87.17.20 problem 20

Internal problem ID [23612]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 127
Problem number : 20
Date solved : Thursday, October 02, 2025 at 09:43:27 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to \frac {1}{6} e^x \left (x^3+6 c_2 x+6 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.130 (sec). Leaf size: 15

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

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