30.31 problem 891

Internal problem ID [3619]

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]

Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }\right )^{2}-a^{2}=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 20

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

\begin{align*} y \relax (x ) = a \ln \relax (x )+c_{1} \\ y \relax (x ) = -a \ln \relax (x )+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*}