First order Isobaric ODE’s

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

Table 2.552: isobaric


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

5793	\[ {}2 x y^{\prime } \left (x -y^{2}\right )+y^{3} = 0 \]	1	1	1	[[_homogeneous, ‘class G‘], _rational]	✓	✓	0.254

5794	\[ {}x^{3} \left (y^{\prime }-x \right ) = y^{2} \]	1	1	1	[[_homogeneous, ‘class G‘], _rational, _Riccati]	✓	✓	0.309

5795	\[ {}2 x^{2} y^{\prime } = y^{3}+x y \]	1	1	2	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	✓	0.221

5796	\[ {}y+x \left (1+2 x y\right ) y^{\prime } = 0 \]	1	1	1	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓	0.223

5797	\[ {}2 y^{\prime }+x = 4 \sqrt {y} \]	1	1	1	[[_1st_order, _with_linear_symmetries], _Chini]	✓	✓	0.579

5798	\[ {}y^{\prime } = y^{2}-\frac {2}{x^{2}} \]	1	1	1	[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]	✓	✓	0.358

5799	\[ {}y+2 x y^{\prime } = y^{2} \sqrt {x -x^{2} y^{2}} \]	1	1	1	[[_homogeneous, ‘class G‘]]	✓	✓	0.716

5800	\[ {}\frac {2 x y y^{\prime }}{3} = \sqrt {x^{6}-y^{4}}+y^{2} \]	1	1	1	[[_homogeneous, ‘class G‘]]	✓	✓	1.222

5801	\[ {}2 y+\left (x^{2} y+1\right ) x y^{\prime } = 0 \]	1	1	1	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓	0.233

5802	\[ {}y \left (1+x y\right )+x \left (1-x y\right ) y^{\prime } = 0 \]	1	1	1	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓	0.231

5803	\[ {}y \left (x^{2} y^{2}+1\right )+\left (x^{2} y^{2}-1\right ) x y^{\prime } = 0 \]	1	1	1	[[_homogeneous, ‘class G‘], _rational]	✓	✓	0.245

5804	\[ {}\left (x^{2}-y^{4}\right ) y^{\prime }-x y = 0 \]	1	1	4	[[_homogeneous, ‘class G‘], _rational]	✓	✓	0.489

5805	\[ {}y \left (1+\sqrt {x^{2} y^{4}-1}\right )+2 x y^{\prime } = 0 \]	1	1	1	[[_homogeneous, ‘class G‘]]	✓	✓	0.726

2.21.1.19 First order Isobaric ODE’s