Internal problem ID [2149]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-2 y-\left (\left \{\begin {array}{cc} 1 & x \le 1 \\ 0 & 1<x \end {array}\right .\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.078 (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)
\[ y \relax (x ) = \frac {7 \,{\mathrm e}^{2 x}}{2}-\frac {\left (\left \{\begin {array}{cc} 1 & x <1 \\ {\mathrm e}^{2 x -2} & 1\le x \end {array}\right .\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 42
DSolve[{ode = y'[x] - 2*y[x] == Piecewise[{{1, x <= 1}, {0, x > 1}}],{y[0]==3}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to {cc} \{ & {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{align*}