An introduction to the solution and applications of diﬀerential equations, J.W. Searl, 1966

Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.

Table 2.418: An introduction to the solution and applications of diﬀerential equations, J.W. Searl, 1966


#	ODE	A	B	C	Program classiﬁcation	CAS classiﬁcation	Solved?	Veriﬁed?	time (sec)

3134	\[ {}2 x y+x^{2} y^{\prime } = 0 \]	1	1	1	exact, linear, separable, homogeneousTypeD2, ﬁrst_order_ode_lie_symmetry_lookup	[_separable]	✓	✓	0.918

3135	\[ {}x +y+\left (x -y\right ) y^{\prime } = 0 \] i.c.	1	3	2	dAlembert	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	1.664

3136	\[ {}\ln \left (x \right ) y^{\prime }+\frac {x +y}{x} = 0 \]	1	1	1	exact, linear, ﬁrst_order_ode_lie_symmetry_lookup	[_linear]	✓	✓	0.897

3137	\[ {}\cos \left (y\right )-x \sin \left (y\right ) y^{\prime } = \sec \left (x \right )^{2} \] i.c.	1	1	2	exact	[_exact]	✓	✓	32.435

3138	\[ {}y \sin \left (\frac {x}{y}\right )+x \cos \left (\frac {x}{y}\right )-1+\left (x \sin \left (\frac {x}{y}\right )-\frac {x^{2} \cos \left (\frac {x}{y}\right )}{y}\right ) y^{\prime } = 0 \]	1	1	1	exact	[_exact]	✓	✓	32.579

3139	\[ {}\frac {x}{x^{2}+y^{2}}+\frac {y}{x^{2}}+\left (\frac {y}{x^{2}+y^{2}}-\frac {1}{x}\right ) y^{\prime } = 0 \] i.c.	1	1	1	exact, homogeneousTypeD2, ﬁrst_order_ode_lie_symmetry_calculated	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	✓	2.257

3140	\[ {}x^{2} \left (1+y^{2}\right ) y^{\prime }+y^{2} \left (x^{2}+1\right ) = 0 \]	1	2	2	separable	[_separable]	✓	✓	0.589

3141	\[ {}x \left (-1+x \right ) y^{\prime } = \cot \left (y\right ) \]	1	1	1	separable	[_separable]	✓	✓	0.505

3142	\[ {}r y^{\prime } = \frac {\left (a^{2}-r^{2}\right ) \tan \left (y\right )}{a^{2}+r^{2}} \]	1	1	1	separable	[_separable]	✓	✓	0.743

3143	\[ {}\sqrt {x^{2}+1}\, y^{\prime }+\sqrt {1+y^{2}} = 0 \]	1	1	1	separable	[_separable]	✓	✓	0.44

3144	\[ {}y^{\prime } = \frac {x \left (1+y^{2}\right )}{y \left (x^{2}+1\right )} \] i.c.	1	1	1	separable	[_separable]	✓	✓	1.624

3145	\[ {}y^{2} y^{\prime } = 2+3 y^{6} \] i.c.	1	3	3	separable	[_quadrature]	✓	✓	1.841

2.20.20 An introduction to the solution and applications of diﬀerential equations, J.W. Searl, 1966