73.14.6 problem 21.8

Internal problem ID [15416]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 21. Nonhomogeneous equations in general. Additional exercises page 391
Problem number : 21.8
Date solved : Tuesday, January 28, 2025 at 07:54:59 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-6 \,{\mathrm e}^{4 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=8 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 21

dsolve([diff(y(x),x$2)-3*diff(y(x),x)-10*y(x)=-6*exp(4*x),y(0) = 6, D(y)(0) = 8],y(x), singsol=all)
 

\[ y = \left (2 \,{\mathrm e}^{7 x}+{\mathrm e}^{6 x}+3\right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 25

DSolve[{D[y[x],{x,2}]-3*D[y[x],x]-10*y[x]==-6*Exp[4*x],{y[0]==6,Derivative[1][y][0] ==8}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (e^{6 x}+2 e^{7 x}+3\right ) \]