29.37.2 problem 1115

Internal problem ID [5660]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 37
Problem number : 1115
Date solved : Monday, January 27, 2025 at 01:02:09 PM
CAS classification : [[_homogeneous, `class G`], _Clairaut]

\begin{align*} 2 \sqrt {a y^{\prime }}+x y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.113 (sec). Leaf size: 15

dsolve(2*sqrt(a*diff(y(x),x))+x*diff(y(x),x)-y(x) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = 2 \sqrt {c_{1} a}+c_{1} x \]

✓ Solution by Mathematica

Time used: 0.082 (sec). Leaf size: 25

DSolve[2 Sqrt[a D[y[x],x]]+x D[y[x],x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 2 \sqrt {a c_1}+c_1 x \\ y(x)\to 0 \\ \end{align*}