69.18.24 problem 613

Internal problem ID [18399]
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 : 613
Date solved : Friday, October 03, 2025 at 07:32:26 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=8 \,{\mathrm e}^{x}+9 \end{align*}

With initial conditions

\begin{align*} y \left (-\infty \right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.084 (sec). Leaf size: 14

ode:=diff(diff(y(x),x),x)+4*diff(y(x),x)+3*y(x) = 8*exp(x)+9; 
ic:=[y(-infinity) = 3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\operatorname {signum}\left (c_2 \,{\mathrm e}^{-x}\right ) \infty \]

✗ Mathematica

ode=D[y[x],{x,2}]+4*D[y[x],x]+3*y[x]==8*Exp[x]+9; 
ic={y[-Infinity]==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

{}

✓ Sympy. Time used: 0.127 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*y(x) - 8*exp(x) + 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 9,0) 
ics = {y(-inf): 3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{2} e^{- x} + \left (- C_{2} e^{- 2 inf} - e^{- 4 inf}\right ) e^{- 3 x} + e^{x} + 3 \]