2.3.98 Problems 9701 to 9800

Table 2.745: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
9701	10465	\begin{align*} 3 y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.729
9702	15072	\begin{align*} y^{\prime \prime }+y&=\cosh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.729
9703	20367	\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=x^{2} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.729
9704	20598	\begin{align*} {\mathrm e}^{x} \left (-y^{\prime }+y^{\prime \prime } x \right )&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.729
9705	22858	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-4 x^{2}+3\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.729
9706	600	\begin{align*} x^{\prime }&=y+z+{\mathrm e}^{-t} \\ y^{\prime }&=x+z \\ z^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.730
9707	2286	\begin{align*} y_{1}^{\prime }&=-11 y_{1}+4 y_{2} \\ y_{2}^{\prime }&=-26 y_{1}+9 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.730
9708	3754	\begin{align*} y^{\prime \prime }+y&=\csc \left (x \right )+2 x^{2}+5 x +1 \\ \end{align*}	✓	✓	✓	✓	0.730
9709	4460	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=\sin \left (x \right )+\cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	0.730
9710	7288	\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=120 \sin \left (5 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.730
9711	7781	\begin{align*} x^{\prime \prime }+5 x^{\prime }+6 x&=\cos \left (t \right ) \\ x \left (0\right ) &= {\frac {1}{10}} \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.730
9712	9183	\begin{align*} x^{2} y^{\prime \prime }&=2 y^{\prime } x +{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.730
9713	11379	\begin{align*} y^{\prime }+a \sin \left (\alpha y+\beta x \right )+b&=0 \\ \end{align*}	✓	✓	✓	✗	0.730
9714	17492	\begin{align*} y^{\prime \prime }+12 y^{\prime }+37 y&={\mathrm e}^{-6 t} \csc \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.730
9715	18152	\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&={\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	0.730
9716	19965	\begin{align*} \left (x^{3} y^{3}+y^{2} x^{2}+y x +1\right ) y+\left (x^{3} y^{3}-y^{2} x^{2}-y x +1\right ) x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.730
9717	26069	\begin{align*} y^{\prime }&=y-2 z \\ z^{\prime }&=4 y+5 z \\ \end{align*}	✓	✓	✓	✓	0.730
9718	10183	\begin{align*} 2 x^{2} y^{\prime \prime }+2 y^{\prime } x -y x&=1 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.731
9719	18819	\begin{align*} y^{\prime \prime }+9 y&=t^{2} {\mathrm e}^{3 t}+6 \\ \end{align*}	✓	✓	✓	✓	0.731
9720	19359	\begin{align*} y^{\prime \prime } x&=y^{\prime }+{y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✓	0.731
9721	26188	\begin{align*} y^{\prime }&=\left (-1+y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.731
9722	2828	\begin{align*} x_{1}^{\prime }&=x_{1}-4 x_{2} \\ x_{2}^{\prime }&=-8 x_{1}+4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.732
9723	7108	\begin{align*} y^{\prime \prime }+y&=\csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.732
9724	10469	\begin{align*} y^{\prime \prime }+y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.732
9725	10586	\begin{align*} x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.732
9726	18158	\begin{align*} y^{\prime \prime }+4 y^{\prime }+8 y&={\mathrm e}^{2 x} \left (\cos \left (2 x \right )+\sin \left (2 x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.732
9727	24570	\begin{align*} 2 y^{\prime \prime }-5 y^{\prime }-3 y&=-9 x^{2}-1 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.732
9728	25749	\begin{align*} y^{\prime \prime }+y&=2 \cos \left (x \right )-2 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.732
9729	25948	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=x^{2}+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.732
9730	988	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\ x_{2}^{\prime }&=-4 x_{1}-3 x_{2}-x_{3} \\ x_{3}^{\prime }&=4 x_{1}+4 x_{2}+2 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.733
9731	3916	\begin{align*} x_{1}^{\prime }&=10 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1}+2 x_{2}+\frac {{\mathrm e}^{6 t}}{t} \\ \end{align*}	✓	✓	✓	✓	0.733
9732	6394	\begin{align*} 2+4 y^{\prime } x +x^{2} {y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.733
