ﬁrst order ode homog type C

2.4.17 ﬁrst order ode homog type C

Table 2.1163: ﬁrst order ode homog type C [60]


#	ODE	CAS classiﬁcation	Solved	Maple	Mma	Sympy	time(sec)

120	\begin{align} y^{\prime }&=\sqrt {x +y+1} \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	2.969

121	\begin{align} y^{\prime }&=\left (4 x +y\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	1.897

122	\begin{align} \left (x +y\right ) y^{\prime }&=1 \\ \end{align}	[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓	✓	✓	✓	4.279

208	\begin{align} y^{\prime }&=\sqrt {x +y} \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	3.250

744	\begin{align} y^{\prime }&=\sqrt {x +y+1} \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	3.079

745	\begin{align} y^{\prime }&=\left (4 x +y\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	1.930

1619	\begin{align} y^{\prime }&=\sqrt {x +y} \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	4.158

3467	\begin{align} y^{\prime }&=\frac {1}{x +2 y+1} \\ \end{align}	[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓	✓	✓	✓	4.693

3671	\begin{align} y^{\prime }&=\left (9 x -y\right )^{2} \\ y \left (0\right ) &= 0 \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	3.319

3672	\begin{align} y^{\prime }&=\left (4 x +y+2\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	8.557

4245	\begin{align} y^{\prime }&=\left (x +y\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	2.839

4655	\begin{align} y^{\prime }&=\left (x +y\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	3.226

4664	\begin{align} y^{\prime }&=\left (3+x -4 y\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	14.872

4665	\begin{align} y^{\prime }&=\left (1+4 x +9 y\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	23.953

5066	\begin{align} \left (2 x -y+3\right ) y^{\prime }+2&=0 \\ \end{align}	[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓	✓	✓	✓	6.920

5228	\begin{align} \left (x +y\right )^{2} y^{\prime }&=a^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	27.965

7006	\begin{align} y^{\prime }&=\left (x +y\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	1.685

7490	\begin{align} \left (y-4 x -1\right )^{2}-y^{\prime }&=0 \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	9.270

7506	\begin{align} y^{\prime }&=\left (x +y+2\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	4.559

7541	\begin{align} y^{\prime }&=\left (2 x +y-1\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	5.918

7879	\begin{align} y^{\prime }&=-2 \left (2 x +3 y\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	11.639

8688	\begin{align} y^{\prime }&=2 \sqrt {2 x +y+1} \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	8.144

8689	\begin{align} y^{\prime }&=\left (x +y+1\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	6.703

10318	\begin{align} y^{\prime }&=\sqrt {1+6 x +y} \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	4.395

10319	\begin{align} y^{\prime }&=\left (1+6 x +y\right )^{{1}/{3}} \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	2.848

10320	\begin{align} y^{\prime }&=\left (1+6 x +y\right )^{{1}/{4}} \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	5.260

10321	\begin{align} y^{\prime }&=\left (a +b x +y\right )^{4} \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✗	1.177

10323	\begin{align} y^{\prime }&=\left (a +b x +c y\right )^{6} \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✗	6.796

10418	\begin{align} y^{\prime }&=\left (x +y\right )^{4} \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	1.413

11321	\begin{align} y^{\prime }-\left (x +y\right )^{2}&=0 \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	1.546

11574	\begin{align} \left (x +y\right )^{2} y^{\prime }-a^{2}&=0 \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	9.491

14012	\begin{align} \left (x +y\right ) y^{\prime }-1&=0 \\ \end{align}	[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓	✓	✓	✓	8.019

14226	\begin{align} x^{\prime }&=\left (4 t -x\right )^{2} \\ x \left (0\right ) &= 1 \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	6.445

14264	\begin{align} x^{\prime }&=\left (t +x\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	3.963

16285	\begin{align} y^{\prime }&=\frac {1}{\left (3 x +3 y+2\right )^{2}} \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	11.556

16306	\begin{align} y^{\prime }&=2 \sqrt {2 x +y-3} \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	5.368

16335	\begin{align} y^{\prime }&=\sqrt {x +y} \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	6.053

16358	\begin{align} 1-\left (x +2 y\right ) y^{\prime }&=0 \\ \end{align}	[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓	✓	✓	✓	5.242

17130	\begin{align} y^{\prime }&=\left (x +y-4\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	6.647

17891	\begin{align} \left (x +y\right )^{2} y^{\prime }&=a^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	22.116

19077	\begin{align} \left (x +y\right )^{2} y^{\prime }&=a^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	5.575

19285	\begin{align} y^{\prime }&=\left (x +y\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	2.143

19735	\begin{align} y^{\prime }&=\left (x +y\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	2.252

19935	\begin{align} \left (x +y\right )^{2} y^{\prime }&=a^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	11.718

20299	\begin{align} \left (x +y\right )^{2} y^{\prime }&=a^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	6.488

20300	\begin{align} y^{\prime }&=\left (4 x +y+1\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	6.637

22394	\begin{align} y^{\prime }&=\left (x +y\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	4.071

22395	\begin{align} y^{\prime }&=\sqrt {2 x +3 y} \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	12.613

22454	\begin{align} y^{\prime }&=\frac {1}{x -3 y} \\ \end{align}	[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓	✓	✓	✓	11.938

22534	\begin{align} \left (x +y\right ) y^{\prime }&=1 \\ \end{align}	[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓	✓	✓	✓	12.026

22564	\begin{align} s^{\prime }&=\frac {1}{s+t +1} \\ \end{align}	[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓	✓	✓	✓	12.892

22596	\begin{align} y^{\prime }&=\frac {2}{x +2 y-3} \\ \end{align}	[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓	✓	✓	✓	13.992

23950	\begin{align} 1+\left (1-3 x +y\right ) y^{\prime }&=0 \\ y \left (4\right ) &= 0 \\ \end{align}	[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓	✓	✓	✓	4.704

24318	\begin{align} y^{\prime }&=\left (9 x +4 y+1\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	20.426

24350	\begin{align} \left (2 x -y+3\right ) y^{\prime }+2&=0 \\ \end{align}	[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓	✓	✓	✓	5.724

25022	\begin{align} y^{\prime }&=\frac {1}{\left (t +y\right )^{2}} \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	19.882

26224	\begin{align} \left (x +y\right )^{2} y^{\prime }&=a^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	6.751

27227	\begin{align} y^{\prime }&=\sqrt {4 x +2 y-1} \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	2.986

27425	\begin{align} \left (x +y\right )^{2} y^{\prime }&=1 \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	151.775

27457	\begin{align} y^{\prime }&=\left (4 x +y-3\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	13.030

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