8.11.3 problem 3

Internal problem ID [871]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 3
Date solved : Monday, January 27, 2025 at 03:10:59 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=2 \sin \left (3 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 34

dsolve(diff(y(x),x$2)-diff(y(x),x)-6*y(x)=2*sin(3*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{-2 x} \left (\frac {\left (\cos \left (3 x \right )-5 \sin \left (3 x \right )\right ) {\mathrm e}^{2 x}}{39}+{\mathrm e}^{5 x} c_2 +c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 37

DSolve[D[y[x],{x,2}]-D[y[x],x]-6*y[x]==2*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{-2 x}+c_2 e^{3 x}+\frac {1}{39} (\cos (3 x)-5 \sin (3 x)) \]