67.15.47 problem 22.11 (f)

Internal problem ID [16765]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.11 (f)
Date solved : Thursday, October 02, 2025 at 01:38:38 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{3 x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)-5*diff(y(x),x)+6*y(x) = 4*exp(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{2 x} \left (\left (c_2 +4 x \right ) {\mathrm e}^{x}+c_1 \right ) \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 25

ode=D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==4*Exp[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{2 x} \left (e^x (4 x-4+c_2)+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.129 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*y(x) - 4*exp(3*x) - 5*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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