84.3.2 problem 2.2

Internal problem ID [22079]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 2. Solutions. Solved problems page 5
Problem number : 2.2
Date solved : Thursday, October 02, 2025 at 08:23:35 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 50

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

\begin{align*} y(x)&\to x+c_2 e^{-x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_1 e^{-x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )-1 \end{align*}

✓ Sympy. Time used: 0.095 (sec). Leaf size: 34

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

\[ y{\left (x \right )} = x + \left (C_{1} \sin {\left (\frac {\sqrt {3} x}{2} \right )} + C_{2} \cos {\left (\frac {\sqrt {3} x}{2} \right )}\right ) e^{- \frac {x}{2}} - 1 \]