88.22.13 problem 17

Internal problem ID [24173]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 5. Special Techniques for Linear Equations. Exercises at page 160 (Laplace transform)
Problem number : 17
Date solved : Thursday, October 02, 2025 at 10:00:26 PM
CAS classification : [[_linear, `class A`]]

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

Using Laplace method With initial conditions

\begin{align*} y \left (2\right )&=\frac {4 \,{\mathrm e}^{2}}{3} \\ \end{align*}

✓ Maple. Time used: 0.042 (sec). Leaf size: 15

ode:=2*diff(y(x),x)+y(x) = exp(x); 
ic:=[y(2) = 4/3*exp(2)]; 
dsolve([ode,op(ic)],y(x),method='laplace');
 

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

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 30

ode=2*D[y[x],{x,1}]+y[x]==Exp[x]; 
ic={y[0]==4/3*Exp[2]}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{3} e^{-x/2} \left (e^{3 x/2}-1+4 e^2\right ) \end{align*}

✓ Sympy. Time used: 0.109 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - exp(x) + 2*Derivative(y(x), x),0) 
ics = {y(0): 4*exp(2)/3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {e^{x}}{3} + \left (- \frac {1}{3} + \frac {4 e^{2}}{3}\right ) e^{- \frac {x}{2}} \]