20.8.6 problem Problem 6

Internal problem ID [3739]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.4, Complex-Valued Trial Solutions. page 529
Problem number : Problem 6
Date solved : Monday, January 27, 2025 at 07:57:08 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=3 \,{\mathrm e}^{x} \cos \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 29

dsolve(diff(y(x),x$2)+y(x)=3*exp(x)*cos(2*x),y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {3 \cos \left (2 x \right ) {\mathrm e}^{x}}{10}+\cos \left (x \right ) c_{1} +c_{2} \sin \left (x \right )+\frac {3 \sin \left (2 x \right ) {\mathrm e}^{x}}{5} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 34

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

\[ y(x)\to -\frac {3}{10} e^x (\cos (2 x)-2 \sin (2 x))+c_1 \cos (x)+c_2 \sin (x) \]