1.10 problem 10

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]

\[ \boxed {y^{\prime }=x \,{\mathrm e}^{-x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 21

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

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