88.20.3 problem 3

Internal problem ID [24141]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 5. Special Techniques for Linear Equations. Exercises at page 146
Problem number : 3
Date solved : Thursday, October 02, 2025 at 10:00:10 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 33

ode=D[y[x],{x,2}]-3*D[y[x],{x,1}]+2*y[x]==x*Exp[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} e^x \left (-x^2-2 x+2 \left (c_2 e^x-1+c_1\right )\right ) \end{align*}

✓ Sympy. Time used: 0.139 (sec). Leaf size: 19

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

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