second order adjoint

Table 2.495: second order adjoint


#	ODE	ODE classiﬁcation	Solved?

8954	\[ {}\frac {x y^{\prime \prime }}{1-x}+x y = 0 \]	[[_2nd_order, _with_linear_symmetries]]	✓

11411	\[ {}y^{\prime \prime } = -\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\frac {\left (-17 \sin \left (x \right )^{2}-1\right ) y}{4 \sin \left (x \right )^{2}} \]	[[_2nd_order, _with_linear_symmetries]]	✓

12558	\[ {}x^{2} y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }-b y = 0 \]	[[_2nd_order, _with_linear_symmetries]]	✓

12651	\[ {}\left (a \,x^{2}+b \right )^{2} y^{\prime \prime }+\left (a \,x^{2}+b \right ) \left (c \,x^{2}+d \right ) y^{\prime }+2 \left (-a d +b c \right ) x y = 0 \]	[[_2nd_order, _with_linear_symmetries]]	✓

12685	\[ {}\left (a \,x^{n}+b \right )^{m +1} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }-a n m \,x^{n -1} y = 0 \]	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓

17040	\[ {}y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{-x} \] i.c.	[[_2nd_order, _with_linear_symmetries]]	✓

17045	\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right ) \] i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓

17091	\[ {}4 x y^{\prime \prime }+2 y^{\prime }+y = 1 \] i.c.	[[_2nd_order, _with_linear_symmetries]]	✓