46.6.2 problem 22

Internal problem ID [9623]
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 : Tuesday, September 30, 2025 at 06:21:34 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*}

✓ Maple. Time used: 0.091 (sec). Leaf size: 15

ode:=diff(y(t),t)-y(t) = 1+t*exp(t); 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

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

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 19

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

\begin{align*} y(t)&\to \frac {1}{2} e^t \left (t^2+2\right )-1 \end{align*}

✓ Sympy. Time used: 0.095 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t*exp(t) - y(t) + Derivative(y(t), t) - 1,0) 
ics = {y(0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

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