33.5.3 problem Problem 24.19

Internal problem ID [7832]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 24. Solutions of linear DE by Laplace transforms. Supplementary Problems. page 248
Problem number : Problem 24.19
Date solved : Tuesday, September 30, 2025 at 05:06:07 PM
CAS classification : [[_linear, `class A`]]

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

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.089 (sec). Leaf size: 15

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

\[ y = \frac {{\mathrm e}^{x}}{3}+\frac {2 \,{\mathrm e}^{-2 x}}{3} \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 21

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

\begin{align*} y(x)&\to \frac {1}{3} e^{-2 x} \left (e^{3 x}+2\right ) \end{align*}

✓ Sympy. Time used: 0.078 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = \frac {e^{x}}{3} + \frac {2 e^{- 2 x}}{3} \]