35.6.24 problem 24

Internal problem ID [6174]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number : 24
Date solved : Sunday, March 30, 2025 at 10:41:59 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=12 x \,{\mathrm e}^{3 x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)-6*diff(y(x),x)+9*y(x) = 12*x*exp(3*x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 23

ode=D[y[x],{x,2}]-6D[y[x],x]+9*y[x]==12*x*Exp[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{3 x} \left (2 x^3+c_2 x+c_1\right ) \]

✓ Sympy. Time used: 0.225 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-12*x*exp(3*x) + 9*y(x) - 6*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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