64.11.2 problem 2

Internal problem ID [13452]
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 : 2
Date solved : Tuesday, January 28, 2025 at 05:43:16 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=4 \,{\mathrm e}^{2 x}-21 \,{\mathrm e}^{-3 x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 28

dsolve(diff(y(x),x$2)-2*diff(y(x),x)-8*y(x)=4*exp(2*x)-21*exp(-3*x),y(x), singsol=all)
 

\[ y = -\frac {\left (-2 \,{\mathrm e}^{7 x} c_{1} +{\mathrm e}^{5 x}-2 \,{\mathrm e}^{x} c_{2} +6\right ) {\mathrm e}^{-3 x}}{2} \]

✓ Solution by Mathematica

Time used: 0.147 (sec). Leaf size: 38

DSolve[D[y[x],{x,2}]-2*D[y[x],x]-8*y[x]==4*Exp[2*x]-21*Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{2} e^{-3 x} \left (e^{5 x}+6\right )+c_1 e^{-2 x}+c_2 e^{4 x} \]