2.3.88 Problems 8701 to 8800

Table 2.707: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
8701	7097	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \left (2 x -3\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.438
8702	8384	\begin{align*} y^{\prime }&=\left (y-1\right )^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	0.438
8703	9350	\begin{align*} y^{\prime }+y&=1 \\ \end{align*}	✓	✓	✓	✓	0.438
8704	14081	\begin{align*} x {y^{\prime }}^{2}-2 y^{\prime } y-x&=0 \\ \end{align*}	✓	✓	✓	✓	0.438
8705	14103	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.438
8706	14106	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.438
8707	14330	\begin{align*} x^{\prime \prime }+x&=\tan \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.438
8708	16102	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=t^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.438
8709	17696	\begin{align*} y^{\prime \prime }+y^{\prime } x&=\sin \left (x \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.438
8710	22081	\begin{align*} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }+\left (x +1\right ) y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	0.438
8711	25371	\begin{align*} y_{1}^{\prime }&=-y_{1}+2 y_{2} \\ y_{2}^{\prime }&=-2 y_{1}-y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.438
8712	1816	\begin{align*} \left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y&=\left (2 x +1\right )^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✗	0.439
8713	3169	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.439
8714	3188	\begin{align*} y^{\prime \prime }+2 y&=x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.439
8715	3505	\begin{align*} z y^{\prime \prime }-2 y^{\prime }+y z&=0 \\ \end{align*} Series expansion around \(z=0\).	✓	✓	✓	✓	0.439
8716	3767	\begin{align*} y^{\prime \prime }+5 y^{\prime }+4 y&=F \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.439
8717	4416	\begin{align*} 2 y \left (x \,{\mathrm e}^{x^{2}}+\sin \left (x \right ) \cos \left (x \right ) y\right )+\left (2 \,{\mathrm e}^{x^{2}}+3 y \sin \left (x \right )^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.439
8718	7759	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=4 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.439
8719	8161	\begin{align*} 2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.439
8720	9585	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (16 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.439
8721	9848	\begin{align*} y^{\prime \prime }+2 y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.439
8722	14130	\begin{align*} y^{\prime \prime }+y&=\cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	0.439
8723	14624	\begin{align*} y^{\prime \prime }+6 y^{\prime }+5 y&=2 \,{\mathrm e}^{x}+10 \,{\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	0.439
8724	15404	\begin{align*} -{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	0.439
8725	15987	\begin{align*} x^{\prime }&=-5 x-2 y \\ y^{\prime }&=-x-4 y \\ \end{align*}	✓	✓	✓	✓	0.439
8726	16525	\begin{align*} y^{\prime \prime }-y^{\prime }+\left (\frac {1}{4}+4 \pi ^{2}\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -{\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	0.439
8727	16707	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 y^{\prime } x +9 y&=12 x \sin \left (x^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.439
8728	17377	\begin{align*} y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	0.439
8729	17440	\begin{align*} y^{\prime \prime }+2 y^{\prime }+26 y&=-338 t \\ \end{align*}	✓	✓	✓	✓	0.439
8730	22575	\begin{align*} i^{\prime }&=\frac {i t^{2}}{t^{3}-i^{3}} \\ \end{align*}	✓	✓	✓	✓	0.439
8731	22851	\begin{align*} 2 y^{\prime \prime } x +y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.439
8732	22859	\begin{align*} y^{\prime \prime } x +y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.439
8733	25091	\begin{align*} y^{\prime \prime }+2 y^{\prime }+3 y&={\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.439
8734	25308	\begin{align*} y^{\prime }-4 y&=\delta \left (t -4\right ) \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.439
8735	3862	\begin{align*} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=3 x_{2}+2 x_{3} \\ x_{3}^{\prime }&=2 x_{1}-2 x_{2}-x_{3} \\ \end{align*}	✓	✓	✓	✓	0.440
8736	3975	\begin{align*} y^{\prime }-5 y&=2 \,{\mathrm e}^{-t}+\delta \left (t -3\right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.440
8737	7689	\begin{align*} 2 y^{\prime \prime } x -y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.440
8738	14685	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\frac {1}{{\mathrm e}^{2 x}+1} \\ \end{align*}	✓	✓	✓	✗	0.440
8739	15233	\begin{align*} y^{\prime \prime }+4 y&=3 \operatorname {Heaviside}\left (t \right )-3 \operatorname {Heaviside}\left (t -4\right )+\left (2 t -5\right ) \operatorname {Heaviside}\left (t -4\right ) \\ y \left (0\right ) &= {\frac {3}{4}} \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.440
8740	15306	\begin{align*} \left (x^{2}-1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.440
8741	16586	\begin{align*} y^{\prime \prime }+2 y^{\prime }-8 y&=8 x^{2}-3 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.440
8742	16609	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-5 \,{\mathrm e}^{3 x} \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.440
8743	16690	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\left (24 x^{2}+2\right ) {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.440
8744	20176	\begin{align*} 3 x^{2} y^{\prime \prime }+\left (-6 x^{2}+2\right ) y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.440
8745	21521	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.440
8746	21731	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.440
8747	22627	\begin{align*} y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y x&=x \\ \end{align*}	✓	✓	✓	✗	0.440
8748	24669	\begin{align*} y^{\prime \prime }+y&=12 \cos \left (2 x \right )-\sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.440
