75.16.37 problem 510

Internal problem ID [16939]
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 : 510
Date solved : Monday, March 31, 2025 at 03:35:55 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=-2 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 23

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

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

✓ Sympy. Time used: 0.148 (sec). Leaf size: 12

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

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