73.16.16 problem 24.2 (b)

Internal problem ID [15528]
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 : 24.2 (b)
Date solved : Tuesday, January 28, 2025 at 08:01:19 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=12 \,{\mathrm e}^{2 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=8 \end{align*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 23

dsolve([diff(y(x),x$2)-diff(y(x),x)-6*y(x)=12*exp(2*x),y(0) = 0, D(y)(0) = 8],y(x), singsol=all)
 

\[ y = \left (4 \,{\mathrm e}^{5 x}-3 \,{\mathrm e}^{4 x}-1\right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 27

DSolve[{D[y[x],{x,2}]-D[y[x],x]-6*y[x]==12*Exp[2*x],{y[0]==0,Derivative[1][y][0] ==8}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (-3 e^{4 x}+4 e^{5 x}-1\right ) \]