2.3.72 Problems 7101 to 7200

Table 2.693: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
7101	23473	\begin{align*} y^{\prime \prime }-3 y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.532
7102	24673	\begin{align*} y^{\prime \prime }-y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.532
7103	24779	\begin{align*} {y^{\prime }}^{2}-y^{2} x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.532
7104	26577	\begin{align*} y^{\prime \prime }+y&=x^{2} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.532
7105	4520	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=54 t \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.533
7106	9671	\begin{align*} x^{\prime }&=2 x+2 y \\ y^{\prime }&=x+3 y \\ \end{align*}	✓	✓	✓	✓	0.533
7107	12901	\begin{align*} b x +a y {y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.533
7108	13876	\begin{align*} x^{2} \left (x -a \right )^{2} y^{\prime \prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✗	0.533
7109	14298	\begin{align*} x^{\prime \prime }+x^{\prime }+x&=t^{2} {\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	0.533
7110	15514	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.533
7111	15525	\begin{align*} y^{\prime }&=x -1 \\ \end{align*}	✓	✓	✓	✓	0.533
7112	16176	\begin{align*} y^{\prime }&=\frac {x -1}{x +1} \\ y \left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	0.533
7113	16442	\begin{align*} y^{\prime \prime }&=2 y^{\prime }-5 y+30 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.533
7114	16507	\begin{align*} y^{\prime \prime }-8 y^{\prime }+16 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.533
7115	19839	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.533
7116	22142	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.533
7117	22621	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=x^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.533
7118	24924	\begin{align*} y^{\prime }&=t \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.533
7119	3807	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.534
7120	4158	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y&=2 x^{2}-4 x -1+2 x^{2} {\mathrm e}^{2 x}+5 x \,{\mathrm e}^{2 x}+{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.534
7121	5477	\begin{align*} x {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.534
7122	6611	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=x^{3}+\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.534
7123	7263	\begin{align*} y^{\prime \prime }-2 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.534
7124	8496	\begin{align*} y^{\prime \prime }+\sin \left (x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.534
7125	8941	\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.534
7126	14299	\begin{align*} x^{\prime \prime }+x^{\prime }+x&=5 \sin \left (7 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.534
7127	14540	\begin{align*} \left (2+x \right ) y^{\prime }+y&=\left \{\begin {array}{cc} 2 x & 0\le x \le 2 \\ 4 & 2<x \end {array}\right . \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✗	0.534
7128	16658	\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=3 x^{2} {\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	0.534
7129	18653	\begin{align*} x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }&=\frac {3 x}{4}+\frac {5 y}{4} \\ \end{align*}	✓	✓	✓	✓	0.534
7130	18698	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.534
7131	19194	\begin{align*} y^{\prime \prime }-2 y&=4 x^{2} {\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.534
7132	23789	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=5 x-y \\ \end{align*}	✓	✓	✓	✓	0.534
7133	24586	\begin{align*} y^{\prime \prime }+y&=4 x +1 \\ \end{align*}	✓	✓	✓	✓	0.534
7134	26432	\begin{align*} y^{\prime \prime }+6 y {y^{\prime }}^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	0.534
7135	1360	\begin{align*} u^{\prime \prime }+u^{\prime }+\frac {u^{3}}{5}&=\cos \left (t \right ) \\ u \left (0\right ) &= 2 \\ u^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	0.535
7136	1871	\begin{align*} \left (3 x^{2}+6 x +5\right ) y^{\prime \prime }+9 \left (x +1\right ) y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=-1\).	✓	✓	✓	✓	0.535
7137	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*}	✓	✓	✓	✓	0.535
7138	5968	\begin{align*} -b \left (b \,x^{2}+a \right ) y+a y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.535
7139	6773	\begin{align*} 6 y^{\prime \prime } x +6 x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.535
7140	7364	\begin{align*} y^{\prime } x&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.535
7141	9245	\begin{align*} y^{\prime \prime }+3 y^{\prime }-10 y&=6 \,{\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.535
7142	9608	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=\sin \left (3 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.535
7143	14127	\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.535
7144	16119	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=\cos \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.535
7145	18696	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.535
7146	19566	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=x^{3} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.535
7147	20839	\begin{align*} 8 y^{\prime \prime }+4 y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.535
7148	23485	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.535
7149	24440	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.535
7150	25127	\begin{align*} y^{\prime \prime }-5 y^{\prime }-6 y&={\mathrm e}^{3 t} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.535
