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	25686	\begin{align*} y^{\prime \prime }+4 y^{\prime }+6 y&=10 \\ \end{align*}	✓	✓	✓	✓	0.638
8702	25963	\begin{align*} y^{\prime \prime }+y&=x^{5}-2 x^{2}+6 \\ \end{align*}	✓	✓	✓	✓	0.638
8703	26591	\begin{align*} y^{\prime \prime }+9 y&=6 \,{\mathrm e}^{3 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.638
8704	26595	\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (x \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.638
8705	26964	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\cos \left ({\mathrm e}^{-x}\right ) \\ \end{align*}	✓	✓	✓	✓	0.638
8706	2056	\begin{align*} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.639
8707	3796	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=4 \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.639
8708	3859	\begin{align*} x_{1}^{\prime }&=-2 x_{1} \\ x_{2}^{\prime }&=x_{1}-3 x_{2}-x_{3} \\ x_{3}^{\prime }&=-x_{1}+x_{2}-x_{3} \\ \end{align*}	✓	✓	✓	✓	0.639
8709	12283	\begin{align*} y^{\prime \prime }+y-\sin \left (n x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.639
8710	13065	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=2 x+2 y \\ \end{align*}	✓	✓	✓	✓	0.639
8711	19456	\begin{align*} x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.639
8712	19697	\begin{align*} x^{\prime \prime }-x&={\mathrm e}^{t} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.639
8713	20711	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=x \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.639
8714	20904	\begin{align*} y^{\prime \prime }+\frac {y}{4 x^{2}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.639
8715	21213	\begin{align*} x^{\prime }&=3 x+t \\ y^{\prime }&=-y+2 t \\ \end{align*}	✓	✓	✓	✓	0.639
8716	23477	\begin{align*} y^{\prime \prime }+y&=x +2 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.639
8717	23490	\begin{align*} 4 y+y^{\prime \prime }&=4 x^{3}-8 x^{2}-14 x +7 \\ \end{align*}	✓	✓	✓	✓	0.639
8718	9995	\begin{align*} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.640
8719	12320	\begin{align*} y^{\prime \prime }-x y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.640
8720	16867	\begin{align*} y^{\prime }+y \ln \left (x \right )&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✗	0.640
8721	17484	\begin{align*} y^{\prime \prime }+16 y&=2 \cos \left (4 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.640
8722	26729	\begin{align*} x^{\prime }&=3 x-\frac {y}{2}-3 t^{2}-\frac {t}{2}+\frac {3}{2} \\ y^{\prime }&=2 y-2 t -1 \\ \end{align*}	✓	✓	✓	✓	0.640
8723	27164	\begin{align*} x_{1}^{\prime }&=5 x_{1}+2 x_{2}-3 \,{\mathrm e}^{t} \\ x_{2}^{\prime }&=-2 x_{1}+x_{2}+{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	0.640
8724	5512	\begin{align*} {y^{\prime }}^{2} x^{2}-5 x y y^{\prime }+6 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.641
8725	7142	\begin{align*} x y y^{\prime \prime }-2 {y^{\prime }}^{2} x +\left (y+1\right ) y^{\prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.641
8726	9728	\begin{align*} x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✓	0.641
8727	10585	\begin{align*} 4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (x +1\right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.641
8728	14819	\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=4 t \,{\mathrm e}^{-3 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.641
8729	15858	\begin{align*} y^{\prime }&=\frac {1}{\left (y+2\right )^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.641
8730	23735	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.641
8731	24567	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=x \\ y \left (0\right ) &= -3 \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.641
8732	25166	\begin{align*} y_{1}^{\prime }-6 y_{1}&=-4 y_{2} \\ y_{2}^{\prime }&=2 y_{1} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 2 \\ y_{2} \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.641
8733	25805	\begin{align*} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.641
8734	26419	\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.641
8735	158	\begin{align*} y y^{\prime \prime }&=3 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.642
8736	257	\begin{align*} y^{\prime \prime }+y&=3 x \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.642
8737	1921	\begin{align*} \left (3 x^{2}+8 x +4\right ) y^{\prime \prime }+\left (16+12 x \right ) y^{\prime }+6 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.642
8738	2597	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.642
8739	2753	\begin{align*} x_{1}^{\prime }&=-x_{1}+x_{2}+2 x_{3} \\ x_{2}^{\prime }&=-x_{1}+x_{2}+x_{3} \\ x_{3}^{\prime }&=-2 x_{1}+x_{2}+3 x_{3} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.642
8740	17697	\begin{align*} y^{\prime \prime }+y^{\prime }+y x&=\cos \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.642
8741	18817	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=-3 t \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.642
8742	19214	\begin{align*} y^{\prime \prime }&=x +y^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	0.642
8743	23536	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{-x} \ln \left (x \right )}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.642
8744	23558	\begin{align*} x^{\prime }&=5 x-6 y+1 \\ y^{\prime }&=6 x-7 y+1 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.642
8745	23625	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=-x+z \\ z^{\prime }&=x+3 y+z \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ z \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.642
8746	24063	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=1+\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.642
8747	24139	\begin{align*} x -\sqrt {a^{2}-x^{2}}\, y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.642
8748	24629	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x}+3 x \\ \end{align*}	✓	✓	✓	✓	0.642
8749	25988	\begin{align*} x^{\prime }-x+2 y&=0 \\ y^{\prime }+3 x-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.642
