83.8.23 problem 24

Internal problem ID [19149]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Misc examples on chapter II at page 25
Problem number : 24
Date solved : Tuesday, January 28, 2025 at 08:30:17 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

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

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 5.485 (sec). Leaf size: 29

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

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