Internal problem ID [7694]
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]
Solve \begin {gather*} \boxed {x y^{\prime }+a \sqrt {y^{2}+x^{2}}-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 33
dsolve(x*diff(y(x),x) + a*sqrt(y(x)^2 + x^2) - y(x)=0,y(x), singsol=all)
\[ \frac {x^{a} \sqrt {x^{2}+y \relax (x )^{2}}}{x}+\frac {x^{a} y \relax (x )}{x}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 44.963 (sec). Leaf size: 62
DSolve[x*y'[x] + a*Sqrt[y[x]^2 + x^2] - y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x \tanh (-a \log (x)+c_1)}{\sqrt {\operatorname {sech}^2(-a \log (x)+c_1)}} \\ y(x)\to \frac {x \tanh (-a \log (x)+c_1)}{\sqrt {\operatorname {sech}^2(-a \log (x)+c_1)}} \\ \end{align*}