78.16.4 problem 4

Internal problem ID [18383]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 23. Operator Methods for Finding Particular Solutions. Problems at page 169
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 11:48:37 AM
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: 0.003 (sec). Leaf size: 17

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

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

✓ 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]
 

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