Internal problem ID [10220]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter V, Singular solutions. Article 32. Page 69
Problem number: Ex 5.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`], _Clairaut]
\[ \boxed {x^{2} {y^{\prime }}^{2}-2 \left (x y-2\right ) y^{\prime }+y^{2}=0} \]
✓ Solution by Maple
Time used: 0.187 (sec). Leaf size: 35
dsolve(x^2*diff(y(x),x)^2-2*(x*y(x)-2)*diff(y(x),x)+y(x)^2=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {1}{x} \\ y \left (x \right ) = x c_{1} -2 \sqrt {-c_{1}} \\ y \left (x \right ) = x c_{1} +2 \sqrt {-c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.264 (sec). Leaf size: 43
DSolve[x^2*(y'[x])^2-2*(x*y[x]-2)*y'[x]+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {4 (-x+c_1)}{c_1{}^2} \\ y(x)\to -\frac {4 (x+c_1)}{c_1{}^2} \\ y(x)\to 0 \\ y(x)\to \frac {1}{x} \\ \end{align*}