ﬁrst order nonlinear in y′ but linear in x y

Solves \((y')^{\frac {n}{m}}= A x + b y + c \) Number of problems in this table is 4

Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.

Table 2.532: ﬁrst_order_nonlinear_p_but_linear_in_x_y


#	ODE	A	B	C	CAS classiﬁcation	Solved?	Veriﬁed?	time (sec)

2339	\[ {}x = y-{y^{\prime }}^{3} \]	3	4	3	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	2.114

3991	\[ {}{y^{\prime }}^{2} = x -y \]	2	2	1	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	0.408

4242	\[ {}{y^{\prime }}^{3}+x -y = 0 \]	3	4	3	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	0.728

7366	\[ {}{y^{\prime }}^{2} = x +y \]	2	2	1	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	1.018