2.3.75 Problems 7401 to 7500

Table 2.681: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
7401	19436	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.374
7402	19474	\begin{align*} 16 y^{\prime \prime }-8 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.374
7403	20003	\begin{align*} y^{2} \left (1-{y^{\prime }}^{2}\right )&=b \\ \end{align*}	✓	✓	✓	✓	0.374
7404	20531	\begin{align*} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+x \left (x^{2}+2\right ) y^{\prime }+3 x^{2} y&=2 x \\ \end{align*}	✓	✓	✓	✗	0.374
7405	23016	\begin{align*} z^{\prime \prime }-3 z^{\prime }+z&=0 \\ z \left (0\right ) &= 1 \\ z^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.374
7406	23071	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }-5 y&=2 \sin \left (2 x \right )+3 \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.374
7407	23497	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.374
7408	23674	\begin{align*} \left (x -1\right )^{4} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.374
7409	24745	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=\sin \left ({\mathrm e}^{-x}\right ) \\ \end{align*}	✓	✓	✓	✓	0.374
7410	24760	\begin{align*} y^{\prime \prime }-y&=\frac {2}{{\mathrm e}^{x}-{\mathrm e}^{-x}} \\ \end{align*}	✓	✓	✓	✓	0.374
7411	25611	\begin{align*} y^{\prime \prime \prime \prime }-y&=t^{3} \cos \left (5 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.374
7412	969	\begin{align*} x_{1}^{\prime }&=6 x_{1}-7 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.375
7413	2151	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y&={\mathrm e}^{x} \left (16 x^{3}+24 x^{2}+2 x -1\right ) \\ \end{align*}	✓	✓	✓	✓	0.375
7414	2697	\begin{align*} x^{\prime }&=6 x-3 y \\ y^{\prime }&=2 x+y \\ \end{align*}	✓	✓	✓	✓	0.375
7415	2787	\begin{align*} x_{1}^{\prime }&=3 x_{1} \\ x_{2}^{\prime }&=x_{1}+3 x_{2} \\ x_{3}^{\prime }&=3 x_{3} \\ x_{4}^{\prime }&=2 x_{3}+3 x_{4} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 1 \\ x_{4} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.375
7416	4172	\begin{align*} 2 y_{1}^{\prime }&=y_{1}+y_{2} \\ 2 y_{2}^{\prime }&=5 y_{2}-3 y_{1} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 3 \\ y_{2} \left (0\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	0.375
7417	5891	\begin{align*} -\left (x +1\right ) y+y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.375
7418	6507	\begin{align*} x y y^{\prime \prime }&=-\left (1+y\right ) y^{\prime }+2 x {y^{\prime }}^{2} \\ \end{align*}	✗	✓	✓	✗	0.375
7419	8796	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.375
7420	9025	\begin{align*} \cos \left (x \right ) \cos \left (y\right )^{2}-\sin \left (x \right ) \sin \left (2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.375
7421	10230	\begin{align*} \frac {x y^{\prime \prime }}{-x^{2}+1}+y&=0 \\ \end{align*}	✗	✗	✗	✗	0.375
7422	12518	\begin{align*} \left (x^{2}+x -2\right ) y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }-\left (6 x^{2}+7 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.375
7423	12668	\begin{align*} y^{\prime \prime }&=\frac {\left (2 x^{2}+1\right ) y^{\prime }}{x^{3}}-\frac {\left (a \,x^{4}+10 x^{2}+1\right ) y}{4 x^{6}} \\ \end{align*}	✓	✓	✓	✗	0.375
7424	13187	\(\left [\begin {array}{ccc} 3 & -2 & 0 \\ 0 & 1 & 0 \\ -4 & 4 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.375
7425	14656	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y&=3 x \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}-\sin \left (x \right ) \\ y \left (0\right ) &= {\frac {33}{40}} \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.375
7426	15428	\begin{align*} s^{\prime \prime }-a^{2} s&=t +1 \\ \end{align*}	✓	✓	✓	✓	0.375
7427	16067	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.375
7428	16076	\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&={\mathrm e}^{4 t} \\ \end{align*}	✓	✓	✓	✓	0.375
7429	16192	\begin{align*} y^{\prime } x&=\sin \left (x \right ) \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.375
7430	16266	\begin{align*} 2 y+y^{\prime }&=6 \\ \end{align*}	✓	✓	✓	✓	0.375
7431	16411	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=y^{\prime } \\ \end{align*}	✓	✓	✓	✗	0.375
7432	16636	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=24 \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.375
7433	17642	\begin{align*} x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+70 y^{\prime } x +80 y&=\frac {1}{x^{13}} \\ \end{align*}	✓	✓	✓	✓	0.375
7434	17691	\begin{align*} y^{\prime \prime }-y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.375
7435	20504	\begin{align*} x^{2} y^{\prime \prime \prime }+3 y^{\prime \prime } x +2 y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.375
7436	21726	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.375
7437	22528	\begin{align*} u^{2} v-\left (u^{3}+v^{3}\right ) v^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.375
7438	24852	\begin{align*} 4 y^{2} {y^{\prime }}^{3}-2 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.375
7439	25513	\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.375
7440	25514	\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.375
7441	1861	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-10 y^{\prime } x +28 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.376
7442	2785	\begin{align*} x_{1}^{\prime }&=-x_{1}-x_{2}+2 x_{3}+{\mathrm e}^{t} \\ 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 ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.376
7443	3728	\begin{align*} y^{\prime \prime }-4 y^{\prime }+6 y&=7 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.376
7444	4596	\begin{align*} y^{\prime \prime } x +y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.376
7445	7838	\begin{align*} y^{\prime \prime }-2 y^{\prime } x -2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.376
7446	8194	\begin{align*} {y^{\prime }}^{2}&=9-y^{2} \\ \end{align*}	✓	✓	✓	✓	0.376
7447	8258	\begin{align*} y^{\prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.376
7448	8911	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.376
7449	9419	\begin{align*} y^{\prime \prime }+2 y x&=x^{2} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.376
