67.8.4 problem 13.1 (d)

Internal problem ID [16499]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 13. Higher order equations: Extending first order concepts. Additional exercises page 259
Problem number : 13.1 (d)
Date solved : Thursday, October 02, 2025 at 01:35:36 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }&=8 \,{\mathrm e}^{2 x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)+2*diff(y(x),x) = 8*exp(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {{\mathrm e}^{-2 x} c_1}{2}+{\mathrm e}^{2 x}+c_2 \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 24

ode=D[y[x],{x,2}]+2*D[y[x],x]==8*Exp[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{2 x}-\frac {1}{2} c_1 e^{-2 x}+c_2 \end{align*}

✓ Sympy. Time used: 0.103 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*exp(2*x) + 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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