2.3.72 Problems 7101 to 7200

Table 2.717: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
7101	387	\begin{align*} m x^{\prime \prime }+k x&=F_{0} \cos \left (\omega t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.444
7102	453	\begin{align*} y^{\prime \prime }+{\mathrm e}^{-x} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.444
7103	1365	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.444
7104	1442	\begin{align*} x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.444
7105	6640	\begin{align*} 2 a^{2} y-a^{2} y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=\sinh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.444
7106	6779	\begin{align*} \operatorname {A4} y+\operatorname {A3} x y^{\prime }+\operatorname {A2} \,x^{2} y^{\prime \prime }+\operatorname {A1} \,x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.444
7107	7099	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.444
7108	7449	\begin{align*} y \,{\mathrm e}^{y x}+2 x +\left (x \,{\mathrm e}^{y x}-2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.444
7109	7999	\begin{align*} y^{\prime \prime }+y&=\csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.444
7110	10948	\begin{align*} \left (1+3 x \right ) y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.444
7111	11675	\begin{align*} {y^{\prime }}^{2}+\left (a x +b \right ) y^{\prime }-a y+c&=0 \\ \end{align*}	✓	✓	✓	✓	0.444
7112	13921	\begin{align*} \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+\left (\lambda -x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✗	✗	0.444
7113	14164	\begin{align*} y y^{\prime \prime }+2 y^{\prime }-{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.444
7114	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*}	✓	✓	✓	✓	0.444
7115	14327	\begin{align*} t^{2} x^{\prime \prime }+t x^{\prime }&=0 \\ x \left (1\right ) &= 0 \\ x^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.444
7116	14739	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +2 y x&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.444
7117	15810	\begin{align*} y^{\prime }&=t^{2}+1 \\ \end{align*}	✓	✓	✓	✓	0.444
7118	16504	\begin{align*} 16 y^{\prime \prime }-24 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.444
7119	17201	\begin{align*} 3 t y^{2}+y^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.444
7120	23362	\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.444
7121	23788	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=x+3 y \\ \end{align*}	✓	✓	✓	✓	0.444
7122	26243	\begin{align*} \sin \left (y^{\prime }\right )&=x \\ \end{align*}	✓	✓	✓	✓	0.444
7123	27159	\begin{align*} x_{1}^{\prime }&=3 x_{1}+2 x_{2} \\ x_{2}^{\prime }&=3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.444
7124	27698	\begin{align*} x^{2} y^{\prime \prime }-6 y&=5 x^{3}+8 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.444
7125	495	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (1-x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.445
7126	818	\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.445
7127	1855	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.445
7128	5436	\begin{align*} 2 {y^{\prime }}^{2}-\left (1-x \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.445
7129	6205	\begin{align*} -2 y x -2 \left (-x^{2}+1\right ) y^{\prime }+x \left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.445
7130	8579	\begin{align*} \left (x -2\right )^{2} y^{\prime \prime }+\left (2+x \right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.445
7131	9265	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {1}{1+{\mathrm e}^{-x}} \\ \end{align*}	✓	✓	✓	✗	0.445
7132	9504	\begin{align*} 2 y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.445
7133	9742	\begin{align*} y&=y^{\prime } x +k {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.445
7134	10057	\begin{align*} x^{\prime }&=9 x+4 y \\ y^{\prime }&=-6 x-y \\ z^{\prime }&=6 x+4 y+3 z \\ \end{align*}	✓	✓	✓	✓	0.445
7135	13700	\begin{align*} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+x \left (a b \,x^{2}+b c +2 a \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.445
7136	13703	\begin{align*} y^{\prime \prime }+\left (a \,x^{3}+b x \right ) y^{\prime }+2 \left (2 a \,x^{2}+b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.445
7137	14049	\begin{align*} {y^{\prime }}^{3}-\left (2 x +y^{2}\right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 x y^{2}\right ) y^{\prime }-\left (x^{2}-y^{2}\right ) y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.445
7138	14792	\begin{align*} x^{\prime }&=5 x-y \\ y^{\prime }&=3 x+y \\ \end{align*}	✓	✓	✓	✓	0.445
7139	15429	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=8 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.445
7140	15473	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=x+3 y \\ \end{align*}	✓	✓	✓	✓	0.445
7141	15972	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=2 x+y \\ \end{align*}	✓	✓	✓	✓	0.445
7142	22713	\begin{align*} y^{\prime \prime }-2 y^{\prime }-y&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.445
7143	22732	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+y&={\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.445
7144	23551	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=\left (x^{2}+1\right )^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	0.445
7145	24728	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.445
7146	25995	\begin{align*} -y+y^{\prime }&={\mathrm e}^{3 t} \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.445
7147	26955	\begin{align*} y^{\prime \prime }-2 \alpha y^{\prime }+\alpha ^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.445
7148	27111	\(\left [\begin {array}{cc} 5 & 3 \\ 1 & 3 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.445
7149	27696	\begin{align*} x^{3} y^{\prime \prime }-2 y x&=6 \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.445
