78.13.6 problem 1 (f)

Internal problem ID [18328]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 18. The Method of Undetermined Coefficients. Problems at page 132
Problem number : 1 (f)
Date solved : Tuesday, January 28, 2025 at 11:46:44 AM
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: 0.003 (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)
 

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

✓ Solution by Mathematica

Time used: 0.016 (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]
 

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