Internal problem ID [8450]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 113.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {y^{\prime } x +a \sqrt {x^{2}+y^{2}}-y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve(x*diff(y(x),x) + a*sqrt(y(x)^2 + x^2) - y(x)=0,y(x), singsol=all)
\[ \frac {x^{a} \sqrt {y \left (x \right )^{2}+x^{2}}}{x}+\frac {x^{a} y \left (x \right )}{x}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.253 (sec). Leaf size: 36
DSolve[x*y'[x] + a*Sqrt[y[x]^2 + x^2] - y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-c_1} x^{1-a} \left (-x^{2 a}+e^{2 c_1}\right ) \]