20.1.22 problem Problem 30

Internal problem ID [3579]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number : Problem 30
Date solved : Monday, January 27, 2025 at 07:45:29 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

\begin{align*} y^{\prime }&=\frac {\left (1-y \,{\mathrm e}^{y x}\right ) {\mathrm e}^{-y x}}{x} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.053 (sec). Leaf size: 10

dsolve([diff(y(x),x)=(1-y(x)*exp(x*y(x)))/(x*exp(x*y(x))),y(1) = 0],y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\ln \left (x \right )}{x} \]

✓ Solution by Mathematica

Time used: 0.389 (sec). Leaf size: 11

DSolve[{D[y[x],x]==(1-y[x]*Exp[x*y[x]])/(x*Exp[x*y[x]]),{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\log (x)}{x} \]