Internal problem ID [2061]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 12, page 46
Problem number: 30.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {\sqrt {x^{2}+y^{2}}\, y+y x -y^{\prime } x^{2}=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 25
dsolve(y(x)*sqrt(x^2+y(x)^2)+x*y(x)=x^2*diff(y(x),x),y(x), singsol=all)
\[ -c_{1} +\frac {x \left (\sqrt {x^{2}+y^{2}}+x \right )}{y} = 0 \]
✓ Solution by Mathematica
Time used: 0.295 (sec). Leaf size: 47
DSolve[y[x]*Sqrt[x^2+y[x]^2]+x*y[x]==x^2*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \sqrt {-\text {sech}^2(\log (x)+c_1)} y(x)\to x \sqrt {-\text {sech}^2(\log (x)+c_1)} y(x)\to 0 \end{align*}