73.17.36 problem 36

Internal problem ID [15491]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 36
Date solved : Thursday, March 13, 2025 at 06:05:31 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-12 y^{\prime }+36 y&=3 x \,{\mathrm e}^{6 x}-2 \,{\mathrm e}^{6 x} \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 27

ode:=diff(diff(y(x),x),x)-12*diff(y(x),x)+36*y(x) = 3*x*exp(6*x)-2*exp(6*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{6 x} \left (c_{2} +c_{1} x +\frac {1}{2} x^{3}-x^{2}+\frac {4}{9} x \right ) \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 32

ode=D[y[x],{x,2}]-12*D[y[x],x]+36*y[x]==3*x*Exp[6*x]-2*Exp[6*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{2} e^{6 x} \left (x^3-2 x^2+2 c_2 x+2 c_1\right ) \]

✓ Sympy. Time used: 0.296 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x*exp(6*x) + 36*y(x) + 2*exp(6*x) - 12*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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