75.16.48 problem 521

Internal problem ID [16950]
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 : 521
Date solved : Monday, March 31, 2025 at 03:36:12 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=8 \,{\mathrm e}^{-2 x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)+4*diff(y(x),x)+4*y(x) = 8*exp(-2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-2 x} \left (c_1 x +4 x^{2}+c_2 \right ) \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 23

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

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

✓ Sympy. Time used: 0.232 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = \left (C_{1} + x \left (C_{2} + 4 x\right )\right ) e^{- 2 x} \]