75.16.49 problem 522

Internal problem ID [16943]
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. Trial and error method. Exercises page 132
Problem number : 522
Date solved : Thursday, March 13, 2025 at 09:00:53 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 24

ode:=diff(diff(y(x),x),x)+4*diff(y(x),x)+3*y(x) = 9*exp(-3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-9 x +2 c_{2} \right ) {\mathrm e}^{-3 x}}{2}+c_{1} {\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 32

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

\[ y(x)\to \frac {1}{4} e^{-3 x} \left (-18 x+4 c_2 e^{2 x}-9+4 c_1\right ) \]

✓ Sympy. Time used: 0.271 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = \left (C_{1} + \left (C_{2} - \frac {9 x}{2}\right ) e^{- 2 x}\right ) e^{- x} \]