Internal problem ID [4316]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 37
Problem number: 1115.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`], _Clairaut]
\[ \boxed {2 \sqrt {a y^{\prime }}+x y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.094 (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: 0.078 (sec). Leaf size: 25
DSolve[2 Sqrt[a y'[x]]+x y'[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*}