Internal problem ID [2725]
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: 92.
ODE order: 1.
ODE degree: -1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _dAlembert]
Solve \begin {gather*} \boxed {2 y^{\prime } x -y-\ln \left (y^{\prime }\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 65
dsolve(2*x*diff(y(x),x) -y(x) = ln(diff(y(x),x)),y(x), singsol=all)
\begin{align*} y \relax (x ) = 1+\sqrt {4 c_{1} x +1}-\ln \left (\frac {1+\sqrt {4 c_{1} x +1}}{2 x}\right ) \\ y \relax (x ) = 1-\sqrt {4 c_{1} x +1}-\ln \left (-\frac {-1+\sqrt {4 c_{1} x +1}}{2 x}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.119 (sec). Leaf size: 34
DSolve[2*x*y'[x] -y[x] == Log[y'[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\text {ProductLog}\left (-2 x e^{-y(x)}\right )-\log \left (\text {ProductLog}\left (-2 x e^{-y(x)}\right )+2\right )+y(x)=c_1,y(x)\right ] \]