4.15.34 $x(1-\sqrt{x^2-y(x{)}^2})y^{\prime }(x)=y(x)$

ODE
$$x(1-\sqrt{x^2-y(x{)}^2})y^{\prime }(x)=y(x)$$ ODE Classification

[`y=_G(x,y')`]

Book solution method
Exact equation, integrating factor

Mathematica ✓
cpu = 1.13682 (sec), leaf count = 40

$$\text{Solve}[c_1+i\log \left(\frac{2(\sqrt{x^2-y(x{)}^2}-iy(x))}{x}\right)=y(x),y(x)]$$

Maple ✓
cpu = 0.283 (sec), leaf count = 27

$$\{y\left(x\right)-\arctan \left(y\left(x\right)\frac{1}{\sqrt{x^2-{\left(y\left(x\right)\right)}^2}}\right)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$ Mathematica raw input

DSolve[x*(1 - Sqrt[x^2 - y[x]^2])*y'[x] == y[x],y[x],x]

Mathematica raw output

Solve[C[1] + I*Log[(2*((-I)*y[x] + Sqrt[x^2 - y[x]^2]))/x] == y[x], y[x]]

Maple raw input

dsolve(x*(1-(x^2-y(x)^2)^(1/2))*diff(y(x),x) = y(x), y(x),'implicit')

Maple raw output

y(x)-arctan(1/(x^2-y(x)^2)^(1/2)*y(x))-_C1 = 0