Internal problem ID [221]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y^{\prime }-6 y-2 \sin \left (3 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)-diff(y(x),x)-6*y(x)=2*sin(3*x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{3 x}+{\mathrm e}^{-2 x} c_{1}+\frac {\cos \left (3 x \right )}{39}-\frac {5 \sin \left (3 x \right )}{39} \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 37
DSolve[y''[x]-y'[x]-6*y[x]==2*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-2 x}+c_2 e^{3 x}+\frac {1}{39} (\cos (3 x)-5 \sin (3 x)) \\ \end{align*}