73.16.4 problem 24.1 (d)

Internal problem ID [15516]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 24. Variation of parameters. Additional exercises page 444
Problem number : 24.1 (d)
Date solved : Tuesday, January 28, 2025 at 08:00:48 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&=6 \,{\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 23

dsolve(diff(y(x),x$2)-7*diff(y(x),x)+10*y(x)=6*exp(3*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{5 x} c_{2} +{\mathrm e}^{2 x} c_{1} -3 \,{\mathrm e}^{3 x} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 27

DSolve[D[y[x],{x,2}]-7*D[y[x],x]+10*y[x]==6*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

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