10.2.11 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 : Monday, January 27, 2025 at 04:35:26 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*}

✓ Solution by Maple

Time used: 0.063 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 1.758 (sec). Leaf size: 19

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

\[ y(x)\to \sqrt {-2 e^x (x-1)-1} \]