2.3.78 Problems 7701 to 7800

Table 2.729: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
7701	2416	\begin{align*} t \left (2-t \right ) y^{\prime \prime }-6 \left (t -1\right ) y^{\prime }-4 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*} Series expansion around \(t=1\).	✓	✓	✓	✓	0.572
7702	2621	\begin{align*} y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y&={\mathrm e}^{t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✗	0.572
7703	2779	\begin{align*} x_{1}^{\prime }&=4 x_{1}+5 x_{2}+4 \,{\mathrm e}^{t} \cos \left (t \right ) \\ x_{2}^{\prime }&=-2 x_{1}-2 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.572
7704	3413	\begin{align*} {y^{\prime }}^{2}-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.572
7705	3500	\begin{align*} \left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+\lambda y&=0 \\ \end{align*} Series expansion around \(z=0\).	✓	✓	✓	✓	0.572
7706	3993	\begin{align*} \left (x^{2}-3\right ) y^{\prime \prime }-3 x y^{\prime }-5 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.572
7707	6726	\begin{align*} y^{\prime \prime \prime \prime }&=x \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.572
7708	6951	\begin{align*} y \left (2 x +y^{3}\right )-x \left (2 x -y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.572
7709	7203	\begin{align*} u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.572
7710	7950	\begin{align*} x {y^{\prime }}^{5}-y {y^{\prime }}^{4}+\left (x^{2}+1\right ) {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+\left (x +y^{2}\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.572
7711	9403	\begin{align*} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.572
7712	9671	\begin{align*} x^{\prime }&=2 x+2 y \\ y^{\prime }&=x+3 y \\ \end{align*}	✓	✓	✓	✓	0.572
7713	10485	\begin{align*} y^{\prime \prime }+x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.572
7714	14088	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.572
7715	16060	\begin{align*} x^{\prime }&=-3 x+y \\ y^{\prime }&=-x \\ \end{align*}	✓	✓	✓	✓	0.572
7716	16625	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\left (12 x -4\right ) {\mathrm e}^{-5 x} \\ \end{align*}	✓	✓	✓	✓	0.572
7717	17485	\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&=2 t \,{\mathrm e}^{-2 t} \\ \end{align*}	✓	✓	✓	✓	0.572
7718	17755	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=3 \,{\mathrm e}^{-2 t} \\ \end{align*}	✓	✓	✓	✓	0.572
7719	20176	\begin{align*} 3 x^{2} y^{\prime \prime }+\left (-6 x^{2}+2\right ) y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.572
7720	20614	\begin{align*} y^{\prime \prime }+4 x y^{\prime }+4 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.572
7721	24067	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=12 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.572
7722	24536	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.572
7723	24672	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=\sin \left (2 x \right ) {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.572
7724	25111	\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	0.572
7725	26653	\begin{align*} y^{\prime \prime }+y&=\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.572
7726	352	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.573
7727	468	\begin{align*} \left (x -2\right )^{3} y^{\prime \prime }+3 \left (x -2\right )^{2} y^{\prime }+x^{3} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.573
7728	3496	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=2 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.573
7729	3741	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=4 \cos \left (2 x \right ) {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.573
7730	4588	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.573
7731	7207	\begin{align*} y^{\prime \prime }+n^{2} y&=\frac {6 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.573
7732	7303	\begin{align*} y^{\prime \prime }-y&=\sinh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.573
7733	7771	\begin{align*} y^{\prime \prime }-2 y^{\prime }+3 y&=x^{2}-1 \\ \end{align*}	✓	✓	✓	✓	0.573