8750	26065	\begin{align*} y_{1}^{\prime }&=3 y_{1}+6 y_{2} \\ y_{2}^{\prime }&=2 y_{1}-6 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.642
8751	2054	\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.643
8752	2602	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=2 \cos \left (t \right )^{2} {\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.643
8753	7965	\begin{align*} {y^{\prime }}^{3}-4 x^{4} y^{\prime }+8 x^{3} y&=0 \\ \end{align*}	✓	✓	✗	✗	0.643
8754	10015	\begin{align*} y&={y^{\prime }}^{2} x +{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.643
8755	15140	\begin{align*} y^{\prime \prime }&=x^{2}+y \\ \end{align*}	✓	✓	✓	✓	0.643
8756	18381	\begin{align*} y^{\prime \prime }-x y^{\prime }+y&=1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.643
8757	2058	\begin{align*} x^{2} \left (3 x +4\right ) y^{\prime \prime }-x \left (-3 x +4\right ) y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.644
8758	6681	\begin{align*} 4 y^{\prime }+5 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.644
8759	6692	\begin{align*} x^{3} y^{\prime \prime \prime }&=a \\ \end{align*}	✓	✓	✓	✓	0.644
8760	7576	\begin{align*} y^{\prime \prime }+2 y^{\prime }+4 y&=5 \sin \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.644
8761	8811	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=50 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.644
8762	9666	\begin{align*} x^{\prime }&=-x+\frac {y}{4} \\ y^{\prime }&=x-y \\ \end{align*}	✓	✓	✓	✓	0.644
8763	10363	\begin{align*} a y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.644
8764	12392	\begin{align*} x y^{\prime \prime }+\left (2 a \,x^{3}-1\right ) y^{\prime }+\left (a^{2} x^{3}+a \right ) x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.644
8765	12610	\begin{align*} y^{\prime \prime }&=-\frac {y^{\prime }}{x}-\frac {y}{x^{4}} \\ \end{align*}	✓	✓	✓	✓	0.644
8766	14101	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.644
8767	20365	\begin{align*} y^{\prime \prime }+4 y^{\prime }-12 y&=\left (x -1\right ) {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.644
8768	21115	\begin{align*} x^{\prime \prime }+x^{\prime }-\beta x&=0 \\ \end{align*}	✓	✓	✓	✓	0.644
8769	24584	\begin{align*} y^{\prime \prime }+6 y^{\prime }+14 y&=42 \,{\mathrm e}^{x}-7 \\ \end{align*}	✓	✓	✓	✓	0.644
8770	24770	\begin{align*} 2 v^{\prime }+2 v+w^{\prime }-w&=3 x \\ v^{\prime }+v+w^{\prime }+w&=1 \\ \end{align*}	✓	✓	✓	✓	0.644
8771	25121	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.644
8772	25995	\begin{align*} -y+y^{\prime }&={\mathrm e}^{3 t} \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.644
8773	26241	\begin{align*} \cos \left (y^{\prime }\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.644
8774	4003	\begin{align*} y^{\prime \prime }+2 x^{2} y^{\prime }+y x&=2 \cos \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.645
8775	7109	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.645
8776	7884	\begin{align*} 2 x +3 y+4+\left (3 x +4 y+5\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.645
8777	8022	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 x}}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.645
8778	8112	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+\frac {1}{4}\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.645
8779	8615	\begin{align*} 16 \left (x +1\right )^{2} y^{\prime \prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.645
8780	15430	\begin{align*} y^{\prime \prime }-y&=2+5 x \\ \end{align*}	✓	✓	✓	✓	0.645
8781	16805	\begin{align*} y^{\prime }+2 y&=4 \delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.645
8782	16940	\begin{align*} x^{\prime }&=4 x-13 y \\ y^{\prime }&=x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.645
8783	17002	\begin{align*} y^{\prime }&=\sin \left (2 t \right )-\cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.645
8784	17687	\begin{align*} \left (-2-2 x \right ) y^{\prime \prime }+2 y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.645
8785	18412	\begin{align*} x^{\prime }+3 x+4 y&=0 \\ y^{\prime }+2 x+5 y&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.645
8786	19511	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.645
8787	20118	\begin{align*} x y^{\prime \prime }+2 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.645
8788	21632	\begin{align*} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.645
8789	22691	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&={\mathrm e}^{x}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.645
8790	23455	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{x}+{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.645
8791	23554	\begin{align*} x^{\prime \prime }+2 x^{\prime }+x&=-\frac {{\mathrm e}^{-t}}{\left (t +1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	0.645
8792	24689	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=6 x^{2} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.645
8793	24811	\begin{align*} {y^{\prime }}^{2} x +\left (x -y\right ) y^{\prime }+1-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.645
8794	27031	\begin{align*} y^{\prime \prime }-4 y^{\prime }-5 y&=f \left (t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.645
8795	27170	\begin{align*} x_{1}^{\prime }&=5 x_{1}-4 x_{2}+2 \,{\mathrm e}^{t} \\ x_{2}^{\prime }&=4 x_{1}-3 x_{2}+2 \,{\mathrm e}^{t} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= -1 \\ x_{2} \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✗	0.645
8796	918	\begin{align*} x^{\prime \prime }+6 x^{\prime }+13 x&=10 \sin \left (5 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.646
8797	2601	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=2 \cos \left (t \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.646
8798	3151	\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{x}+\sin \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.646
8799	5477	\begin{align*} {y^{\prime }}^{2} x -\left (y x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.646
8800	20892	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.646