Internal problem ID [8426]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 89.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime } x=\sqrt {a^{2}-x^{2}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 56
dsolve(x*diff(y(x),x) - sqrt(a^2 - x^2)=0,y(x), singsol=all)
\[ y \left (x \right ) = \sqrt {a^{2}-x^{2}}-\frac {a^{2} \ln \left (\frac {2 a^{2}+2 \sqrt {a^{2}}\, \sqrt {a^{2}-x^{2}}}{x}\right )}{\sqrt {a^{2}}}+c_{1} \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 42
DSolve[x*y'[x] - Sqrt[a^2 - x^2]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -a \text {arctanh}\left (\frac {\sqrt {a^2-x^2}}{a}\right )+\sqrt {a^2-x^2}+c_1 \]