29.30.31 problem 891

Internal problem ID [5471]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 30
Problem number : 891
Date solved : Monday, January 27, 2025 at 11:25:13 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 24

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

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