7734	8341	\begin{align*} y^{\prime }-\left (-1+y\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.573
7735	10483	\begin{align*} y^{\prime \prime }+x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.573
7736	12414	\begin{align*} a y+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.573
7737	12702	\begin{align*} y^{\prime \prime }&=-\frac {x y^{\prime }}{f \left (x \right )}+\frac {y}{f \left (x \right )} \\ \end{align*}	✓	✓	✓	✗	0.573
7738	15205	\begin{align*} y^{\prime \prime \prime }+8 y^{\prime \prime }+16 y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= -8 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.573
7739	16806	\begin{align*} y^{\prime \prime }+y&=\delta \left (t \right )+\delta \left (t -\pi \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.573
7740	16845	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\lambda y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.573
7741	17338	\begin{align*} y-t y^{\prime }&=-4 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.573
7742	18371	\begin{align*} y^{\prime }&=-y x +1 \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.573
7743	21708	\begin{align*} y+y^{\prime }&=\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.573
7744	24614	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.573
7745	25168	\begin{align*} y_{1}^{\prime }&=2 y_{2} \\ y_{2}^{\prime }&=-2 y_{1} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.573
7746	25611	\begin{align*} y^{\prime \prime \prime \prime }-y&=t^{3} \cos \left (5 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.573
7747	26744	\begin{align*} x^{\prime }&=x+5 y \\ y^{\prime }&=-x-3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= -2 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.573
7748	27126	\(\left [\begin {array}{ccc} 5 & 0 & 2 \\ 0 & 0 & 0 \\ 2 & 0 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.573
7749	1404	\begin{align*} x_{1}^{\prime }&=2 x_{1}-\frac {5 x_{2}}{2} \\ x_{2}^{\prime }&=\frac {9 x_{1}}{5}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.574
7750	11773	\begin{align*} y^{2} {y^{\prime }}^{2}-a^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.574
7751	16106	\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=2 t +{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.574
7752	17826	\begin{align*} x_{1}^{\prime }&=-x_{1}+1 \\ x_{2}^{\prime }&=x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.574
7753	22189	\begin{align*} y^{\prime \prime }+y x&=2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.574
7754	24587	\begin{align*} y^{\prime \prime }+y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.574
7755	1257	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.575
7756	1795	\begin{align*} y^{\prime }+y^{2}+14 y+50&=0 \\ \end{align*}	✓	✓	✓	✓	0.575
7757	1874	\begin{align*} \left (3 x^{2}-6 x +5\right ) y^{\prime \prime }+\left (x -1\right ) y^{\prime }+12 y&=0 \\ y \left (1\right ) &= -1 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.575
7758	1912	\begin{align*} \left (2 x +3\right ) y^{\prime \prime }-3 y^{\prime }-\left (x +2\right ) y&=0 \\ y \left (-2\right ) &= -2 \\ y^{\prime }\left (-2\right ) &= 3 \\ \end{align*} Series expansion around \(x=-2\).	✓	✓	✓	✓	0.575
7759	3484	\begin{align*} f^{\prime \prime }+2 f^{\prime }+5 f&=0 \\ f \left (0\right ) &= 1 \\ f^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.575
7760	3861	\begin{align*} x_{1}^{\prime }&=4 x_{1} \\ x_{2}^{\prime }&=x_{1}+4 x_{2} \\ x_{3}^{\prime }&=x_{2}+4 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.575
7761	4533	\begin{align*} 2 x^{\prime }+x-5 y^{\prime }-4 y&=0 \\ -y^{\prime }-2 x+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.575
7762	8034	\begin{align*} \left (x +1\right ) y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+\left (x +2\right ) y&=\left (x^{2}+2 x +1\right ) {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	0.575
7763	8571	\begin{align*} y^{\prime \prime }-y^{\prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.575
7764	9024	\begin{align*} {\mathrm e}^{x}+{\mathrm e}^{y} \left (y+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.575
