓	1.107
9704	25288	\begin{align*} 3 y+y^{\prime }&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t <\infty \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✗	✓	✗	1.107
9705	10686	\begin{align*} 4 y^{\prime \prime }+y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.108
9706	15904	\begin{align*} y^{\prime }&=\frac {y}{2}+4 \,{\mathrm e}^{\frac {t}{2}} \\ \end{align*}	✓	✓	✓	✓	1.108
9707	20017	\begin{align*} y&=y^{\prime } x +a \sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	1.108
9708	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*}	✓	✓	✓	✓	1.108
9709	3296	\begin{align*} y \left (1+{y^{\prime }}^{2}\right )&=2 \\ \end{align*}	✓	✓	✓	✓	1.109
9710	14199	\begin{align*} t^{2} x^{\prime \prime }-6 x&=0 \\ \end{align*}	✓	✓	✓	✓	1.109
9711	15534	\begin{align*} y^{\prime }&=x +y \\ \end{align*}	✓	✓	✓	✓	1.109
9712	991	\begin{align*} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=2 x_{1}+2 x_{2} \\ x_{3}^{\prime }&=3 x_{2}+3 x_{3} \\ x_{4}^{\prime }&=4 x_{3}+4 x_{4} \\ \end{align*}	✓	✓	✓	✓	1.110
9713	3328	\begin{align*} y&=y^{\prime } x +\frac {3}{{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	1.110
9714	6476	\begin{align*} 2 y y^{\prime \prime }&=3 y^{4}+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.110
9715	18641	\begin{align*} x^{\prime }&=-x+y+1 \\ y^{\prime }&=x+y-3 \\ \end{align*}	✓	✓	✓	✓	1.110
9716	21924	\begin{align*} x^{\prime }+y^{\prime }-y&=0 \\ y^{\prime }+2 y+z^{\prime }+2 z&=2 \\ x+z^{\prime }-z&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ z \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.110
9717	9986	\begin{align*} x^{\prime }&=6 x-7 y+10 \\ y^{\prime }&=x-2 y-2 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	1.111
9718	15662	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.111
9719	15750	\begin{align*} y_{1}^{\prime }&=2 y_{2} \\ y_{2}^{\prime }&=3 y_{1} \\ y_{3}^{\prime }&=2 y_{3}-y_{1} \\ \end{align*}	✓	✓	✓	✓	1.111
9720	4038	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.112
9721	9865	\begin{align*} 8 x^{2} y^{\prime \prime }+10 y^{\prime } x -\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.112
9722	24951	\begin{align*} \frac {y^{\prime }}{y}&=-t +y \\ \end{align*}	✓	✓	✓	✓	1.112
9723	9963	\begin{align*} y^{\prime \prime } x +\left (-x^{2}+1\right ) y^{\prime }+2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.114
9724	22900	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=z \\ z^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	1.114
9725	1633	\begin{align*} y^{\prime }-y x&=x^{3} y^{3} \\ \end{align*}	✓	✓	✓	✓	1.115
9726	7425	\begin{align*} y^{\prime }&=\frac {y}{x}+2 x +1 \\ \end{align*}	✓	✓	✓	✓	1.115
9727	17719	\begin{align*} x^{2} y^{\prime \prime }+7 y^{\prime } x -7 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.115
9728	25406	\begin{align*} y^{\prime }&=3 y+{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	1.115
9729	1119	\begin{align*} -y+2 y^{\prime }&={\mathrm e}^{\frac {t}{3}} \\ y \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✓	1.116
9730	6972	\begin{align*} 2 y+y^{\prime }&=3 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	1.116
9731	16816	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=\delta \left (t -4\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.116
9732	22036	\begin{align*} y^{\prime } x -y+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.116
9733	5488	\begin{align*} 4 x {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	1.117
9734	10754	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.117
9735	9899	\begin{align*} 4 \left (x -4\right )^{2} y^{\prime \prime }+\left (x -4\right ) \left (x -8\right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=4\).	✓	✓	✓	✓	1.118
9736	14372	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.118
9737	19168	\begin{align*} \sin \left (x \right )^{2} y^{\prime \prime }&=2 y \\ \end{align*}	✓	✓	✓	✗	1.118
