80.5.3 problem 4

Internal problem ID [18561]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 32. Problems at page 89
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 12:00:07 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&={\mathrm e}^{z -y^{\prime }} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 16

dsolve(diff(y(z),z)=exp(z-diff(y(z),z)),y(z), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 22

DSolve[D[y[z],z]==Exp[z-D[y[z],z]],y[z],z,IncludeSingularSolutions -> True]
 

\[ y(z)\to \frac {1}{2} W\left (e^z\right )^2+W\left (e^z\right )+c_1 \]