39.5.3 problem Problem 24.19

Internal problem ID [6545]
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 : Wednesday, March 05, 2025 at 12:56:22 AM
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: 0.152 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.046 (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]
 

\[ y(x)\to \frac {1}{3} e^{-2 x} \left (e^{3 x}+2\right ) \]

✓ Sympy. Time used: 0.161 (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)
 

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