9738	22147	\begin{align*} y^{\prime \prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.118
9739	2484	\begin{align*} y^{\prime }-2 t y&=1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.119
9740	5554	\begin{align*} y {y^{\prime }}^{2}+y&=a \\ \end{align*}	✓	✓	✓	✓	1.119
9741	8241	\begin{align*} y^{\prime }&=y^{2} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.119
9742	9680	\begin{align*} x^{\prime }&=-x-y \\ y^{\prime }&=\frac {3 x}{4}-\frac {3 y}{2}+3 z \\ z^{\prime }&=\frac {x}{8}+\frac {y}{4}-\frac {z}{2} \\ \end{align*}	✓	✓	✓	✓	1.119
9743	21896	\begin{align*} x^{\prime }-2 x+y^{\prime }-2 y&=1 \\ y^{\prime }+z^{\prime }+z&=2 \\ 3 x+z^{\prime }+z&=3 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ z \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.119
9744	22808	\begin{align*} y^{\prime \prime }+y&=f \left (x \right ) \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.119
9745	12295	\begin{align*} y^{\prime \prime }-\left (a^{2} x^{2 n}-1\right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	1.120
9746	14843	\begin{align*} f \left (t \right ) x^{\prime \prime }+x g \left (t \right )&=0 \\ \end{align*}	✗	✗	✗	✗	1.120
9747	18015	\begin{align*} y&=\frac {3 y^{\prime } x}{2}+{\mathrm e}^{y^{\prime }} \\ \end{align*}	✓	✓	✓	✗	1.120
9748	20562	\begin{align*} y y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.120
9749	24937	\begin{align*} y^{\prime }&=y \left (y+t \right ) \\ \end{align*}	✓	✓	✓	✓	1.120
9750	574	\begin{align*} x^{\prime \prime }+6 x^{\prime }+8 x&=f \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.121
9751	18348	\begin{align*} x^{\prime \prime }-x \,{\mathrm e}^{x^{\prime }}&=0 \\ \end{align*}	✓	✓	✓	✗	1.121
9752	20134	\begin{align*} y^{\prime \prime }-a {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.121
9753	20768	\begin{align*} y+3 y^{\prime } x +2 y {y^{\prime }}^{2}+\left (x^{2}+2 y^{2} y^{\prime }\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	1.121
9754	21496	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	1.121
9755	24852	\begin{align*} 4 y^{2} {y^{\prime }}^{3}-2 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	1.121
9756	2092	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x -\left (-x^{2}+3\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.122
9757	2103	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.122
9758	2696	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t}+3 \delta \left (t -3\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.122
9759	9904	\begin{align*} 4 x^{2} y^{\prime \prime }+8 x \left (x +1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.122
9760	9905	\begin{align*} x^{2} y^{\prime \prime }+3 x \left (x +1\right ) y^{\prime }+\left (1-3 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.122
9761	15944	\begin{align*} y^{\prime }&=y+{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	1.122
9762	19007	\begin{align*} x_{1}^{\prime }&=-2 x_{2}-x_{3} \\ x_{2}^{\prime }&=x_{1}-x_{2}+x_{3} \\ x_{3}^{\prime }&=x_{1}-2 x_{2}-2 x_{3} \\ \end{align*}	✓	✓	✓	✓	1.122
9763	21052	\begin{align*} x^{\prime }&=\frac {x^{2}+x}{2 x+1} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.122
9764	2705	\begin{align*} x^{\prime }&=4 x+5 y+4 \,{\mathrm e}^{t} \cos \left (t \right ) \\ y^{\prime }&=-2 x-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.123
9765	9902	\begin{align*} y^{\prime \prime } x +\left (-x^{2}+1\right ) y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.123
9766	10520	\begin{align*} y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.123
9767	16917	\begin{align*} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+\left (4 x^{2}+5 x \right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.123
9768	8103	\begin{align*} x \left (2+x \right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.125