7450	14279	\begin{align*} x^{\prime \prime }-4 x^{\prime }+4 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.376
7451	15260	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.376
7452	15318	\begin{align*} y^{\prime \prime }+\beta y^{\prime }+\gamma y&=0 \\ \end{align*}	✓	✓	✓	✓	0.376
7453	18784	\begin{align*} 9 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.376
7454	19460	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.376
7455	20009	\begin{align*} {y^{\prime }}^{3}-4 x y^{\prime } y+8 y^{2}&=0 \\ \end{align*}	✓	✓	✗	✗	0.376
7456	20936	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=-2 x+2 y \\ \end{align*}	✓	✓	✓	✓	0.376
7457	22141	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.376
7458	24741	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {1}{\sqrt {1+{\mathrm e}^{-2 x}}} \\ \end{align*}	✓	✓	✓	✓	0.376
7459	24848	\begin{align*} x^{6} {y^{\prime }}^{2}-2 y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.376
7460	330	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=1+x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.377
7461	1938	\begin{align*} \left (x^{2}+2 x +1\right ) y^{\prime \prime }+\left (1-x \right ) y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.377
7462	2781	\begin{align*} x_{1}^{\prime }&=2 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=4 x_{1}-2 x_{2}+\delta \left (t -\pi \right ) \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.377
7463	4563	\begin{align*} x_{1}^{\prime }&=5 x_{1}+3 x_{2} \\ x_{2}^{\prime }&=-3 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*}	✓	✓	✓	✓	0.377
7464	5525	\begin{align*} \left (a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y^{\prime } y+b +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.377
7465	7636	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.377
7466	7774	\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=6 \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.377
7467	7844	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +x^{2} y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.377
7468	14080	\begin{align*} y&=y^{\prime } x +\frac {1}{y^{\prime }} \\ \end{align*}	✓	✓	✓	✗	0.377
7469	14740	\begin{align*} \left (2 x^{2}-3\right ) y^{\prime \prime }-2 y^{\prime } x +y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.377
7470	15572	\begin{align*} y^{\prime }&=2 \sin \left (x \right ) \\ y \left (\pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.377
7471	16129	\begin{align*} y^{\prime \prime }+4 y&=-\cos \left (\frac {t}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.377
7472	16229	\begin{align*} y^{\prime }-4 y&=2 \\ \end{align*}	✓	✓	✓	✓	0.377
7473	17483	\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&={\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	0.377
7474	17763	\begin{align*} y^{\prime \prime }+10 y^{\prime }+16 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.377
7475	18211	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&={\mathrm e}^{4 x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.377
7476	18395	\begin{align*} y^{\prime \prime }+\frac {5 y^{\prime }}{x}+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.377
7477	18665	\begin{align*} x^{\prime }&=2 x-5 y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.377
7478	19469	\begin{align*} 4 y^{\prime \prime }+20 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.377
7479	20020	\begin{align*} x^{2} {y^{\prime }}^{2}-3 x y^{\prime } y+x^{3}+2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.377
7480	22187	\begin{align*} y^{\prime \prime }+y^{\prime } x +\left (2 x -1\right ) y&=0 \\ y \left (-1\right ) &= 2 \\ y^{\prime }\left (-1\right ) &= -2 \\ \end{align*} Series expansion around \(x=-1\).	✓	✓	✓	✓	0.377
7481	22727	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.377
7482	22826	\begin{align*} y^{\prime \prime } x +y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.377
7483	24898	\begin{align*} x^{2} y^{\prime \prime }&=y^{\prime } \left (2 x -y^{\prime }\right ) \\ y \left (-1\right ) &= 5 \\ y^{\prime }\left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.377
7484	2239	\begin{align*} y_{1}^{\prime }&=-\frac {5 y_{1}}{4}+\frac {3 y_{2}}{4} \\ y_{2}^{\prime }&=\frac {3 y_{1}}{4}-\frac {5 y_{2}}{4} \\ \end{align*}	✓	✓	✓	✓	0.378
7485	2381	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.378
7486	2414	\begin{align*} \left (t^{2}+2\right ) y^{\prime \prime }-t y^{\prime }-3 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.378
7487	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 \(t=0\).	✓	✓	✓	✓	0.378
7488	5023	\begin{align*} y^{\prime } \sqrt {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.378
7489	5916	\begin{align*} 3 y-\left (x +3\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.378
7490	8841	\begin{align*} x_{1}^{\prime }&=3 x_{1}-18 x_{2} \\ x_{2}^{\prime }&=2 x_{1}-9 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.378
7491	8905	\begin{align*} y^{\prime \prime }+9 y&=\sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.378
7492	9376	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.378
7493	9507	\begin{align*} \left (x -1\right ) y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.378
7494	9799	\begin{align*} y^{\prime }-y^{\prime \prime } x +{y^{\prime \prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.378
7495	10069	\begin{align*} z^{\prime \prime }+3 z^{\prime }+2 z&=24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t} \\ \end{align*}	✓	✓	✓	✓	0.378
7496	14209	\begin{align*} x^{\prime }&=\frac {{\mathrm e}^{-t}}{\sqrt {t}} \\ x \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.378
7497	14854	\begin{align*} x^{\prime }&=3 x+2 y \\ y^{\prime }&=x+2 y \\ \end{align*}	✓	✓	✓	✓	0.378
7498	15446	\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=x-y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.378
7499	15579	\begin{align*} y^{\prime }&=\tan \left (x \right ) \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.378
7500	16115	\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=-4 \cos \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.378