74.2.7 problem 12

Internal problem ID [15848]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Review exercises, page 23
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 08:09:28 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 25

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+2*y(x)=x,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 33

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

\[ y(x)\to \frac {x-1}{2}+c_2 e^{-x} \cos (x)+c_1 e^{-x} \sin (x) \]