ﬁrst order ode reduced riccati

Table 2.439: ﬁrst order ode reduced riccati


#	ODE	CAS classiﬁcation	Solved	Maple	Mma	Sympy

40	$y^{'} = x + \frac{y^{2}}{2}$ i.c.	[[_Riccati, _special]]	✓	✓	✓	✗

527	$y^{'} = x^{2} + y^{2}$	[[_Riccati, _special]]	✓	✓	✓	✗

528	$y^{'} = x^{2} + y^{2}$ i.c.	[[_Riccati, _special]]	✓	✓	✓	✗

676	$y^{'} = x^{2} - y^{2}$	[_Riccati]	✓	✓	✓	✗

2349	$y^{'} = t + y^{2}$ i.c.	[[_Riccati, _special]]	✓	✓	✓	✗

2359	$y^{'} = t^{2} + y^{2}$ i.c.	[[_Riccati, _special]]	✓	✓	✓	✗

2524	$y^{'} = t + y^{2}$ i.c.	[[_Riccati, _special]]	✓	✓	✓	✗

2534	$y^{'} = t^{2} + y^{2}$ i.c.	[[_Riccati, _special]]	✓	✓	✓	✗

4647	$y^{'} = x^{2} - y^{2}$	[_Riccati]	✓	✓	✓	✗

4663	$y^{'} = a x + b y^{2}$	[[_Riccati, _special]]	✓	✓	✓	✗

4666	$y^{'} = a x^{2} + b y^{2}$	[[_Riccati, _special]]	✓	✓	✓	✗

4771	$y^{'} x + a + x y^{2} = 0$	[_rational, [_Riccati, _special]]	✓	✓	✓	✗

4866	$x^{2} y^{'} = a + b x^{2} y^{2}$	[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]	✓	✓	✓	✓

4970	$x^{4} y^{'} + a^{2} + x^{4} y^{2} = 0$	[_rational, [_Riccati, _special]]	✓	✓	✓	✓

4997	$x^{3 / 2} y^{'} = a + b x^{3 / 2} y^{2}$	[_rational, [_Riccati, _special]]	✓	✓	✓	✗

6075	$y^{'} + y^{2} = \frac{a^{2}}{x^{4}}$	[_rational, _Riccati]	✓	✓	✓	✓

6992	$y^{'} = x^{2} + y^{2}$ i.c.	[[_Riccati, _special]]	✓	✓	✓	✗

7013	$y^{'} = x^{2} - y^{2}$ i.c.	[_Riccati]	✓	✓	✓	✗

7014	$y^{'} = x^{2} - y^{2}$ i.c.	[_Riccati]	✓	✓	✓	✗

7016	$y^{'} = x^{2} - y^{2}$ i.c.	[_Riccati]	✓	✓	✓	✗

7046	$y^{'} = x^{2} + y^{2}$	[[_Riccati, _special]]	✓	✓	✓	✗

8792	$y^{'} = x^{2} + y^{2}$	[[_Riccati, _special]]	✓	✓	✓	✗

8994	$y^{'} = a x + b y^{2}$	[[_Riccati, _special]]	✓	✓	✓	✗

9002	$c y^{'} = a x + b y^{2}$	[[_Riccati, _special]]	✓	✓	✓	✗

9003	$c y^{'} = \frac{a x + b y^{2}}{r}$	[[_Riccati, _special]]	✓	✓	✓	✗

9163	$y^{'} = x - y^{2}$	[[_Riccati, _special]]	✓	✓	✓	✗

10027	$y^{'} + y^{2} + a x^{m} = 0$	[[_Riccati, _special]]	✓	✓	✓	✗

10037	$y^{'} + a y^{2} - b x^{ν} = 0$	[[_Riccati, _special]]	✓	✓	✓	✗

10111	$y^{'} x + a + x y^{2} = 0$	[_rational, [_Riccati, _special]]	✓	✓	✓	✗

10153	$x^{2} (y^{'} + a y^{2}) - b = 0$	[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]	✓	✓	✓	✓

10191	$x^{4} (y^{'} + y^{2}) + a = 0$	[_rational, [_Riccati, _special]]	✓	✓	✓	✓

11929	$y^{'} = a y^{2} + b x^{n}$	[[_Riccati, _special]]	✓	✓	✓	✗

11938	$x^{2} y^{'} = a x^{2} y^{2} + b$	[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]	✓	✓	✓	✓

11943	$x^{4} y^{'} = - x^{4} y^{2} - a^{2}$	[_rational, [_Riccati, _special]]	✓	✓	✓	✓

12958	$x^{'} = x^{2} + t^{2}$	[[_Riccati, _special]]	✓	✓	✓	✗

13000	$x^{'} = t - x^{2}$	[[_Riccati, _special]]	✓	✓	✓	✗

13792	$y^{'} = x + y^{2}$ i.c.	[[_Riccati, _special]]	✓	✓	✓	✗

13794	$y^{'} = x^{2} - y^{2}$	[_Riccati]	✓	✓	✓	✗

13798	$y^{'} = x - y^{2}$ i.c.	[[_Riccati, _special]]	✓	✓	✓	✗

14282	$y^{'} = x^{2} - y^{2}$	[_Riccati]	✓	✓	✓	✗

14283	$y^{'} = y^{2} - x^{2}$	[_Riccati]	✓	✓	✓	✗

14951	$y^{'} - y^{2} = x$	[[_Riccati, _special]]	✓	✓	✓	✗

15784	$y^{'} + t^{2} = y^{2}$ i.c.	[_Riccati]	✓	✓	✓	✗

16095	$y^{'} = - x + y^{2}$ i.c.	[[_Riccati, _special]]	✓	✓	✓	✗

16587	$y^{'} = x^{2} + y^{2}$	[[_Riccati, _special]]	✓	✓	✓	✗

16607	$y^{'} = x^{2} - y^{2}$	[_Riccati]	✓	✓	✓	✗

16621	$y^{'} = x^{2} - y^{2}$ i.c.	[_Riccati]	✓	✓	✓	✗

16622	$y^{'} = x + y^{2}$ i.c.	[[_Riccati, _special]]	✓	✓	✓	✗

17838	$y^{'} = \frac{y^{2}}{3} + \frac{2}{3 x^{2}}$	[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]	✓	✓	✓	✓

17841	$y^{'} = y^{2} + \frac{1}{x^{4}}$	[_rational, [_Riccati, _special]]	✓	✓	✓	✓

17847	$y^{'} = y^{2} - x^{2}$	[_Riccati]	✓	✓	✓	✗

2.3.23 ﬁrst order ode reduced riccati