2.404 problem 980

Internal problem ID [8560]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 980.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], _Abel]

Solve \begin {gather*} \boxed {y^{\prime }-\frac {y^{3} x^{3}+6 y^{2} x^{2}+12 y x +8+2 x}{x^{3}}=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 35

dsolve(diff(y(x),x) = (x^3*y(x)^3+6*x^2*y(x)^2+12*x*y(x)+8+2*x)/x^3,y(x), singsol=all)
 

\begin{align*} y \relax (x ) = -\frac {1}{\sqrt {c_{1}-2 x}}-\frac {2}{x} \\ y \relax (x ) = \frac {1}{\sqrt {c_{1}-2 x}}-\frac {2}{x} \\ \end{align*}

Solution by Mathematica

Time used: 0.24 (sec). Leaf size: 53

DSolve[y'[x] == (8 + 2*x + 12*x*y[x] + 6*x^2*y[x]^2 + x^3*y[x]^3)/x^3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {2+\frac {x}{\sqrt {-2 x+c_1}}}{x} \\ y(x)\to -\frac {2}{x}+\frac {1}{\sqrt {-2 x+c_1}} \\ y(x)\to -\frac {2}{x} \\ \end{align*}