Internal problem ID [11586]
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(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+y=2 x \,{\mathrm e}^{-x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve([diff(y(x),x)+y(x)=2*x*exp(-x),y(0) = 2],y(x), singsol=all)
\[ y \left (x \right ) = \left (x^{2}+2\right ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.087 (sec). Leaf size: 16
DSolve[{y'[x]+y[x]==2*x*Exp[-x],{y[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (x^2+2\right ) \]