52.6.2 problem 22

Internal problem ID [8337]
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. 7.3.1 TRANSLATION ON THE s-AXIS. Page 297
Problem number : 22
Date solved : Monday, January 27, 2025 at 03:49:12 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-y&=1+t \,{\mathrm e}^{t} \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.628 (sec). Leaf size: 15

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

\[ y = -1+\frac {{\mathrm e}^{t} t^{2}}{2}+{\mathrm e}^{t} \]

✓ Solution by Mathematica

Time used: 0.055 (sec). Leaf size: 19

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

\[ y(t)\to \frac {1}{2} e^t \left (t^2+2\right )-1 \]