81.5.8 problem 8

Internal problem ID [18671]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter IV. Ordinary linear differential equations with constant coefficients. Exercises at page 58
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 12:09:08 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 21

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

\[ y(x)\to x+c_2 e^x x+c_1 e^x+2 \]