28.1.129 problem 152

Internal problem ID [4435]
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 : 152
Date solved : Monday, January 27, 2025 at 09:17:18 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} y^{\prime }-6 x \,{\mathrm e}^{x -y}-1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 15

dsolve(diff(y(x),x)-6*x*exp(x-y(x))-1=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \ln \left ({\mathrm e}^{x} \left (3 x^{2}+c_{1} \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.446 (sec). Leaf size: 16

DSolve[D[y[x],x]-6*x*Exp[x-y[x]]-1==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x+\log \left (3 x^2+c_1\right ) \]