64.11.29 problem 29

Internal problem ID [13479]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page 151
Problem number : 29
Date solved : Tuesday, January 28, 2025 at 05:45:00 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=8 \,{\mathrm e}^{-2 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 18

dsolve([diff(y(x),x$2)+8*diff(y(x),x)+16*y(x)=8*exp(-2*x),y(0) = 2, D(y)(0) = 0],y(x), singsol=all)
 

\[ y = 4 \,{\mathrm e}^{-4 x} x +2 \,{\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 21

DSolve[{D[y[x],{x,2}]+8*D[y[x],x]+16*y[x]==8*Exp[-2*x],{y[0]==2,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

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