Internal problem ID [1920]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 6, page 25
Problem number: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y}{x -k \sqrt {x^{2}+y^{2}}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.036 (sec). Leaf size: 32
dsolve(diff(y(x),x)=y(x)/(x-k*sqrt(x^2+y(x)^2)),y(x), singsol=all)
\[ -c_{1}+\sqrt {x^{2}+y \relax (x )^{2}}\, y \relax (x )^{k -1}+x y \relax (x )^{k -1} = 0 \]
✓ Solution by Mathematica
Time used: 0.215 (sec). Leaf size: 59
DSolve[y'[x]==y[x]/(x-k*Sqrt[x^2+y[x]^2]),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{2} \left ((k-1) \log \left (\sqrt {\frac {y(x)^2}{x^2}+1}-1\right )+(k+1) \log \left (\sqrt {\frac {y(x)^2}{x^2}+1}+1\right )\right )=-k \log (x)+c_1,y(x)\right ] \]