8.11.25 problem 48

Internal problem ID [893]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 48
Date solved : Monday, January 27, 2025 at 03:16:45 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=3 \,{\mathrm e}^{-2 x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 24

dsolve(diff(y(x),x$2)-2*diff(y(x),x)-8*y(x)=3*exp(-2*x),y(x), singsol=all)
 

\[ y = \frac {\left (-x +2 c_2 \right ) {\mathrm e}^{-2 x}}{2}+{\mathrm e}^{4 x} c_1 \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 32

DSolve[D[y[x],{x,2}]-2*D[y[x],x]-8*y[x]==3*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{12} e^{-2 x} \left (-6 x+12 c_2 e^{6 x}-1+12 c_1\right ) \]