Internal problem ID [10569]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 1, section 1.3. Exercises page 22
Problem number: 2(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+y-2 \,{\mathrm e}^{-x} x=0} \] With initial conditions \begin {align*} [y \left (-1\right ) = {\mathrm e}+3] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 17
dsolve([diff(y(x),x)+y(x)=2*x*exp(-x),y(-1) = exp(1)+3],y(x), singsol=all)
\[ y \left (x \right ) = \left (x^{2}+3 \,{\mathrm e}^{-1}\right ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 20
DSolve[{y'[x]+y[x]==2*x*Exp[-x],{y[-1]==Exp[1]+3}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x-1} \left (e x^2+3\right ) \\ \end{align*}