ﬁrst order ode homogC

Table 2.405: ﬁrst order ode homogC


#	ODE	CAS classiﬁcation	Solved?

120	\[ {}y^{\prime } = \sqrt {x +y+1} \]	[[_homogeneous, ‘class C‘], _dAlembert]	✓

121	\[ {}y^{\prime } = \left (4 x +y\right )^{2} \]	[[_homogeneous, ‘class C‘], _Riccati]	✓

122	\[ {}\left (x +y\right ) y^{\prime } = 1 \]	[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓

208	\[ {}y^{\prime } = \sqrt {x +y} \]	[[_homogeneous, ‘class C‘], _dAlembert]	✓

744	\[ {}y^{\prime } = \sqrt {x +y+1} \]	[[_homogeneous, ‘class C‘], _dAlembert]	✓

745	\[ {}y^{\prime } = \left (4 x +y\right )^{2} \]	[[_homogeneous, ‘class C‘], _Riccati]	✓

1619	\[ {}y^{\prime } = \sqrt {x +y} \]	[[_homogeneous, ‘class C‘], _dAlembert]	✓

3468	\[ {}y^{\prime } = \frac {1}{x +2 y+1} \]	[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓

3672	\[ {}y^{\prime } = \left (9 x -y\right )^{2} \] i.c.	[[_homogeneous, ‘class C‘], _Riccati]	✓

3673	\[ {}y^{\prime } = \left (4 x +y+2\right )^{2} \]	[[_homogeneous, ‘class C‘], _Riccati]	✓

4246	\[ {}y^{\prime } = \left (x +y\right )^{2} \]	[[_homogeneous, ‘class C‘], _Riccati]	✓

4650	\[ {}y^{\prime } = \left (x +y\right )^{2} \]	[[_homogeneous, ‘class C‘], _Riccati]	✓

4659	\[ {}y^{\prime } = \left (3+x -4 y\right )^{2} \]	[[_homogeneous, ‘class C‘], _Riccati]	✓

4660	\[ {}y^{\prime } = \left (1+4 x +9 y\right )^{2} \]	[[_homogeneous, ‘class C‘], _Riccati]	✓

5882	\[ {}y^{\prime } = \left (x +y\right )^{2} \]	[[_homogeneous, ‘class C‘], _Riccati]	✓

7414	\[ {}y^{\prime } = \left (x +y+1\right )^{2} \]	[[_homogeneous, ‘class C‘], _Riccati]	✓

9044	\[ {}y^{\prime } = \sqrt {1+6 x +y} \]	[[_homogeneous, ‘class C‘], _dAlembert]	✓

9045	\[ {}y^{\prime } = \left (1+6 x +y\right )^{{1}/{3}} \]	[[_homogeneous, ‘class C‘], _dAlembert]	✓

9046	\[ {}y^{\prime } = \left (1+6 x +y\right )^{{1}/{4}} \]	[[_homogeneous, ‘class C‘], _dAlembert]	✓

9047	\[ {}y^{\prime } = \left (a +b x +y\right )^{4} \]	[[_homogeneous, ‘class C‘], _dAlembert]	✓

9048	\[ {}y^{\prime } = \left (\pi +x +7 y\right )^{{7}/{2}} \]	[[_homogeneous, ‘class C‘], _dAlembert]	✓

9049	\[ {}y^{\prime } = \left (a +b x +c y\right )^{6} \]	[[_homogeneous, ‘class C‘], _dAlembert]	✓

9130	\[ {}y^{\prime } = \left (x +y\right )^{4} \]	[[_homogeneous, ‘class C‘], _dAlembert]	✓

10033	\[ {}y^{\prime }-\left (x +y\right )^{2} = 0 \]	[[_homogeneous, ‘class C‘], _Riccati]	✓

12844	\[ {}\left (x +y\right ) y^{\prime }-1 = 0 \]	[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓

13059	\[ {}x^{\prime } = \left (4 t -x\right )^{2} \] i.c.	[[_homogeneous, ‘class C‘], _Riccati]	✓

13097	\[ {}x^{\prime } = \left (t +x\right )^{2} \]	[[_homogeneous, ‘class C‘], _Riccati]	✓

15112	\[ {}y^{\prime } = \frac {1}{\left (3 x +3 y+2\right )^{2}} \]	[[_homogeneous, ‘class C‘], _dAlembert]	✓

15162	\[ {}y^{\prime } = \sqrt {x +y} \]	[[_homogeneous, ‘class C‘], _dAlembert]	✓

15185	\[ {}1-\left (x +2 y\right ) y^{\prime } = 0 \]	[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓

15957	\[ {}y^{\prime } = \left (x +y-4\right )^{2} \]	[[_homogeneous, ‘class C‘], _Riccati]	✓

18114	\[ {}y^{\prime } = \left (x +y\right )^{2} \]	[[_homogeneous, ‘class C‘], _Riccati]	✓

18564	\[ {}y^{\prime } = \left (x +y\right )^{2} \]	[[_homogeneous, ‘class C‘], _Riccati]	✓

19131	\[ {}y^{\prime } = \left (4 x +y+1\right )^{2} \]	[[_homogeneous, ‘class C‘], _Riccati]	✓

2.3.5 ﬁrst order ode homogC