Internal problem ID [4137]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 31
Problem number: 901.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Clairaut]
\[ \boxed {{y^{\prime }}^{2} x^{2}-\left (a +2 y x \right ) y^{\prime }+y^{2}=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 36
dsolve(x^2*diff(y(x),x)^2-(a+2*x*y(x))*diff(y(x),x)+y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {a}{4 x} \\ y \left (x \right ) &= c_{1} x -\sqrt {c_{1} a} \\ y \left (x \right ) &= c_{1} x +\sqrt {c_{1} a} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.35 (sec). Leaf size: 64
DSolve[x^2 (y'[x])^2-(a+2 x y[x])y'[x]+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x-2 \sqrt {a} c_1}{4 c_1{}^2} \\ y(x)\to \frac {x+2 \sqrt {a} c_1}{4 c_1{}^2} \\ y(x)\to 0 \\ y(x)\to -\frac {a}{4 x} \\ \end{align*}