Internal problem ID [8561]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 981.
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} a^{3} x^{3}+3 y^{2} a^{2} x^{2}+3 y a x +1+a^{2} x}{x^{3} a^{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 41
dsolve(diff(y(x),x) = (y(x)^3*a^3*x^3+3*y(x)^2*a^2*x^2+3*y(x)*a*x+1+a^2*x)/x^3/a^3,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {1}{\sqrt {c_{1}-2 x}}-\frac {1}{x a} \\ y \relax (x ) = \frac {1}{\sqrt {c_{1}-2 x}}-\frac {1}{x a} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.268 (sec). Leaf size: 61
DSolve[y'[x] == (1 + a^2*x + 3*a*x*y[x] + 3*a^2*x^2*y[x]^2 + a^3*x^3*y[x]^3)/(a^3*x^3),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{a x}-\frac {1}{\sqrt {-2 x+c_1}} \\ y(x)\to -\frac {1}{a x}+\frac {1}{\sqrt {-2 x+c_1}} \\ y(x)\to -\frac {1}{a x} \\ \end{align*}