Internal problem ID [8816]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 481.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
\[ \boxed {x y {y^{\prime }}^{2}+\left (y^{2}+x^{2}\right ) y^{\prime }+y x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(x*y(x)*diff(y(x),x)^2+(y(x)^2+x^2)*diff(y(x),x)+x*y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {c_{1}}{x} y \left (x \right ) = \sqrt {-x^{2}+c_{1}} y \left (x \right ) = -\sqrt {-x^{2}+c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.104 (sec). Leaf size: 54
DSolve[x*y[x] + (x^2 + y[x]^2)*y'[x] + x*y[x]*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1}{x} y(x)\to -\sqrt {-x^2+2 c_1} y(x)\to \sqrt {-x^2+2 c_1} y(x)\to 0 \end{align*}