29.31.17 problem 916

Internal problem ID [5496]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 31
Problem number : 916
Date solved : Monday, January 27, 2025 at 11:32:24 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: 40

dsolve((a^2+x^2)*diff(y(x),x)^2 = b^2,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: 48

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

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