Internal problem ID [6307]
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]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }+2 y=14 \sin \left (2 x \right )-18 \cos \left (2 x \right )} \]
✓ 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)
\[ y \left (x \right ) = {\mathrm e}^{2 x} c_{1} +{\mathrm e}^{x} c_{2} +2 \sin \left (2 x \right )+3 \cos \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.027 (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]
\[ y(x)\to 2 \sin (2 x)+3 \cos (2 x)+e^x \left (c_2 e^x+c_1\right ) \]