69.18.28 problem 617

Internal problem ID [18403]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Initial value problem. Exercises page 140
Problem number : 617
Date solved : Thursday, October 02, 2025 at 03:11:28 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right ) \end{align*}

With initial conditions

\begin{align*} y \left (\infty \right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.104 (sec). Leaf size: 14

ode:=diff(diff(y(x),x),x)-4*diff(y(x),x)+4*y(x) = exp(-x)*(9*x^2+5*x-12); 
ic:=[y(infinity) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\operatorname {signum}\left (c_1 \,{\mathrm e}^{2 x}\right ) \infty \]

✗ Mathematica

ode=D[y[x],{x,2}]-4*D[y[x],x]+4*y[x]==Exp[-x]*(9*x^2+5*x-12); 
ic={y[Infinity]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

{}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-9*x**2 - 5*x + 12)*exp(-x) + 4*y(x) - 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(oo): 0} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Couldnt solve for initial conditions