29.31.19 problem 918

Internal problem ID [5498]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 31
Problem number : 918
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} \end{align*}

✓ Solution by Maple

Time used: 0.042 (sec). Leaf size: 44

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

\begin{align*} y \left (x \right ) &= b \arctan \left (\frac {x}{\sqrt {a^{2}-x^{2}}}\right )+c_{1} \\ y \left (x \right ) &= -b \arctan \left (\frac {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,y[x],x,IncludeSingularSolutions -> True]
 

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