Internal problem ID [10]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.2. Integrals as general and particular solutions. Page 16
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-x \,{\mathrm e}^{-x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve([diff(y(x),x) = x/exp(x),y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = 2+\left (-x -1\right ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 17
DSolve[{y'[x]== x/Exp[x],y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2-e^{-x} (x+1) \\ \end{align*}