20.8.10 problem Problem 10

Internal problem ID [3743]
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 10
Date solved : Monday, January 27, 2025 at 07:57:33 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+10 y&=24 \,{\mathrm e}^{x} \cos \left (3 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 31

dsolve(diff(y(x),x$2)-2*diff(y(x),x)+10*y(x)=24*exp(x)*cos(3*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {{\mathrm e}^{x} \left (3 c_{1} +4\right ) \cos \left (3 x \right )}{3}+4 \,{\mathrm e}^{x} \sin \left (3 x \right ) \left (x +\frac {c_{2}}{4}\right ) \]

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 36

DSolve[D[y[x],{x,2}]-2*D[y[x],x]+10*y[x]==24*Exp[x]*Cos[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} e^x ((2+3 c_2) \cos (3 x)+3 (4 x+c_1) \sin (3 x)) \]