29.31.18 problem 917

Internal problem ID [5497]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 31
Problem number : 917
Date solved : Monday, January 27, 2025 at 11:32:25 AM
CAS classification : [_quadrature]

\begin{align*} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+b^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.041 (sec). Leaf size: 44

dsolve((a^2-x^2)*diff(y(x),x)^2+b^2 = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= b \ln \left (x +\sqrt {-a^{2}+x^{2}}\right )+c_{1} \\ y \left (x \right ) &= -b \ln \left (x +\sqrt {-a^{2}+x^{2}}\right )+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 52

DSolve[(a^2-x^2) (D[y[x],x])^2+b^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -b \log \left (\sqrt {x^2-a^2}+x\right )+c_1 \\ y(x)\to b \log \left (\sqrt {x^2-a^2}+x\right )+c_1 \\ \end{align*}