29.21 problem 843

Internal problem ID [3574]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 29
Problem number: 843.
ODE order: 1.
ODE degree: 2.

CAS Maple gives this as type [_quadrature]

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

Solution by Maple

Time used: 0.172 (sec). Leaf size: 25

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

\begin{align*} y \relax (x ) = 2 \sqrt {a x}+c_{1} \\ y \relax (x ) = -2 \sqrt {a x}+c_{1} \\ \end{align*}

Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 39

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

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