65.13.9 problem 9

Internal problem ID [15816]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 5. The Laplace Transform Method. Exercises 5.2, page 248
Problem number : 9
Date solved : Thursday, October 02, 2025 at 10:28:16 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-y&=2 \,{\mathrm e}^{x} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.088 (sec). Leaf size: 12

ode:=diff(y(x),x)-y(x) = 2*exp(x); 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(x),method='laplace');
 

\[ y = \left (2 x +1\right ) {\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 14

ode=D[y[x],x]-y[x]==2*Exp[x]; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^x (2 x+1) \end{align*}

✓ Sympy. Time used: 0.073 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) - 2*exp(x) + Derivative(y(x), x),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

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