38.4.2 problem 2

Internal problem ID [6488]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 25. Second order differential equations. Further problems 25. page 1094
Problem number : 2
Date solved : Wednesday, March 05, 2025 at 12:51:59 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=54 x +18 \end{align*}

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

ode:=diff(diff(y(x),x),x)-6*diff(y(x),x)+9*y(x) = 54*x+18; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 x +c_2 \right ) {\mathrm e}^{3 x}+6 x +6 \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 27

ode=D[y[x],{x,2}]-6*D[y[x],x]+9*y[x]==54*x+18; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 e^{3 x}+x \left (6+c_2 e^{3 x}\right )+6 \]

✓ Sympy. Time used: 0.168 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-54*x + 9*y(x) - 6*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 18,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 6 x + \left (C_{1} + C_{2} x\right ) e^{3 x} + 6 \]