7765	12889	\begin{align*} x y^{\prime \prime }+2 y^{\prime }+a \,x^{v} y^{n}&=0 \\ \end{align*}	✗	✗	✗	✗	0.575
7766	12905	\begin{align*} 2 y+a y^{3}+9 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.575
7767	16086	\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&={\mathrm e}^{-2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.575
7768	21587	\begin{align*} 4 y+4 y^{\prime }+y^{\prime \prime }+y^{\prime \prime \prime }&=\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.575
7769	21746	\begin{align*} x^{\prime }&=6 x-3 y \\ y^{\prime }&=2 x+y \\ \end{align*}	✓	✓	✓	✓	0.575
7770	23482	\begin{align*} y^{\prime \prime }-y&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.575
7771	24594	\begin{align*} y^{\prime \prime }-y&=\cos \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.575
7772	25931	\begin{align*} y^{\prime \prime }-4 y&=16 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.575
7773	5955	\begin{align*} x^{2} y^{\prime \prime }&=6 y \\ \end{align*}	✓	✓	✓	✓	0.576
7774	8098	\begin{align*} \left (x -1\right ) \left (x -2\right ) y^{\prime \prime }+\left (4 x -6\right ) y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.576
7775	9246	\begin{align*} 4 y+y^{\prime \prime }&=3 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.576
7776	10109	\begin{align*} y^{\prime \prime }-y x -x&=0 \\ \end{align*}	✓	✓	✓	✓	0.576
7777	10306	\begin{align*} x {y^{\prime }}^{n}&=0 \\ \end{align*}	✓	✓	✓	✗	0.576
7778	10509	\begin{align*} x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.576
7779	13934	\begin{align*} y^{\prime \prime }+a y^{\prime }+\left (b \,{\mathrm e}^{\lambda x}+c \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.576
7780	15729	\begin{align*} y^{\prime \prime }+a^{2} y&=\delta \left (x -\pi \right ) f \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.576
7781	16059	\begin{align*} x^{\prime }&=-3 x+y \\ y^{\prime }&=-x+y \\ \end{align*}	✓	✓	✓	✓	0.576
7782	19557	\begin{align*} y^{\prime \prime }-y^{\prime }+y&=x^{3}-3 x^{2}+1 \\ \end{align*}	✓	✓	✓	✓	0.576
7783	21139	\begin{align*} x^{\prime \prime }-x^{\prime }-2 x&=2 t +{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.576
7784	21209	\begin{align*} x^{\prime }&=x+3 y \\ y^{\prime }&=-3 x+y \\ \end{align*}	✓	✓	✓	✓	0.576
7785	24540	\begin{align*} 4 y+y^{\prime \prime }&=15 \,{\mathrm e}^{x}-8 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.576
7786	25083	\begin{align*} y^{\prime \prime }+9 y&=36 t \sin \left (3 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.576
7787	26069	\begin{align*} y^{\prime }&=y-2 z \\ z^{\prime }&=4 y+5 z \\ \end{align*}	✓	✓	✓	✓	0.576
7788	1022	\begin{align*} x_{1}^{\prime }&=-2 x_{1}-9 x_{2} \\ x_{2}^{\prime }&=x_{1}+4 x_{2} \\ x_{3}^{\prime }&=x_{1}+3 x_{2}+x_{3} \\ \end{align*}	✓	✓	✓	✓	0.577
7789	3154	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.577
7790	3242	\begin{align*} x^{\prime }&=3 x \\ y^{\prime }&=2 x+3 y \\ z^{\prime }&=3 y-2 z \\ \end{align*}	✓	✓	✓	✓	0.577
7791	4125	\begin{align*} 4 y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.577
7792	7598	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= {\frac {25}{3}} \\ \end{align*}	✓	✓	✓	✓	0.577
7793	12891	\begin{align*} b \,{\mathrm e}^{y} x +a y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.577
7794	15760	\begin{align*} y_{1}^{\prime }&=-2 y_{1}-y_{2}+y_{3} \\ y_{2}^{\prime }&=-y_{1}-2 y_{2}-y_{3} \\ y_{3}^{\prime }&=y_{1}-y_{2}-2 y_{3} \\ \end{align*}	✓	✓	✓	✓	0.577
7795	20401	\begin{align*} 3 {y^{\prime }}^{5}-y y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✗	0.577
7796	23471	\begin{align*} y^{\prime \prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	0.577
7797	12949	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+f \left (x \right ) y^{2}+a&=0 \\ \end{align*}	✗	✗	✗	✗	0.578
7798	14580	\begin{align*} y^{\prime \prime }-8 y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.578
7799	15731	\begin{align*} y_{1}^{\prime }&=y_{1}-2 y_{2} \\ y_{2}^{\prime }&=y_{1}+3 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.578
7800	16169	\begin{align*} 1&=\left (x^{2}-9\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.578