73.17.34 problem 34

Internal problem ID [15497]
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 : 34
Date solved : Monday, March 31, 2025 at 01:39:32 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-12 y^{\prime }+36 y&=81 \,{\mathrm e}^{3 x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

ode:=diff(diff(y(x),x),x)-12*diff(y(x),x)+36*y(x) = 81*exp(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = 9 \,{\mathrm e}^{3 x}+{\mathrm e}^{6 x} \left (c_1 x +c_2 \right ) \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 26

ode=D[y[x],{x,2}]-12*D[y[x],x]+36*y[x]==81*Exp[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{3 x} \left (9+e^{3 x} (c_2 x+c_1)\right ) \]

✓ Sympy. Time used: 0.204 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(36*y(x) - 81*exp(3*x) - 12*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (\left (C_{1} + C_{2} x\right ) e^{3 x} + 9\right ) e^{3 x} \]