42.3.12 problem Example 3.41

Internal problem ID [8822]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.5 HIGHER ORDER ODE. Page 181
Problem number : Example 3.41
Date solved : Tuesday, September 30, 2025 at 05:52:56 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=50 \,{\mathrm e}^{2 x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 20

ode:=diff(diff(y(x),x),x)+6*diff(y(x),x)+9*y(x) = 50*exp(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (2 \,{\mathrm e}^{5 x}+c_1 x +c_2 \right ) {\mathrm e}^{-3 x} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 25

ode=D[y[x],{x,2}]+6*D[y[x],x]+9*y[x]==50*Exp[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-3 x} \left (2 e^{5 x}+c_2 x+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.114 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) - 50*exp(2*x) + 6*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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