Internal problem ID [11211]
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 24. Equations solvable for \(p\). Page 49
Problem number: Ex 2.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {x {y^{\prime }}^{2}-2 y^{\prime } y=x} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 31
dsolve(x*diff(y(x),x)^2-2*y(x)*diff(y(x),x)-x=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -i x y \left (x \right ) = i x y \left (x \right ) = -\frac {\left (-\frac {x^{2}}{c_{1}^{2}}+1\right ) c_{1}}{2} \end{align*}
✓ Solution by Mathematica
Time used: 0.225 (sec). Leaf size: 71
DSolve[x*(y'[x])^2-2*y[x]*y'[x]-x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{-c_1} \left (-x^2+e^{2 c_1}\right ) y(x)\to \frac {1}{2} e^{-c_1} \left (-1+e^{2 c_1} x^2\right ) y(x)\to -i x y(x)\to i x \end{align*}