ﬁrst order ode homogC

Table 2.339: 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]	✓

3401	\[ {}y^{\prime } = \frac {1}{x +2 y+1} \]	[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓

3605	\[ {}y^{\prime } = \left (9 x -y\right )^{2} \] i.c.	[[_homogeneous, ‘class C‘], _Riccati]	✓

3606	\[ {}y^{\prime } = \left (4 x +y+2\right )^{2} \]	[[_homogeneous, ‘class C‘], _Riccati]	✓

3989	\[ {}y^{\prime } = \left (x +y\right )^{2} \]	[[_homogeneous, ‘class C‘], _Riccati]	✓

4210	\[ {}y^{\prime } = \left (x +y\right )^{2} \]	[[_homogeneous, ‘class C‘], _Riccati]	✓

4219	\[ {}y^{\prime } = \left (3+x -4 y\right )^{2} \]	[[_homogeneous, ‘class C‘], _Riccati]	✓

4220	\[ {}y^{\prime } = \left (1+4 x +9 y\right )^{2} \]	[[_homogeneous, ‘class C‘], _Riccati]	✓

5442	\[ {}y^{\prime } = \left (x +y\right )^{2} \]	[[_homogeneous, ‘class C‘], _Riccati]	✓

6650	\[ {}y^{\prime } = \left (x +y+1\right )^{2} \]	[[_homogeneous, ‘class C‘], _Riccati]	✓

8280	\[ {}y^{\prime } = \sqrt {1+6 x +y} \]	[[_homogeneous, ‘class C‘], _dAlembert]	✓

8281	\[ {}y^{\prime } = \left (1+6 x +y\right )^{{1}/{3}} \]	[[_homogeneous, ‘class C‘], _dAlembert]	✓

8282	\[ {}y^{\prime } = \left (1+6 x +y\right )^{{1}/{4}} \]	[[_homogeneous, ‘class C‘], _dAlembert]	✓

8283	\[ {}y^{\prime } = \left (a +b x +y\right )^{4} \]	[[_homogeneous, ‘class C‘], _dAlembert]	✓

8284	\[ {}y^{\prime } = \left (\pi +x +7 y\right )^{{7}/{2}} \]	[[_homogeneous, ‘class C‘], _dAlembert]	✓

8285	\[ {}y^{\prime } = \left (a +b x +c y\right )^{6} \]	[[_homogeneous, ‘class C‘], _dAlembert]	✓

8352	\[ {}y^{\prime } = \left (x +y\right )^{4} \]	[[_homogeneous, ‘class C‘], _dAlembert]	✓

9255	\[ {}y^{\prime }-\left (x +y\right )^{2} = 0 \]	[[_homogeneous, ‘class C‘], _Riccati]	✓

12066	\[ {}\left (x +y\right ) y^{\prime }-1 = 0 \]	[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓

12281	\[ {}x^{\prime } = \left (4 t -x\right )^{2} \] i.c.	[[_homogeneous, ‘class C‘], _Riccati]	✓

12319	\[ {}x^{\prime } = \left (t +x\right )^{2} \]	[[_homogeneous, ‘class C‘], _Riccati]	✓

14274	\[ {}y^{\prime } = \frac {1}{\left (3 x +3 y+2\right )^{2}} \]	[[_homogeneous, ‘class C‘], _dAlembert]	✓

14324	\[ {}y^{\prime } = \sqrt {x +y} \]	[[_homogeneous, ‘class C‘], _dAlembert]	✓

14347	\[ {}1-\left (x +2 y\right ) y^{\prime } = 0 \]	[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓

15119	\[ {}y^{\prime } = \left (x +y-4\right )^{2} \]	[[_homogeneous, ‘class C‘], _Riccati]	✓

2.3.4 ﬁrst order ode homogC