Internal problem ID [3976]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 25
Problem number: 730.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {x \left (1-\sqrt {x^{2}-y^{2}}\right ) y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 27
dsolve(x*(1-sqrt(x^2-y(x)^2))*diff(y(x),x) = y(x),y(x), singsol=all)
\[ y \left (x \right )-\arctan \left (\frac {y \left (x \right )}{\sqrt {x^{2}-y \left (x \right )^{2}}}\right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.84 (sec). Leaf size: 29
DSolve[x(1-Sqrt[x^2-y[x]^2])y'[x]==y[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\arctan \left (\frac {\sqrt {x^2-y(x)^2}}{y(x)}\right )+y(x)=c_1,y(x)\right ] \]