89.23.12 problem 12

Internal problem ID [24816]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 10. Nonhomogeneous Equations: Operational methods. Miscellaneous Exercises at page 162
Problem number : 12
Date solved : Thursday, October 02, 2025 at 10:48:16 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=72 x \,{\mathrm e}^{-x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 26

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x)+2*y(x) = 72*x*exp(-x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left ({\mathrm e}^{3 x} c_1 +c_2 \,{\mathrm e}^{2 x}+12 x +10\right ) {\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 32

ode=D[y[x],{x,2}]-3*D[y[x],{x,1}]+2*y[x]==72*x*Exp[-x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 e^{-x} (6 x+5)+c_1 e^x+c_2 e^{2 x} \end{align*}

✓ Sympy. Time used: 0.147 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-72*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)
 

\[ y{\left (x \right )} = C_{1} e^{x} + C_{2} e^{2 x} + 2 \left (6 x + 5\right ) e^{- x} \]