4.2.11 problem 11

Internal problem ID [1139]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 11
Date solved : Tuesday, September 30, 2025 at 04:23:34 AM
CAS classification : [_separable]

\begin{align*} x +y y^{\prime } {\mathrm e}^{-x}&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.124 (sec). Leaf size: 17

ode:=x+y(x)*diff(y(x),x)/exp(x) = 0; 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \sqrt {-1-2 x \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}} \]

✓ Mathematica. Time used: 1.711 (sec). Leaf size: 19

ode=x+y[x]*D[y[x],x]/Exp[x] == 0; 
ic=y[0]==1; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \sqrt {-2 e^x (x-1)-1} \end{align*}

✓ Sympy. Time used: 0.327 (sec). Leaf size: 22

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

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