29.29.21 problem 843

Internal problem ID [5426]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 29
Problem number : 843
Date solved : Monday, January 27, 2025 at 11:23:18 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.039 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 39

DSolve[x (D[y[x],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*}