Internal problem ID [489]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x +y y^{\prime } {\mathrm e}^{-x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 17
dsolve([x+y(x)*diff(y(x),x)/exp(x) = 0,y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \sqrt {-1-2 x \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}} \]
✓ Solution by Mathematica
Time used: 0.152 (sec). Leaf size: 19
DSolve[{x+y[x]*y'[x]/Exp[x] == 0,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {-2 e^x (x-1)-1} \\ \end{align*}