78.13.9 problem 1 (i)

Internal problem ID [18331]
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 18. The Method of Undetermined Coefficients. Problems at page 132
Problem number : 1 (i)
Date solved : Tuesday, January 28, 2025 at 11:46:52 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=6 \,{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 17

dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=6*exp(x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} \left (c_{1} x +3 x^{2}+c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 21

DSolve[D[y[x],{x,2}] -2*D[y[x],x]+y[x]==6*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (3 x^2+c_2 x+c_1\right ) \]