65.14.2 problem 8

Internal problem ID [15823]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 5. The Laplace Transform Method. Exercises 5.3, page 255
Problem number : 8
Date solved : Thursday, October 02, 2025 at 10:28:20 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&={\mathrm e}^{x} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&={\frac {5}{2}} \\ \end{align*}

✓ Maple. Time used: 0.103 (sec). Leaf size: 13

ode:=diff(y(x),x)+y(x) = exp(x); 
ic:=[y(0) = 5/2]; 
dsolve([ode,op(ic)],y(x),method='laplace');
 

\[ y = \frac {5 \cosh \left (x \right )}{2}-\frac {3 \sinh \left (x \right )}{2} \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 20

ode=D[y[x],x]+y[x]==Exp[x]; 
ic={y[0]==5/2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 e^{-x}+\frac {e^x}{2} \end{align*}

✓ Sympy. Time used: 0.073 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - exp(x) + Derivative(y(x), x),0) 
ics = {y(0): 5/2} 
dsolve(ode,func=y(x),ics=ics)
 

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