Internal problem ID [2150]
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 21.
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 & x <1 \\ 0 & 1\le x \end {array}\right .\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.146 (sec). Leaf size: 31
dsolve([diff(y(x),x)-2*y(x)=piecewise(x<1,1-x,x>=1,0),y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {5 \,{\mathrm e}^{2 x}}{4}+\frac {\left (\left \{\begin {array}{cc} 2 x -1 & x <1 \\ {\mathrm e}^{2 x -2} & 1\le x \end {array}\right .\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 45
DSolve[{y'[x] - 2*y[x] == Piecewise[{{1-x, x < 1}, {0, x >= 1}}],{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to {cc} \{ & {cc} \frac {1}{4} \left (2 x+5 e^{2 x}-1\right ) & x\leq 1 \\ \frac {1}{4} e^{2 x-2} \left (1+5 e^2\right ) & \text {True} \\ \\ \\ \\ \\ \end{align*}