20.3.20 problem Problem 20

Internal problem ID [3629]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.6, First-Order Linear Differential Equations. page 59
Problem number : Problem 20
Date solved : Monday, January 27, 2025 at 07:47:54 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-2 y&=\left \{\begin {array}{cc} 1 & x \le 1 \\ 0 & 1<x \end {array}\right . \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.201 (sec). Leaf size: 27

dsolve([diff(y(x),x)-2*y(x)=piecewise(x<=1,1,x>1,0),y(0) = 3],y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {7 \,{\mathrm e}^{2 x}}{2}-\frac {\left (\left \{\begin {array}{cc} 1 & x <1 \\ {\mathrm e}^{2 x -2} & 1\le x \end {array}\right .\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 42

DSolve[{D[y[x],x] - 2*y[x] == Piecewise[{{1, x <= 1}, {0, x > 1}}],{y[0]==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \begin {array}{cc} \{ & \begin {array}{cc} \frac {1}{2} \left (-1+7 e^{2 x}\right ) & x\leq 1 \\ \frac {1}{2} e^{2 x-2} \left (-1+7 e^2\right ) & \text {True} \\ \end {array} \\ \end {array} \]