7150	2061	\begin{align*} 9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.446
7151	10155	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+1+x {y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	0.446
7152	14296	\begin{align*} x^{\prime \prime }+x^{\prime }+x&=3 \cos \left (t \right )-2 \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.446
7153	14935	\begin{align*} x^{\prime \prime }+x^{\prime }-2 x&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.446
7154	16719	\begin{align*} x^{2} y^{\prime \prime }+\frac {5 y}{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.446
7155	16722	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.446
7156	17706	\begin{align*} x \left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}+5 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.446
7157	21999	\begin{align*} y^{\prime }+\frac {1}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	0.446
7158	24725	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.446
7159	1629	\begin{align*} y^{\prime }+y&=y^{2} \\ \end{align*}	✓	✓	✓	✓	0.447
7160	1634	\begin{align*} y^{\prime }-\frac {\left (x +1\right ) y}{3 x}&=y^{4} \\ \end{align*}	✓	✓	✓	✓	0.447
7161	2059	\begin{align*} 4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (2 x +3\right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.447
7162	2242	\begin{align*} y_{1}^{\prime }&=2 y_{1}-4 y_{2} \\ y_{2}^{\prime }&=-y_{1}-y_{2} \\ \end{align*}	✓	✓	✓	✓	0.447
7163	2744	\begin{align*} x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=4 x_{1}-x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.447
7164	2799	\begin{align*} x^{\prime }&=-3 x-4 y \\ y^{\prime }&=2 x+y \\ \end{align*}	✓	✓	✓	✓	0.447
7165	3114	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.447
7166	6340	\begin{align*} f \left (x \right ) y^{\prime }+g \left (x \right ) {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.447
7167	9073	\begin{align*} y^{\prime }&=2 \cos \left (x \right ) \sin \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.447
7168	9248	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=25 x^{2}+12 \\ \end{align*}	✓	✓	✓	✓	0.447
7169	10027	\begin{align*} 5 y^{\prime \prime }+2 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.447
7170	14878	\begin{align*} x^{\prime }&=2 \sin \left (t \right )^{2} \\ x \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✓	0.447
7171	14976	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.447
7172	16134	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=2 \,{\mathrm e}^{t} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.447
7173	16716	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.447
7174	17383	\begin{align*} y^{\prime \prime }+8 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.447
7175	17412	\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.447
7176	17677	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+10 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+21 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.447
7177	18321	\begin{align*} y^{\prime \prime }+y&=\frac {1}{\sin \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	0.447
7178	23834	\begin{align*} y^{\prime }&=\frac {t^{2}+1}{t \left (-2+t \right )} \\ \end{align*}	✓	✓	✓	✓	0.447
7179	25364	\begin{align*} y_{1}^{\prime }&=5 y_{1}-2 y_{2} \\ y_{2}^{\prime }&=4 y_{1}-y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 0 \\ y_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.447
7180	26829	\begin{align*} x^{\prime \prime }-4 x^{\prime }+4 x&=\left (t -1\right ) {\mathrm e}^{2 t} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.447
7181	478	\begin{align*} 2 x^{2} y^{\prime \prime }+y^{\prime } x -\left (-2 x^{2}+3\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.448
7182	5386	\begin{align*} {y^{\prime }}^{2}+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.448
7183	6376	\begin{align*} a \,x^{m} y^{n}+2 y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✗	✗	✗	0.448
7184	8614	\begin{align*} \left (x -1\right )^{2} y^{\prime \prime }-\left (x -1\right ) y^{\prime }-35 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.448
7185	9045	\begin{align*} y_{1}^{\prime }&=y_{2} \\ y_{2}^{\prime }&=6 y_{1}+y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.448
7186	9075	\begin{align*} \left (x^{2}-1\right ) y^{\prime }&=1 \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.448
7187	10211	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.448
7188	13014	\begin{align*} 2 y^{3} y^{\prime \prime }+y^{4}-a^{2} x y^{2}-1&=0 \\ \end{align*}	✗	✗	✗	✗	0.448
7189	14860	\begin{align*} x^{\prime }&=x+7 y \\ y^{\prime }&=3 x+5 y \\ \end{align*}	✓	✓	✓	✓	0.448
7190	19563	\begin{align*} y^{\prime \prime }+y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.448
7191	20057	\begin{align*} y^{\prime \prime \prime }+y&=\sin \left (3 x \right )-\cos \left (\frac {x}{2}\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.448
7192	20059	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{2 x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.448
7193	21650	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-6 y^{\prime } x -4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.448
7194	23004	\begin{align*} 8 y^{\prime \prime }-10 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.448
7195	23398	\begin{align*} x^{2} y^{\prime \prime \prime \prime }-x y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.448
7196	24625	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=20-3 x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.448
7197	24697	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=24 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.448
7198	25958	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.448
7199	27104	\(\left [\begin {array}{cc} 4 & -2 \\ -2 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.448
7200	27360	\begin{align*} {y^{\prime }}^{2}+y x&=y^{\prime } x +y^{2} \\ \end{align*}	✓	✓	✓	✓	0.448