Internal problem ID [2890]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 5
Problem number: 142.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime } x -\sqrt {a^{2}-x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 56
dsolve(x*diff(y(x),x) = sqrt(a^2-x^2),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: 0.028 (sec). Leaf size: 40
DSolve[x y'[x]==Sqrt[a^2-x^2],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*}