Internal problem ID [4127]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 30
Problem number: 891.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x^{2} {y^{\prime }}^{2}=a^{2}} \]
✓ Solution by Maple
Time used: 0.016 (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 (y'[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*}