ODE
\[ x \left (1-\sqrt {x^2-y(x)^2}\right ) y'(x)=y(x) \] ODE Classification
[`y=_G(x,y')`]
Book solution method
Exact equation, integrating factor
Mathematica ✓
cpu = 1.07549 (sec), leaf count = 29
\[\text {Solve}\left [\tan ^{-1}\left (\frac {\sqrt {x^2-y(x)^2}}{y(x)}\right )+y(x)=c_1,y(x)\right ]\]
Maple ✓
cpu = 0.259 (sec), leaf count = 27
\[\left [y \left (x \right )-\arctan \left (\frac {y \left (x \right )}{\sqrt {x^{2}-y \left (x \right )^{2}}}\right )-\textit {\_C1} = 0\right ]\] Mathematica raw input
DSolve[x*(1 - Sqrt[x^2 - y[x]^2])*y'[x] == y[x],y[x],x]
Mathematica raw output
Solve[ArcTan[Sqrt[x^2 - y[x]^2]/y[x]] + y[x] == C[1], y[x]]
Maple raw input
dsolve(x*(1-(x^2-y(x)^2)^(1/2))*diff(y(x),x) = y(x), y(x))
Maple raw output
[y(x)-arctan(1/(x^2-y(x)^2)^(1/2)*y(x))-_C1 = 0]