29.31.20 problem 919

Internal problem ID [5499]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 31
Problem number : 919
Date solved : Monday, January 27, 2025 at 11:32:26 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.042 (sec). Leaf size: 52

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

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

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 43

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

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