Internal problem ID [3467]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 25
Problem number: 729.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {\left (x -\sqrt {x^{2}+y^{2}}\right ) y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.023 (sec). Leaf size: 18
dsolve((x-sqrt(x^2+y(x)^2))*diff(y(x),x) = y(x),y(x), singsol=all)
\[ -c_{1}+\sqrt {x^{2}+y \relax (x )^{2}}+x = 0 \]
✓ Solution by Mathematica
Time used: 0.471 (sec). Leaf size: 57
DSolve[(x-Sqrt[x^2+y[x]^2])y'[x]==y[x],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*}