Internal problem ID [8033]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 455.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {x^{3} {y^{\prime }}^{2}+y^{\prime } x^{2} y+a=0} \]
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 66
dsolve(x^3*diff(y(x),x)^2+x^2*y(x)*diff(y(x),x)+a = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {2 \sqrt {a x}}{x} \\ y \left (x \right ) = \frac {2 \sqrt {a x}}{x} \\ y \left (x \right ) = \frac {x \,c_{1}^{2}+4 a}{2 x c_{1}} \\ y \left (x \right ) = \frac {4 a x +c_{1}^{2}}{2 x c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.84 (sec). Leaf size: 57
DSolve[a + x^2*y[x]*y'[x] + x^3*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {e^{-\frac {c_1}{2}} \left (x+4 a e^{c_1}\right )}{2 x} \\ y(x)\to \frac {e^{-\frac {c_1}{2}} \left (x+4 a e^{c_1}\right )}{2 x} \\ \end{align*}