81.5.7 problem 7

Internal problem ID [18670]
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 : 7
Date solved : Tuesday, January 28, 2025 at 12:09:06 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 25

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

\[ y(x)\to \frac {1}{2} e^x \left (x^2+2 c_2 x+2 c_1\right ) \]