2.3.75 Problems 7401 to 7500

Table 2.723: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
7401	1421	\begin{align*} x_{1}^{\prime }&=x_{2}+x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{3} \\ x_{3}^{\prime }&=x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.552
7402	2796	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=2 x-y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.552
7403	3127	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=x^{3} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.552
7404	5510	\begin{align*} {y^{\prime }}^{2} x^{2}+4 x y y^{\prime }-5 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.552
7405	7452	\begin{align*} 2 x +y \cos \left (y x \right )+\left (x \cos \left (y x \right )-2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.552
7406	8105	\begin{align*} y^{\prime \prime }+\left ({\mathrm e}^{x}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.552
7407	9732	\begin{align*} {y^{\prime }}^{2}-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.552
7408	10136	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.552
7409	15497	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.552
7410	16063	\begin{align*} x^{\prime }&=3 x+y \\ y^{\prime }&=-x \\ \end{align*}	✓	✓	✓	✓	0.552
7411	17131	\begin{align*} y^{\prime }&=\left (3 y+1\right )^{4} \\ \end{align*}	✓	✓	✓	✓	0.552
7412	17449	\begin{align*} y^{\prime \prime }-y^{\prime }-20 y&=-2 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.552
7413	18689	\begin{align*} x^{\prime }&=2 x+\frac {y}{2} \\ y^{\prime }&=-\frac {x}{2}+y \\ \end{align*}	✓	✓	✓	✓	0.552
7414	20413	\begin{align*} x^{2}&=a^{2} \left (1+{y^{\prime }}^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.552
7415	22149	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.552
7416	26974	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=3 \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.552
7417	1025	\begin{align*} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=x_{1}+3 x_{2}+x_{3} \\ x_{3}^{\prime }&=-2 x_{1}-4 x_{2}-x_{3} \\ \end{align*}	✓	✓	✓	✓	0.553
7418	1405	\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2} \\ x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.553
7419	2720	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=2 t^{2}+4 \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.553
7420	3111	\begin{align*} y^{\prime \prime }+y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.553
7421	3510	\begin{align*} \left (z^{2}+5 z +7\right ) y^{\prime \prime }+2 y&=0 \\ \end{align*} Series expansion around \(z=0\).	✓	✓	✓	✓	0.553
7422	4374	\begin{align*} 3 x y^{\prime }-3 x y^{4} \ln \left (x \right )-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.553
7423	5508	\begin{align*} {y^{\prime }}^{2} x^{2}+3 x y y^{\prime }+2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.553
7424	7201	\begin{align*} u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.553
7425	7721	\begin{align*} y^{\prime }+y \cot \left (x \right )&=5 \,{\mathrm e}^{\cos \left (x \right )} \\ y \left (\frac {\pi }{2}\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	0.553
7426	8396	\begin{align*} y^{\prime }&=\frac {1}{1+\sin \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	0.553
7427	8815	\begin{align*} 4 y+y^{\prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.553
7428	8941	\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.553
7429	9264	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+y&={\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.553
7430	15215	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 t} t^{2} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.553
7431	15745	\(\left [\begin {array}{cccc} 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.553
7432	16566	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.553
7433	17439	\begin{align*} 16 y^{\prime \prime }-8 y^{\prime }-15 y&=75 t \\ \end{align*}	✓	✓	✓	✓	0.553
7434	19500	\begin{align*} y^{\prime \prime }+y&=2 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.553
7435	21134	\begin{align*} x^{\prime \prime }-x&={\mathrm e}^{-3 t} \\ \end{align*}	✓	✓	✓	✓	0.553
7436	21521	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.553
7437	21649	\begin{align*} y^{\prime \prime }-x y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.553
7438	22241	\begin{align*} y^{\prime }+2 y&={\mathrm e}^{t} \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.553
7439	23744	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.553
7440	24707	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=24 \,{\mathrm e}^{2 x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.553
7441	25326	\begin{align*} y^{\prime \prime }+k^{2} y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.553
7442	26730	\begin{align*} x^{\prime }&=-7 x+y \\ y^{\prime }&=-2 x-5 y \\ \end{align*}	✓	✓	✓	✓	0.553
7443	26742	\begin{align*} x^{\prime }&=4 x-5 y \\ y^{\prime }&=x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.553
7444	2425	\begin{align*} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.554
7445	4534	\begin{align*} x^{\prime }-x+3 y&=0 \\ 3 x-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.554
7446	7798	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.554
7447	9690	\begin{align*} x^{\prime }&=12 x-9 y \\ y^{\prime }&=4 x \\ \end{align*}	✓	✓	✓	✓	0.554
7448	13061	\begin{align*} x^{\prime }&=a y \\ y^{\prime }&=b x \\ \end{align*}	✓	✓	✓	✓	0.554
7449	13162	\(\left [\begin {array}{cccc} 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 2 & 0 \\ 0 & 0 & 0 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.554
7450	16022	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=-x-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.554
7451	17696	\begin{align*} y^{\prime \prime }+x y^{\prime }&=\sin \left (x \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.554
7452	3118	\begin{align*} y^{\prime \prime }-4 y&=x +{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.555
