65.14.1 problem 7

Internal problem ID [15822]
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 : 7
Date solved : Thursday, October 02, 2025 at 10:28:19 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-2 y&=6 \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.112 (sec). Leaf size: 15

ode:=diff(y(x),x)-2*y(x) = 6; 
ic:=[y(0) = 2]; 
dsolve([ode,op(ic)],y(x),method='laplace');
 

\[ y = 2 \,{\mathrm e}^{x} \left (\cosh \left (x \right )+4 \sinh \left (x \right )\right ) \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 14

ode=D[y[x],x]-2*y[x]==6; 
ic={y[0]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 5 e^{2 x}-3 \end{align*}

✓ Sympy. Time used: 0.071 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*y(x) + Derivative(y(x), x) - 6,0) 
ics = {y(0): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 5 e^{2 x} - 3 \]