73.15.21 problem 22.7 (f)

Internal problem ID [15381]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.7 (f)
Date solved : Monday, March 31, 2025 at 01:36:04 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=\left (12 x -4\right ) {\mathrm e}^{-5 x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 23

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)+y(x) = (12*x-4)*exp(-5*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-5 x} \left (\left (c_1 x +c_2 \right ) {\mathrm e}^{6 x}+\frac {x}{3}\right ) \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 27

ode=D[y[x],{x,2}]-2*D[y[x],x]+y[x]==(12*x-4)*Exp[-5*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{3} e^{-5 x} x+e^x (c_2 x+c_1) \]

✓ Sympy. Time used: 0.290 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(12*x - 4)*exp(-5*x) + y(x) - 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x e^{- 5 x}}{3} + \left (C_{1} + C_{2} x\right ) e^{x} \]