Internal problem ID [4093]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 29
Problem number: 854.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Clairaut]
\[ \boxed {{y^{\prime }}^{2} x -y y^{\prime }=-a} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 35
dsolve(x*diff(y(x),x)^2-y(x)*diff(y(x),x)+a = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -2 \sqrt {a x} \\ y \left (x \right ) &= 2 \sqrt {a x} \\ y \left (x \right ) &= \frac {x \,c_{1}^{2}+a}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 53
DSolve[x (y'[x])^2-y[x] y'[x]+a==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {a}{c_1}+c_1 x \\ y(x)\to \text {Indeterminate} \\ y(x)\to -2 \sqrt {a} \sqrt {x} \\ y(x)\to 2 \sqrt {a} \sqrt {x} \\ \end{align*}