9733	7285	\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=100 \cos \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.733
9734	15466	\begin{align*} x^{\prime }&=-4 x+2 y \\ y^{\prime }&=3 x-2 y \\ \end{align*}	✓	✓	✓	✓	0.733
9735	16590	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=7 \,{\mathrm e}^{5 x} \\ y \left (0\right ) &= 12 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.733
9736	17464	\begin{align*} y^{\prime \prime }+6 y^{\prime }+25 y&=-1 \\ y \left (0\right ) &= -{\frac {1}{25}} \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	0.733
9737	21233	\begin{align*} x^{\prime }&=2 x \\ y^{\prime }&=2 y+z \\ z^{\prime }&=-x-z \\ \end{align*}	✓	✓	✓	✓	0.733
9738	22750	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=2 x^{2} {\mathrm e}^{-2 x}+3 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.733
9739	22848	\begin{align*} \cos \left (x \right ) y^{\prime \prime }+\sin \left (x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.733
9740	23524	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{a x} \\ y \left (0\right ) &= y_{0} \\ y^{\prime }\left (0\right ) &= y_{1} \\ \end{align*}	✓	✓	✓	✓	0.733
9741	1989	\begin{align*} 8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.734
9742	4552	\begin{align*} x^{\prime }-2 x+y&=5 \,{\mathrm e}^{t} \cos \left (t \right ) \\ x+y^{\prime }-2 y&=10 \,{\mathrm e}^{t} \sin \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.734
9743	6935	\begin{align*} y^{2} {\mathrm e}^{x y^{2}}+4 x^{3}+\left (2 x y \,{\mathrm e}^{x y^{2}}-3 y^{2}\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.734
9744	9720	\begin{align*} {y^{\prime }}^{2}-y^{\prime } x y \left (x +y\right )+x^{3} y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.734
9745	15465	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.734
9746	15570	\begin{align*} y^{\prime }&=1+3 x \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.734
9747	17002	\begin{align*} y^{\prime }&=\sin \left (2 t \right )-\cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.734
9748	17378	\begin{align*} y^{\prime \prime }+b y^{\prime }+c y&=0 \\ y \left (\pi \right ) &= 0 \\ y \left (2 \pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.734
9749	17855	\begin{align*} y^{\prime }&=\left (-1+y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.734
9750	18912	\begin{align*} y_{1}^{\prime }&=4 y_{1}-4 y_{2} \\ y_{2}^{\prime }&=5 y_{1}-4 y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.734
9751	19112	\begin{align*} {y^{\prime }}^{3} x&=1+y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.734
9752	19620	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+\left (1-3 x \right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.734
9753	20150	\begin{align*} n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.734
9754	22578	\begin{align*} y y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.734
9755	22728	\begin{align*} 4 y+y^{\prime \prime }&=\csc \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.734
9756	24714	\begin{align*} 4 y+y^{\prime \prime }&=2 x -8 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.734
9757	25994	\begin{align*} x^{\prime }&=3 x \\ y^{\prime }&=2 x+3 y \\ z^{\prime }&=3 y-2 z \\ \end{align*}	✓	✓	✓	✓	0.734
9758	9046	\begin{align*} y_{1}^{\prime }&=y_{1}+y_{2} \\ y_{2}^{\prime }&=y_{1}+y_{2}+{\mathrm e}^{3 x} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 0 \\ y_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.735
9759	9844	\begin{align*} \left (-4 x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x -4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.735
9760	10519	\begin{align*} \left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (x -2\right ) y^{\prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.735
9761	12702	\begin{align*} y^{\prime \prime }&=-\frac {x y^{\prime }}{f \left (x \right )}+\frac {y}{f \left (x \right )} \\ \end{align*}	✓	✓	✓	✗	0.735
9762	14159	\begin{align*} y^{\prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.735
9763	14176	\begin{align*} x^{3} y^{\prime \prime }-\left (-y+y^{\prime } x \right )^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	0.735
9764	18910	\begin{align*} y_{1}^{\prime }&=-5 y_{1}+y_{2} \\ y_{2}^{\prime }&=-9 y_{1}+5 y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.735
9765	21652	\begin{align*} y^{\prime \prime }-\left (x -2\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	0.735
