29.5.25 problem 142

Internal problem ID [4742]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 5
Problem number : 142
Date solved : Monday, January 27, 2025 at 09:36:08 AM
CAS classification : [_quadrature]

\begin{align*} x y^{\prime }&=\sqrt {a^{2}-x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 51

dsolve(x*diff(y(x),x) = sqrt(a^2-x^2),y(x), singsol=all)
 

\[ y \left (x \right ) = -a \,\operatorname {csgn}\left (a \right ) \ln \left (\frac {a \left (\operatorname {csgn}\left (a \right ) \sqrt {a^{2}-x^{2}}+a \right )}{x}\right )-a \,\operatorname {csgn}\left (a \right ) \ln \left (2\right )+\sqrt {a^{2}-x^{2}}+c_{1} \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 42

DSolve[x D[y[x],x]==Sqrt[a^2-x^2],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -a \text {arctanh}\left (\frac {\sqrt {a^2-x^2}}{a}\right )+\sqrt {a^2-x^2}+c_1 \]