Internal problem ID [7917]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 337.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {\left (\sqrt {y^{2}+x^{2}}+x \right ) y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.064 (sec). Leaf size: 28
dsolve(((y(x)^2+x^2)^(1/2)+x)*diff(y(x),x)-y(x) = 0,y(x), singsol=all)
\[ -c_{1}+\frac {x}{y \relax (x )^{2}}+\frac {\sqrt {x^{2}+y \relax (x )^{2}}}{y \relax (x )^{2}} = 0 \]
✓ Solution by Mathematica
Time used: 0.506 (sec). Leaf size: 57
DSolve[-y[x] + (x + Sqrt[x^2 + y[x]^2])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -e^{\frac {c_1}{2}} \sqrt {2 x+e^{c_1}} \\ y(x)\to e^{\frac {c_1}{2}} \sqrt {2 x+e^{c_1}} \\ y(x)\to 0 \\ \end{align*}