9766	24090	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.735
9767	24783	\begin{align*} {y^{\prime }}^{2}-y^{\prime } x y \left (x +y\right )+x^{3} y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.735
9768	1958	\begin{align*} 2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (1-2 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.736
9769	1997	\begin{align*} 4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.736
9770	1998	\begin{align*} x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.736
9771	3910	\begin{align*} x_{1}^{\prime }&=-3 x_{1}-x_{2}-2 x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{3} \\ x_{3}^{\prime }&=x_{1} \\ \end{align*}	✓	✓	✓	✓	0.736
9772	6515	\begin{align*} \left (-y+y^{\prime } x \right )^{2}+x^{2} y y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.736
9773	7633	\begin{align*} z^{\prime }-x^{2} z&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.736
9774	12904	\begin{align*} 4 x^{2} y^{\prime \prime }-x^{4} {y^{\prime }}^{2}+4 y&=0 \\ \end{align*}	✗	✗	✗	✗	0.736
9775	12958	\begin{align*} 2 y y^{\prime \prime }-3 {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.736
9776	17831	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=1-x \\ \end{align*}	✓	✓	✓	✓	0.736
9777	18017	\begin{align*} y&=y^{\prime } x +{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.736
9778	18326	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=\frac {{\mathrm e}^{-x}}{\sin \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	0.736
9779	18454	\begin{align*} x^{\prime }&=3 x+y+{\mathrm e}^{t} \\ y^{\prime }&=x+3 y-{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.736
9780	19697	\begin{align*} x^{\prime \prime }-x&={\mathrm e}^{t} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.736
9781	20378	\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y+37 \sin \left (3 x \right )&=0 \\ y \left (\frac {\pi }{2}\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.736
9782	21294	\begin{align*} x^{\prime }&=-x-y \\ y^{\prime }&=4 x-y \\ \end{align*}	✓	✓	✓	✗	0.736
9783	22872	\begin{align*} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (2 x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.736
9784	23076	\begin{align*} y^{\prime \prime }-2 y^{\prime }-y&=2 \cos \left (3 x \right )-3 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.736
9785	1985	\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.737
9786	3290	\begin{align*} y^{2} {y^{\prime }}^{2}+y y^{\prime } x -2 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.737
9787	4107	\begin{align*} y^{\prime }&=x +\frac {1}{x} \\ y \left (-2\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.737
9788	6188	\begin{align*} -y+y^{\prime } x +x^{3} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.737
9789	9833	\begin{align*} y^{\prime \prime }+3 y^{\prime } x +3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.737
9790	10223	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +4 x^{4} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.737
9791	17768	\begin{align*} y^{\prime \prime }+9 y&=\sin \left (3 t \right ) \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.737
9792	19771	\begin{align*} y&=y^{\prime } x +y^{\prime }-{y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.737
9793	22169	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=\cos \left (2 x \right )+\sin \left (2 x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.737
9794	22786	\begin{align*} 4 y+y^{\prime \prime }&=x \left (\cos \left (x \right )+1\right ) \\ \end{align*}	✓	✓	✓	✓	0.737
9795	22870	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-8\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.737
9796	25349	\begin{align*} t^{2} y^{\prime \prime }+t^{2} y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.737
9797	1954	\begin{align*} 2 x^{2} y^{\prime \prime }+x \left (3+2 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.738
9798	2197	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+9 y^{\prime }-10 y&=10 \,{\mathrm e}^{2 x}+20 \,{\mathrm e}^{x} \sin \left (2 x \right )-10 \\ \end{align*}	✓	✓	✓	✓	0.738
9799	5927	\begin{align*} 2 y x -\left (-x^{2}+4\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.738
9800	8807	\begin{align*} y^{\left (5\right )}-\frac {y^{\prime \prime \prime \prime }}{t}&=0 \\ \end{align*}	✓	✓	✓	✓	0.738