Internal problem ID [7670]
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]
Solve \begin {gather*} \boxed {x y^{\prime }-\sqrt {a^{2}-x^{2}}=0} \end {gather*}
✓ 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)
\[ y \relax (x ) = \sqrt {a^{2}-x^{2}}-\frac {a^{2} \ln \left (\frac {2 a^{2}+2 \sqrt {a^{2}}\, \sqrt {a^{2}-x^{2}}}{x}\right )}{\sqrt {a^{2}}}+c_{1} \]
✓ Solution by Mathematica
Time used: 0.05 (sec). Leaf size: 40
DSolve[x*y'[x] - Sqrt[a^2 - x^2]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {a^2-x^2}-a \coth ^{-1}\left (\frac {a}{\sqrt {a^2-x^2}}\right )+c_1 \\ \end{align*}