78.14.7 problem 3 (e)

Internal problem ID [18343]
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 19. The Method of Variation of Parameters. Problems at page 135
Problem number : 3 (e)
Date solved : Tuesday, January 28, 2025 at 11:47:44 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+y&={\mathrm e}^{-3 x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

dsolve(2*diff(y(x),x$2)+3*diff(y(x),x)+y(x)=exp(-3*x),y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-3 x}}{10}-2 \,{\mathrm e}^{-x} c_{1} +{\mathrm e}^{-\frac {x}{2}} c_{2} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 33

DSolve[2*D[y[x],{x,2}] +3*D[y[x],x]+y[x]==Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{-3 x}}{10}+c_1 e^{-x/2}+c_2 e^{-x} \]