Internal problem ID [3585]
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]
Solve \begin {gather*} \boxed {x \left (y^{\prime }\right )^{2}-y y^{\prime }+a=0} \end {gather*}
✓ Solution by Maple
Time used: 0.219 (sec). Leaf size: 21
dsolve(x*diff(y(x),x)^2-y(x)*diff(y(x),x)+a = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = c_{1} x +\frac {a}{c_{1}} \\ y \relax (x ) = c_{1} \sqrt {x} \\ \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*}