Internal problem ID [10219]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IV, differential equations of the first order and higher degree than the first. Article
28. Summary. Page 59
Problem number: Ex 9.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }\right )^{2}-2 \left (y x +2 y^{\prime }\right ) y^{\prime }+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve(x^2*diff(y(x),x)^2-2*(x*y(x)+2*diff(y(x),x))*diff(y(x),x)+y(x)^2=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = c_{1} \left (x -2\right ) \\ y \relax (x ) = c_{1} \left (x +2\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 26
DSolve[x^2*(y'[x])^2-2*(x*y[x]+2*y'[x])*y'[x]+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 (x-2) \\ y(x)\to c_1 (x+2) \\ y(x)\to 0 \\ \end{align*}