78.13.3 problem 1 (c)

Internal problem ID [18325]
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 (c)
Date solved : Tuesday, January 28, 2025 at 11:46:24 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=14 \,{\mathrm e}^{-5 x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)+10*diff(y(x),x)+25*y(x)=14*exp(-5*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{-5 x} \left (c_{1} x +7 x^{2}+c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 23

DSolve[D[y[x],{x,2}] +10*D[y[x],x]+25*y[x]==14*Exp[-5*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-5 x} \left (7 x^2+c_2 x+c_1\right ) \]