50.11.14 problem 3

Internal problem ID [7998]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Second-Order Linear Equations. Section 2.3. THE METHOD OF VARIATION OF PARAMETERS. Page 71
Problem number : 3
Date solved : Monday, January 27, 2025 at 03:36:27 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 26

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

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