Internal problem ID [4138]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 31
Problem number: 902.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {x^{2} {y^{\prime }}^{2}-x \left (-2 y+x \right ) y^{\prime }+y^{2}=0} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 33
dsolve(x^2*diff(y(x),x)^2-x*(x-2*y(x))*diff(y(x),x)+y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {x}{4} y \left (x \right ) = -\frac {c_{1} \left (c_{1} -x \right )}{x} y \left (x \right ) = -\frac {c_{1} \left (x +c_{1} \right )}{x} \end{align*}
✓ Solution by Mathematica
Time used: 0.217 (sec). Leaf size: 64
DSolve[x^2 (y'[x])^2-x(x-2 y[x])y'[x]+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-4 c_1}-2 i e^{-2 c_1} x}{4 x} y(x)\to \frac {2 i e^{-2 c_1} x+e^{-4 c_1}}{4 x} y(x)\to 0 \end{align*}