9769	9875	\begin{align*} -y x -\left (2 x^{2}+1\right ) y^{\prime }+2 y^{\prime \prime } x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.125
9770	3879	\begin{align*} x_{1}^{\prime }&=2 x_{1}-3 x_{2}+34 \sin \left (t \right ) \\ x_{2}^{\prime }&=-4 x_{1}-2 x_{2}+17 \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.126
9771	9949	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (x^{2}+3\right ) y^{\prime }+6 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.126
9772	13002	\begin{align*} 2 \left (1-y\right ) y y^{\prime \prime }-\left (1-3 y\right ) {y^{\prime }}^{2}+h \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	1.126
9773	9431	\begin{align*} 2 y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.127
9774	9906	\begin{align*} y^{\prime \prime } x +\left (1-x \right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.127
9775	22026	\begin{align*} y^{\prime }&=-\frac {2 x y}{x^{2}+1} \\ y \left (2\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	1.127
9776	22282	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.127
9777	24838	\begin{align*} 9 y^{2} {y^{\prime }}^{2}-3 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	1.127
9778	3424	\begin{align*} y^{\prime }&=2 y-4 \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	1.128
9779	11157	\begin{align*} u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	1.128
9780	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*}	✓	✓	✓	✓	1.128
9781	23783	\begin{align*} x^{\prime }&=a x+b y \\ y^{\prime }&=c x+d y \\ \end{align*}	✓	✓	✓	✓	1.128
9782	3306	\begin{align*} x^{2}-3 y y^{\prime }+x {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.129
9783	16483	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.129
9784	19135	\begin{align*} x {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	1.129
9785	9962	\begin{align*} 4 x^{2} y^{\prime \prime }+3 x^{2} y^{\prime }+\left (1+3 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.131
9786	25475	\begin{align*} y^{\prime }&=-y^{2}+y \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	1.131
9787	74	\begin{align*} y^{\prime }-2 y&=3 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.132
9788	5587	\begin{align*} \left (x +y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\ \end{align*}	✓	✓	✓	✓	1.132
9789	8086	\begin{align*} 2 x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=\infty \).	✓	✓	✓	✓	1.132
9790	15947	\begin{align*} y^{\prime }&=3 y+{\mathrm e}^{7 t} \\ \end{align*}	✓	✓	✓	✓	1.132
9791	17197	\begin{align*} y^{2}-\frac {y}{2 \sqrt {t}}+\left (2 t y-\sqrt {t}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.132
9792	10587	\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.133
9793	19867	\begin{align*} y^{\prime \prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.133
9794	497	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+\left (\gamma -\left (\alpha +\beta +1\right ) x \right ) y^{\prime }-\alpha \beta y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.134
9795	649	\begin{align*} x_{1}^{\prime }&=2 x_{1} \\ x_{2}^{\prime }&=-21 x_{1}-5 x_{2}-27 x_{3}-9 x_{4} \\ x_{3}^{\prime }&=5 x_{3} \\ x_{4}^{\prime }&=-21 x_{3}-2 x_{4} \\ \end{align*}	✓	✓	✓	✓	1.135
9796	10671	\begin{align*} t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y&=0 \\ \end{align*}	✓	✓	✓	✗	1.135
9797	20438	\begin{align*} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 y y^{\prime } x +y^{2}+a^{4}&=0 \\ \end{align*}	✓	✓	✓	✗	1.135
9798	21562	\begin{align*} y-\frac {y^{\prime } x}{2}-\frac {x}{2 y^{\prime }}&=0 \\ \end{align*}	✓	✓	✓	✓	1.135
9799	22946	\begin{align*} x^{\prime }+4 x+2 y-z&=12 \,{\mathrm e}^{t} \\ y^{\prime }-2 x-5 y+3 z&=0 \\ z^{\prime }+4 x+z&=30 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	1.135
9800	24559	\begin{align*} y^{\prime \prime }+y&=12 \cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.135