ﬁrst order ode homog type D

Table 2.405: ﬁrst order ode homog type D


#	ODE	ODE classiﬁcation	Solved?

112	$x^{2} y^{'} = x y + x^{2} e^{\frac{y}{x}}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

736	$x^{2} y^{'} = x y + x^{2} e^{\frac{y}{x}}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

1243	$y^{'} x = e^{\frac{y}{x}} x + y$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

1626	$y^{'} = \frac{y + e^{- \frac{y}{x}} x}{x}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

1645	$y^{'} = \frac{y}{x} + \sec (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

2883	$y^{'} x - y - x \sin (\frac{y}{x}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

2884	$y^{'} = \frac{y}{x} + \cosh (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

2887	$e^{\frac{y}{x}} x + y = y^{'} x$ i.c.	[[_homogeneous, ‘class A‘], _dAlembert]	✓

2889	$y^{'} = \frac{y}{x} + \tan (\frac{y}{x})$ i.c.	[[_homogeneous, ‘class A‘], _dAlembert]	✓

2893	$y^{'} = \frac{y}{x} + \tanh (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

3556	$y^{'} x = x \tan (\frac{y}{x}) + y$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

3649	$y^{'} x = x \tan (\frac{y}{x}) + y$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4244	$x \sin (\frac{y}{x}) y^{'} = y \sin (\frac{y}{x}) + x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4245	$y^{'} x = y + 2 e^{- \frac{y}{x}}$	[[_homogeneous, ‘class D‘]]	✓

4315	$y^{'} x - y = x \cot (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4316	$x \cos {(\frac{y}{x})}^{2} - y + y^{'} x = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4350	$y - 2 x^{3} \tan (\frac{y}{x}) - y^{'} x = 0$	[[_homogeneous, ‘class D‘]]	✓

4399	$y^{'} x = y - e^{\frac{y}{x}} x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4405	$y^{'} x - y = x \tan (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4422	$x - y \cos (\frac{y}{x}) + x \cos (\frac{y}{x}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4441	$x + \sin {(\frac{y}{x})}^{2} (y - y^{'} x) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4801	$y^{'} x = y - x \cos {(\frac{y}{x})}^{2}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4805	$y^{'} x - y + x \sec (\frac{y}{x}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4806	$y^{'} x = y + x \sec {(\frac{y}{x})}^{2}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4808	$y^{'} x = y + x \sin (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4811	$y^{'} x = y - x \tan (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4813	$y^{'} x = e^{\frac{y}{x}} x + y$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4818	$y^{'} x = y - 2 x \tanh (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

5708	$x - y \cos (\frac{y}{x}) + x \cos (\frac{y}{x}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

5774	$y^{'} x - y - x \sin (\frac{y}{x}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

5782	$e^{\frac{y}{x}} x + y = y^{'} x$ i.c.	[[_homogeneous, ‘class A‘], _dAlembert]	✓

5783	$y^{'} - \frac{y}{x} + \csc (\frac{y}{x}) = 0$ i.c.	[[_homogeneous, ‘class A‘], _dAlembert]	✓

5893	$y^{'} x - y - x \sin (\frac{y}{x}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

6130	$y^{'} = \frac{y}{x} - \tan (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

7422	$y^{'} x - y = x \tan (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

7423	$y^{'} x = y - e^{\frac{y}{x}} x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

7742	$y^{'} = \frac{y + x e^{- \frac{2 y}{x}}}{x}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

7874	$x \sin (\frac{y}{x}) y^{'} = y \sin (\frac{y}{x}) + x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

7875	$y^{'} x = y + 2 e^{- \frac{y}{x}} x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

8887	$y^{'} = 2 x^{2} \sin {(\frac{y}{x})}^{2} + \frac{y}{x}$	[[_homogeneous, ‘class D‘]]	✓

10134	$y^{'} x - y - x \sin (\frac{y}{x}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

10136	$y^{'} x + x \tan (\frac{y}{x}) - y = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

10370	$(y^{'} x - y) \cos {(\frac{y}{x})}^{2} + x = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

12736	$e^{\frac{y}{x}} x + y - y^{'} x = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

12741	$x + y \cos (\frac{y}{x}) - x \cos (\frac{y}{x}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

13229	$x \tan (\frac{y}{x}) + y - y^{'} x = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

13789	$x^{'} = e^{\frac{x}{t}} + \frac{x}{t}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

14209	$x \cos (\frac{y}{x}) y^{'} = y \cos (\frac{y}{x}) - x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

15112	$y^{'} = \frac{y}{x} + \tan (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

16666	$y^{'} x = y + x \cos {(\frac{y}{x})}^{2}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

17830	$x - y \cos (\frac{y}{x}) + x \cos (\frac{y}{x}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

18036	$x \sin (\frac{y}{x}) y^{'} = y \sin (\frac{y}{x}) + x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

18037	$y^{'} x = y + 2 e^{- \frac{y}{x}} x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

19008	$y^{'} = \frac{y}{x} + \tan (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

19012	$x \sin (\frac{y}{x}) y^{'} = y \sin (\frac{y}{x}) - x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

2.3.6 ﬁrst order ode homog type D