Internal problem ID [2942]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 194.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } x -y-\sqrt {x^{2}+y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 27
dsolve(x*diff(y(x),x) = y(x)+sqrt(x^2+y(x)^2),y(x), singsol=all)
\[ \frac {y \relax (x )}{x^{2}}+\frac {\sqrt {x^{2}+y \relax (x )^{2}}}{x^{2}}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 7.73 (sec). Leaf size: 50
DSolve[x y'[x]==y[x]+Sqrt[x^2+y[x]^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x \tanh (\log (x)+c_1)}{\sqrt {\text {sech}^2(\log (x)+c_1)}} \\ y(x)\to \frac {x \tanh (\log (x)+c_1)}{\sqrt {\text {sech}^2(\log (x)+c_1)}} \\ \end{align*}