Internal problem ID [3234]
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: 0.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _dAlembert]
\[ \boxed {2 x y^{\prime }-y-\ln \left (y^{\prime }\right )=0} \]
✓ 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 \left (x \right ) = 1+\sqrt {4 c_{1} x +1}-\ln \left (\frac {1+\sqrt {4 c_{1} x +1}}{2 x}\right ) y \left (x \right ) = 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: 0.106 (sec). Leaf size: 34
DSolve[2*x*y'[x] -y[x] == Log[y'[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [W\left (-2 x e^{-y(x)}\right )-\log \left (W\left (-2 x e^{-y(x)}\right )+2\right )+y(x)=c_1,y(x)\right ] \]