86.10.4 problem 4

Internal problem ID [23184]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 9. The operational method. Exercise 9b at page 134
Problem number : 4
Date solved : Thursday, October 02, 2025 at 09:24:08 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{3 x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 16

ode:=diff(diff(y(x),x),x)-4*diff(y(x),x)+4*y(x) = exp(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_2 +c_1 x +{\mathrm e}^{x}\right ) {\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 21

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

\begin{align*} y(x)&\to e^{2 x} \left (e^x+c_2 x+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.117 (sec). Leaf size: 15

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

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