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 : Saturday, March 29, 2025 at 04:31:22 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

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

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

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

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

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

✓ Sympy. Time used: 0.167 (sec). Leaf size: 12

from sympy import * 
y = symbols("y") 
x = Function("x") 
ode = Eq((y*exp(y) + x(y))/Derivative(x(y), y) - 1,0) 
ics = {} 
dsolve(ode,func=x(y),ics=ics)
 

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