second order bessel ode form A

2.5.6 second order bessel ode form A

Table 2.1159: second order bessel ode form A [16]


#	ODE	CAS classiﬁcation	Solved	Maple	Mma	Sympy	time(sec)

5759	\begin{align} -\left (a^{2}-b \,{\mathrm e}^{x}\right ) y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.291

5760	\begin{align} -\left (a^{2}-{\mathrm e}^{2 x}\right ) y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.286

5762	\begin{align} a \,{\mathrm e}^{b x} y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.243

5813	\begin{align} \left (b +c \,{\mathrm e}^{x}\right ) y+a y^{\prime }+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.494

5814	\begin{align} b \,{\mathrm e}^{2 a x} y+a y^{\prime }+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.544

5815	\begin{align} b \,{\mathrm e}^{x k} y+a y^{\prime }+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.682

7212	\begin{align} y^{\prime \prime }+y \,{\mathrm e}^{2 x}&=n^{2} y \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.308

12297	\begin{align} y^{\prime \prime }+\left ({\mathrm e}^{2 x}-v^{2}\right ) y&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.411

12298	\begin{align} a \,{\mathrm e}^{b x} y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.246

12308	\begin{align} y^{\prime \prime }+y^{\prime }+a \,{\mathrm e}^{-2 x} y&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	✓	✓	✗	2.049

12309	\begin{align} y^{\prime \prime }-y^{\prime }+y \,{\mathrm e}^{2 x}&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	✓	✓	✗	1.619

13925	\begin{align} y^{\prime \prime }+a \,{\mathrm e}^{\lambda x} y&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.141

13926	\begin{align} y^{\prime \prime }+\left (a \,{\mathrm e}^{x}-b \right ) y&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.152

13932	\begin{align} b \,{\mathrm e}^{2 a x} y+a y^{\prime }+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.174

13933	\begin{align} y^{\prime \prime }-a y^{\prime }+b \,{\mathrm e}^{2 a x} y&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	✓	✓	✗	0.625

13934	\begin{align} y^{\prime \prime }+a y^{\prime }+\left (b \,{\mathrm e}^{\lambda x}+c \right ) y&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.197

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