Internal problem ID [12487]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 5. The Laplace Transform Method. Exercises 5.4, page 265
Problem number: 4 (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+2 y=\left \{\begin {array}{cc} 2 & 0\le x <1 \\ 1 & 1\le x \end {array}\right .} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 22
dsolve([diff(y(x),x)+2*y(x)=piecewise(0<=x and x<1,2,1<=x,1),y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \left \{\begin {array}{cc} 1 & x <1 \\ \frac {1}{2}+\frac {{\mathrm e}^{-2 x +2}}{2} & 1\le x \end {array}\right . \]
✓ Solution by Mathematica
Time used: 0.113 (sec). Leaf size: 37
DSolve[{y'[x]+2*y[x]==Piecewise[{ {2,0<=x<1},{1,1<=x}}],{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \begin {array}{cc} \{ & \begin {array}{cc} e^{-2 x} & x\leq 0 \\ 1 & 0<x\leq 1 \\ \frac {1}{2} \left (1+e^{2-2 x}\right ) & \text {True} \\ \end {array} \\ \end {array} \]