Internal problem ID [5554]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Second-Order Linear Equations. Section 2.2. THE METHOD OF UNDETERMINED
COEFFICIENTS. Page 67
Problem number: 1(f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-3 y^{\prime }+2 y-14 \sin \left (2 x \right )+18 \cos \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=14*sin(2*x)-18*cos(2*x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{2 x} c_{1}+c_{2} {\mathrm e}^{x}+2 \sin \left (2 x \right )+3 \cos \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 31
DSolve[y''[x]-3*y'[x]+2*y[x]==14*Sin[2*x]-18*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 \sin (2 x)+3 \cos (2 x)+e^x \left (c_2 e^x+c_1\right ) \\ \end{align*}