Internal problem ID [2716]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 83.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {x y^{\prime } \left (y^{\prime }+2\right )-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 49
dsolve(x*diff(y(x),x)*(diff(y(x),x)+2)=y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = -x \\ y \relax (x ) = \sqrt {c_{1} x}\, \left (\frac {\sqrt {c_{1} x}}{x}+2\right ) \\ y \relax (x ) = -\sqrt {c_{1} x}\, \left (-\frac {\sqrt {c_{1} x}}{x}+2\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.179 (sec). Leaf size: 63
DSolve[x*y'[x]*(y'[x]+2)==y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{c_1}-2 e^{\frac {c_1}{2}} \sqrt {x} \\ y(x)\to 2 e^{-\frac {c_1}{2}} \sqrt {x}+e^{-c_1} \\ y(x)\to 0 \\ y(x)\to -x \\ \end{align*}