50.10.6 problem 1(f)

Internal problem ID [7975]
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)
Date solved : Monday, January 27, 2025 at 03:34:51 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=14 \sin \left (2 x \right )-18 \cos \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (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)
 

\[ y = {\mathrm e}^{2 x} c_{1} +{\mathrm e}^{x} c_{2} +2 \sin \left (2 x \right )+3 \cos \left (2 x \right ) \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 31

DSolve[D[y[x],{x,2}]-3*D[y[x],x]+2*y[x]==14*Sin[2*x]-18*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 \sin (2 x)+3 \cos (2 x)+e^x \left (c_2 e^x+c_1\right ) \]