second order bessel ode form A

2.5.6 second order bessel ode form A

Table 2.1207: second order bessel ode form A [20]


#	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]]	✓	✓	✓	✗	0.359

5760	\begin{align} -\left (a^{2}-{\mathrm e}^{2 x}\right ) y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.348

5762	\begin{align} a \,{\mathrm e}^{b x} y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.217

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]]	✓	✓	✓	✗	0.710

5814	\begin{align} b \,{\mathrm e}^{2 a x} y+a y^{\prime }+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.647

5815	\begin{align} b \,{\mathrm e}^{k x} y+a y^{\prime }+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.842

7212	\begin{align} y^{\prime \prime }+{\mathrm e}^{2 x} y&=n^{2} y \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.450

12297	\begin{align} y^{\prime \prime }+\left ({\mathrm e}^{2 x}-v^{2}\right ) y&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.381

12298	\begin{align} a \,{\mathrm e}^{b x} y+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.251

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)]‘]]	✓	✓	✓	✗	1.852

12309	\begin{align} y^{\prime \prime }-y^{\prime }+{\mathrm e}^{2 x} y&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	✓	✓	✗	1.589

13925	\begin{align} y^{\prime \prime }+a \,{\mathrm e}^{\lambda x} y&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.337

13926	\begin{align} y^{\prime \prime }+\left (a \,{\mathrm e}^{x}-b \right ) y&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.489

13932	\begin{align} b \,{\mathrm e}^{2 a x} y+a y^{\prime }+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.768

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)]‘]]	✓	✓	✓	✗	3.388

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]]	✓	✓	✓	✗	0.858

26636	\begin{align} y^{\prime \prime }-y^{\prime }+{\mathrm e}^{2 x} y&=x \,{\mathrm e}^{2 x}-1 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	19.644

26659	\begin{align} y^{\prime \prime }+y^{\prime }+y \,{\mathrm e}^{-2 x}&={\mathrm e}^{-3 x} \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✗	18.507

27735	\begin{align} y^{\prime \prime }-y^{\prime }+{\mathrm e}^{4 x} y&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	2.917

27743	\begin{align} y^{\prime \prime }+{\mathrm e}^{2 x} y&=0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.507

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