7453	4064	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-6 x y^{\prime }-4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.555
7454	7291	\begin{align*} y^{\prime \prime }+16 y&=16 \cos \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.555
7455	9683	\begin{align*} x^{\prime }&=\frac {x}{2} \\ y^{\prime }&=x-\frac {y}{2} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.555
7456	12960	\begin{align*} 2 y y^{\prime \prime }-3 {y^{\prime }}^{2}+f \left (x \right ) y^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	0.555
7457	22486	\begin{align*} x y^{\prime \prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.555
7458	25328	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }+2 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.555
7459	26446	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.555
7460	27169	\begin{align*} x_{1}^{\prime }&=2 x_{1}+2 \\ x_{2}^{\prime }&=5 x_{1}+2 x_{2}+10 t \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.555
7461	875	\begin{align*} y^{\prime \prime }-4 y&=\sinh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.556
7462	1023	\begin{align*} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=-2 x_{1}-2 x_{2}-3 x_{3} \\ x_{3}^{\prime }&=2 x_{1}+3 x_{2}+4 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.556
7463	1901	\begin{align*} \left (x +2\right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+y&=0 \\ y \left (-1\right ) &= -2 \\ y^{\prime }\left (-1\right ) &= 3 \\ \end{align*} Series expansion around \(x=-1\).	✓	✓	✓	✓	0.556
7464	2161	\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+24 y^{\prime \prime }+32 y^{\prime }&=-16 \,{\mathrm e}^{-2 x} \left (-x^{3}+x^{2}+x +1\right ) \\ \end{align*}	✓	✓	✓	✓	0.556
7465	2593	\begin{align*} y^{\prime \prime }+3 y&=t^{3}-1 \\ \end{align*}	✓	✓	✓	✓	0.556
7466	2751	\begin{align*} x_{1}^{\prime }&=-x_{1}-x_{2} \\ x_{2}^{\prime }&=-x_{2} \\ x_{3}^{\prime }&=-2 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.556
7467	3509	\begin{align*} \left (z^{2}+5 z +6\right ) y^{\prime \prime }+2 y&=0 \\ \end{align*} Series expansion around \(z=0\).	✓	✓	✓	✓	0.556
7468	3872	\begin{align*} x_{1}^{\prime }&=3 x_{1}+x_{2}+t \,{\mathrm e}^{3 t} \\ x_{2}^{\prime }&=3 x_{2}+{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	0.556
7469	8714	\begin{align*} y^{\prime } \left (y^{\prime }+y\right )&=x \left (x +y\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.556
7470	8842	\begin{align*} x_{1}^{\prime }&=x_{1}+3 x_{2} \\ x_{2}^{\prime }&=5 x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.556
7471	9561	\begin{align*} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.556
7472	9572	\begin{align*} x y^{\prime \prime }+2 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.556
7473	10221	\begin{align*} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.556
7474	14131	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	0.556
7475	16019	\begin{align*} x^{\prime }&=-\frac {9 x}{10}-2 y \\ y^{\prime }&=x+\frac {11 y}{10} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.556
7476	19496	\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=14 \,{\mathrm e}^{-5 x} \\ \end{align*}	✓	✓	✓	✓	0.556
7477	22260	\begin{align*} y^{\prime }+z&=t \\ z^{\prime }-y&=0 \\ \end{align*} With initial conditions \begin{align*} y \left (0\right ) &= 1 \\ z \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.556
7478	23079	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=5 \sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.556
7479	24604	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.556
7480	25999	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=8 t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.556
7481	27729	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.556
7482	453	\begin{align*} y^{\prime \prime }+{\mathrm e}^{-x} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.557
7483	1447	\begin{align*} x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.557
7484	7308	\begin{align*} y y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✗	✗	0.557
7485	12333	\begin{align*} y^{\prime \prime }-x^{2} \left (x +1\right ) y^{\prime }+x \left (x^{4}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.557
7486	15525	\begin{align*} y^{\prime }&=x -1 \\ \end{align*}	✓	✓	✓	✓	0.557
7487	16008	\begin{align*} x^{\prime }&=2 x+2 y \\ y^{\prime }&=-4 x+6 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.557
7488	17409	\begin{align*} y^{\prime \prime }-y^{\prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.557
7489	18690	\begin{align*} x^{\prime }&=x-4 y \\ y^{\prime }&=4 x-7 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.557
7490	19179	\begin{align*} \left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.557
7491	24588	\begin{align*} y^{\prime \prime }+y&=\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.557
7492	25244	\begin{align*} -t y^{\prime \prime }-2 y^{\prime }+y t&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.557
7493	1292	\begin{align*} y^{\prime \prime }+2 a y^{\prime }+\left (a^{2}+1\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.558
7494	1410	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }&=-x_{1}-x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.558
7495	1894	\begin{align*} \left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.558
7496	2833	\begin{align*} x_{1}^{\prime }&=4 x_{2} \\ x_{2}^{\prime }&=-9 x_{1} \\ \end{align*}	✓	✓	✓	✓	0.558
7497	7085	\begin{align*} y^{\prime \prime }+y&=4 x \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.558
7498	9448	\begin{align*} y^{\prime \prime }+3 y^{\prime }-5 y&=1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.558
7499	15992	\begin{align*} x^{\prime }&=2 x-y \\ y^{\prime }&=-x+y \\ \end{align*}	✓	✓	✓	✓	0.558
7500	17757	\begin{align*} y^{\prime \prime }+7 y^{\prime }+12 y&=3 t^{2} {\mathrm e}^{-4 t} \\ \end{align*}	✓	✓	✓	✓	0.558