28.1.133 problem 156

Internal problem ID [4439]
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 : 156
Date solved : Monday, January 27, 2025 at 09:17:26 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime } \left (x -\ln \left (y^{\prime }\right )\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 40

dsolve(diff(y(x),x)*(x-ln(diff(y(x),x)))=1,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-1-\operatorname {LambertW}\left (-{\mathrm e}^{-x}\right )^{2}+\left (-x +c_{1} \right ) \operatorname {LambertW}\left (-{\mathrm e}^{-x}\right )}{\operatorname {LambertW}\left (-{\mathrm e}^{-x}\right )} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 29

DSolve[D[y[x],x]*( x-Log[D[y[x],x]]  )==1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{W\left (-e^{-x}\right )}+\log \left (W\left (-e^{-x}\right )\right )+c_1 \]