Internal problem ID [3398]
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]
\[ \boxed {x y^{\prime }=\sqrt {a^{2}-x^{2}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 56
dsolve(x*diff(y(x),x) = sqrt(a^2-x^2),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: 0.029 (sec). Leaf size: 42
DSolve[x y'[x]==Sqrt[a^2-x^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -a \text {arctanh}\left (\frac {\sqrt {a^2-x^2}}{a}\right )+\sqrt {a^2-x^2}+c_1 \]