20.7.9 problem Problem 33

Internal problem ID [3724]
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 8.3, The Method of Undetermined Coefficients. page 525
Problem number : Problem 33
Date solved : Monday, January 27, 2025 at 07:56:14 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=5 \cos \left (2 x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.031 (sec). Leaf size: 17

dsolve([diff(y(x),x$2)+9*y(x)=5*cos(2*x),y(0) = 2, D(y)(0) = 3],y(x), singsol=all)
 

\[ y \left (x \right ) = \sin \left (3 x \right )+\cos \left (3 x \right )+\cos \left (2 x \right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 18

DSolve[{D[y[x],{x,2}]+9*y[x]==5*Cos[2*x],{y[0]==2,Derivative[1][y][0] ==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sin (3 x)+\cos (2 x)+\cos (3 x) \]