8749	24819	\begin{align*} 2 {y^{\prime }}^{3}+y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✗	✗	0.440
8750	24989	\begin{align*} y^{\prime }+a y&=b \\ \end{align*}	✓	✓	✓	✓	0.440
8751	479	\begin{align*} 6 x^{2} y^{\prime \prime }+7 y^{\prime } x -\left (x^{2}+2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.441
8752	1870	\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*} Series expansion around \(x=2\).	✓	✓	✓	✓	0.441
8753	2559	\begin{align*} y^{\prime \prime }+y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.441
8754	2748	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2}+3 x_{3} \\ x_{2}^{\prime }&=2 x_{2}-x_{3} \\ x_{3}^{\prime }&=2 x_{3} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 2 \\ x_{3} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.441
8755	2832	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2} \\ x_{2}^{\prime }&=-5 x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.441
8756	3416	\begin{align*} \sin \left (x \right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.441
8757	3748	\begin{align*} y^{\prime \prime }-4 y&=\frac {8}{{\mathrm e}^{2 x}+1} \\ \end{align*}	✓	✓	✓	✓	0.441
8758	3751	\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=\frac {2 \,{\mathrm e}^{5 x}}{x^{2}+4} \\ \end{align*}	✓	✓	✓	✗	0.441
8759	4098	\begin{align*} y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.441
8760	4154	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{x}-2 \,{\mathrm e}^{2 x}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.441
8761	4460	\begin{align*} y^{\prime }+y^{\prime \prime \prime }&=\sin \left (x \right )+\cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	0.441
8762	6328	\begin{align*} y^{\prime \prime }&=f \left (x \right ) y^{2}-y^{3}+\left (f \left (x \right )-3 y\right ) y^{\prime } \\ \end{align*}	✗	✓	✗	✗	0.441
8763	8181	\begin{align*} 2 y+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.441
8764	9569	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.441
8765	9575	\begin{align*} y^{\prime \prime } x -5 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.441
8766	10009	\begin{align*} y&=y^{\prime } x +x^{2} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.441
8767	10716	\begin{align*} y^{\prime \prime } x +\left (x +n \right ) y^{\prime }+\left (n +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.441
8768	12352	\begin{align*} 4 y^{\prime \prime }+9 y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.441
8769	13816	\begin{align*} n \left (n +2\right ) y-3 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.441
8770	14225	\begin{align*} y^{\prime }&=\frac {1}{2 y+1} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.441
8771	14338	\begin{align*} x^{\prime \prime }-x&=\frac {{\mathrm e}^{t}}{1+{\mathrm e}^{t}} \\ \end{align*}	✓	✓	✓	✓	0.441
8772	15526	\begin{align*} y^{\prime }&=1-y \\ \end{align*}	✓	✓	✓	✓	0.441
8773	15778	\begin{align*} y^{\prime }&=2-y \\ \end{align*}	✓	✓	✓	✓	0.441
8774	16043	\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=-2 y \\ z^{\prime }&=z \\ \end{align*}	✓	✓	✓	✓	0.441
8775	16079	\begin{align*} y^{\prime \prime }+7 y^{\prime }+12 y&=3 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.441
8776	16096	\begin{align*} y^{\prime \prime }+4 y&={\mathrm e}^{t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.441
8777	16242	\begin{align*} y^{\prime }&={\mathrm e}^{-y} \\ \end{align*}	✓	✓	✓	✓	0.441
8778	16589	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-6 \,{\mathrm e}^{4 x} \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	0.441
8779	16619	\begin{align*} y^{\prime \prime }+9 y&=x^{3} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.441
8780	17693	\begin{align*} \left (3-2 x \right ) y^{\prime \prime }+2 y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.441
8781	17898	\begin{align*} \ln \left (y^{\prime }\right )&=x \\ \end{align*}	✓	✓	✓	✓	0.441
8782	19438	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.441
8783	19647	\begin{align*} x^{\prime }&=-4 x-y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.441
8784	22152	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x^{5}} \\ \end{align*}	✓	✓	✓	✓	0.441
8785	24795	\begin{align*} {y^{\prime }}^{2}-y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.441
8786	24900	\begin{align*} y^{\prime \prime } x&=y^{\prime } \left (2-3 y^{\prime } x \right ) \\ \end{align*}	✓	✓	✓	✓	0.441
8787	3110	\begin{align*} y^{\prime \prime }-4 y&=3 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.442
8788	3756	\begin{align*} y^{\prime \prime }-2 m y^{\prime }+m^{2} y&=\frac {{\mathrm e}^{m x}}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✗	0.442
8789	5953	\begin{align*} x^{2} y^{\prime \prime }&=b x +a \\ \end{align*}	✓	✓	✓	✓	0.442
8790	7110	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{-x}}{x} \\ \end{align*}	✓	✓	✓	✓	0.442
8791	7112	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.442
8792	9696	\begin{align*} x^{\prime }&=4 x+y \\ y^{\prime }&=4 y+z \\ z^{\prime }&=4 z \\ \end{align*}	✓	✓	✓	✓	0.442
8793	14743	\begin{align*} y^{\prime \prime } x +y^{\prime }+2 y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 4 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.442
8794	14940	\begin{align*} x^{\prime \prime }+2 x^{\prime }+10 x&={\mathrm e}^{-t} \cos \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.442
8795	18248	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{x} \sin \left (\frac {x}{2}\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.442
8796	19470	\begin{align*} 3 y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.442
8797	21543	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.442
8798	975	\begin{align*} x_{1}^{\prime }&=x_{1}-2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.443
8799	1192	\begin{align*} y^{\prime }&=\left (1-y\right )^{2} y^{2} \\ \end{align*}	✓	✓	✓	✓	0.443
8800	4065	\begin{align*} y^{\prime \prime } x +y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.443