39.2.1 problem Problem 11.44

Internal problem ID [6518]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. Supplementary Problems. page 101
Problem number : Problem 11.44
Date solved : Monday, January 27, 2025 at 02:11:18 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=x^{2}-1 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=x^2-1,y(x), singsol=all)
 

\[ y = \left (c_1 x +c_2 \right ) {\mathrm e}^{x}+x^{2}+4 x +5 \]

✓ Solution by Mathematica

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

DSolve[D[y[x],{x,2}]-2*D[y[x],x]+y[x]==x^2-1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2+x \left (4+c_2 e^x\right )+c_1 e^x+5 \]