7.4.27 problem 27

Internal problem ID [99]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.5 (linear equations). Problems at page 54
Problem number : 27
Date solved : Friday, February 07, 2025 at 07:49:23 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} \frac {x+y \,{\mathrm e}^{y}}{x^{\prime }}&=1 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

dsolve((x(y)+y*exp(y))*1/diff(x(y),y)=1,x(y), singsol=all)
 

\[ x = \frac {{\mathrm e}^{y} \left (y^{2}+2 c_1 \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 20

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

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