7151	25988	\begin{align*} x^{\prime }-x+2 y&=0 \\ y^{\prime }+3 x-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.535
7152	1869	\begin{align*} \left (2 x^{2}-4 x +1\right ) y^{\prime \prime }+10 \left (x -1\right ) y^{\prime }+6 y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.536
7153	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*}	✓	✓	✓	✓	0.536
7154	8196	\begin{align*} {y^{\prime }}^{2}-2 y^{\prime }+4 y&=4 x -1 \\ \end{align*}	✓	✓	✓	✗	0.536
7155	9132	\begin{align*} -\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.536
7156	10241	\begin{align*} y^{\prime \prime } x -\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y&=6 \,{\mathrm e}^{x} x^{3} \\ \end{align*}	✓	✓	✓	✗	0.536
7157	11006	\begin{align*} x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.536
7158	16521	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.536
7159	20933	\begin{align*} x^{\prime }&=2 x+3 y \\ y^{\prime }&=-3 x+2 y \\ \end{align*}	✓	✓	✓	✓	0.536
7160	21134	\begin{align*} x^{\prime \prime }-x&={\mathrm e}^{-3 t} \\ \end{align*}	✓	✓	✓	✓	0.536
7161	22722	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \left (1+\cos \left (2 x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.536
7162	22831	\begin{align*} 2 y^{\prime \prime }-5 y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.536
7163	23089	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.536
7164	24657	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=12 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.536
7165	24674	\begin{align*} y^{\prime \prime }-y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.536
7166	25122	\begin{align*} y^{\prime \prime }+y&=2 \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.536
7167	1717	\begin{align*} 27 x y^{2}+8 y^{3}+\left (18 x^{2} y+12 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.537
7168	2370	\begin{align*} y^{\prime \prime }-6 y^{\prime }+y&=0 \\ y \left (2\right ) &= 1 \\ y^{\prime }\left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.537
7169	2733	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2} \\ x_{2}^{\prime }&=4 x_{1}+x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.537
7170	6945	\begin{align*} x^{2}+\cos \left (x \right ) y+\left (y^{3}+\sin \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.537
7171	7729	\begin{align*} 2 y^{\prime }+y&=y^{3} \left (x -1\right ) \\ \end{align*}	✓	✓	✓	✓	0.537
7172	8615	\begin{align*} 16 \left (x +1\right )^{2} y^{\prime \prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.537
7173	8938	\begin{align*} y^{\prime \prime \prime \prime }-y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.537
7174	9717	\begin{align*} {y^{\prime }}^{2}-y^{2} x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.537
7175	10336	\begin{align*} y^{\prime } t +y&=0 \\ y \left (x_{0} \right ) &= y_{0} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.537
7176	18787	\begin{align*} 6 y^{\prime \prime }-5 y^{\prime }+y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.537
7177	19204	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.537
7178	19361	\begin{align*} x^{2} y^{\prime \prime }&=2 y^{\prime } x +{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.537
7179	19456	\begin{align*} y^{\prime \prime } x -\left (2+x \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.537
7180	20882	\begin{align*} y^{\prime }&=2 y x -x^{3} \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.537
7181	22196	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*} Series expansion around \(x=-2\).	✓	✓	✓	✓	0.537
7182	22801	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.537
7183	24119	\begin{align*} y^{\prime }-7 y&=-x^{4}+2 \\ y \left (0\right ) &= a \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.537
7184	24857	\begin{align*} x {y^{\prime }}^{2}-\left (x^{2}+1\right ) y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.537
7185	24861	\begin{align*} x^{2} {y^{\prime }}^{2}-\left (x -y\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.537
7186	25519	\begin{align*} y^{\prime \prime }+4 y&=F \cos \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	0.537
7187	26008	\begin{align*} y^{\prime \prime }+y^{\prime } x +3 y&=x^{2} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.537
7188	895	\begin{align*} y^{\prime \prime }-4 y&=\sinh \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.538
7189	3405	\begin{align*} y^{\prime }&={\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.538
7190	5495	\begin{align*} x^{2} {y^{\prime }}^{2}&=y^{2} \\ \end{align*}	✓	✓	✓	✓	0.538
7191	8848	\begin{align*} x_{1}^{\prime }&=x_{1}-2 x_{2} \\ x_{2}^{\prime }&=3 x_{1}-4 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.538
7192	9177	\begin{align*} y^{2}+y x +1+\left (x^{2}+y x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.538
7193	9805	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=12 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.538
7194	16105	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{-t}-4 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.538
7195	16107	\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*}	✓	✓	✓	✓	0.538
7196	19248	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=\arctan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.538
7197	19892	\begin{align*} {y^{\prime }}^{2}+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.538
7198	20205	\begin{align*} x^{\prime }+2 x+y^{\prime }+y&=0 \\ 5 x+y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.538
7199	20940	\begin{align*} x^{\prime }&=4 x+2 y \\ y^{\prime }&=3 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.538
7200	25611	\begin{align*} y^{\prime \prime \prime \prime }-y&=t^{3} \cos \left (5 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.538