52.5.1 problem 31

Internal problem ID [8324]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 7 THE LAPLACE TRANSFORM. 7.2.2 TRANSFORMS OF DERIVATIVES Page 289
Problem number : 31
Date solved : Monday, January 27, 2025 at 03:49:02 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-y&=1 \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.658 (sec). Leaf size: 8

dsolve([diff(y(t),t)-y(t)=1,y(0) = 0],y(t), singsol=all)
 

\[ y = {\mathrm e}^{t}-1 \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 10

DSolve[{D[y[t],t]-y[t]==1,{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^t-1 \]