Internal problem ID [11696]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, Miscellaneous Review. Exercises page 60
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+y=\left \{\begin {array}{cc} 1 & 0\le x <2 \\ 0 & 0<x \end {array}\right .} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.313 (sec). Leaf size: 36
dsolve([diff(y(x),x)+y(x)=piecewise(0<=x and x<2,1,x>0,0),y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \left \{\begin {array}{cc} 0 & x <0 \\ 1-{\mathrm e}^{-x} & x <2 \\ {\mathrm e}^{2-x}-{\mathrm e}^{-x} & 2\le x \end {array}\right . \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 39
DSolve[{y'[x]+y[x]==Piecewise[{{1,0<=x<2},{0,x>2}}],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \begin {array}{cc} \{ & \begin {array}{cc} 0 & x\leq 0 \\ 1-e^{-x} & 0<x\leq 2 \\ e^{-x} \left (-1+e^2\right ) & \text {True} \\ \end {array} \\ \end {array} \]