Internal problem ID [5775]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations
problems. page 12
Problem number: 27.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {y {y^{\prime }}^{2}+2 y^{\prime } x -y=0} \]
✓ Solution by Maple
Time used: 0.219 (sec). Leaf size: 75
dsolve(y(x)*diff(y(x),x)^2+2*x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -i x y \left (x \right ) = i x y \left (x \right ) = 0 y \left (x \right ) = \sqrt {c_{1}^{2}-2 c_{1} x} y \left (x \right ) = \sqrt {c_{1}^{2}+2 c_{1} x} y \left (x \right ) = -\sqrt {c_{1}^{2}-2 c_{1} x} y \left (x \right ) = -\sqrt {c_{1}^{2}+2 c_{1} x} \end{align*}
✓ Solution by Mathematica
Time used: 0.451 (sec). Leaf size: 126
DSolve[y[x]*(y'[x])^2+2*x*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -e^{\frac {c_1}{2}} \sqrt {-2 x+e^{c_1}} y(x)\to e^{\frac {c_1}{2}} \sqrt {-2 x+e^{c_1}} y(x)\to -e^{\frac {c_1}{2}} \sqrt {2 x+e^{c_1}} y(x)\to e^{\frac {c_1}{2}} \sqrt {2 x+e^{c_1}} y(x)\to 0 y(x)\to -i x y(x)\to i x \end{align*}