63.10.3 problem 7(c)

Internal problem ID [13153]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 2, Second order linear equations. Section 2.3.2 Resonance Exercises page 114
Problem number : 7(c)
Date solved : Tuesday, January 28, 2025 at 05:10:46 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+3025 x&=\cos \left (45 t \right ) \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.070 (sec). Leaf size: 17

dsolve([diff(x(t),t$2)+(55)^2*x(t)=cos(45*t),x(0) = 0, D(x)(0) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = -\frac {\cos \left (55 t \right )}{1000}+\frac {\cos \left (45 t \right )}{1000} \]

✓ Solution by Mathematica

Time used: 0.171 (sec). Leaf size: 109

DSolve[{D[x[t],{t,2}]+55^2*x[t]==Cos[45*t],{x[0]==0,Derivative[1][x][0 ]==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to -\sin (55 t) \int _1^0\frac {1}{55} \cos (45 K[2]) \cos (55 K[2])dK[2]+\sin (55 t) \int _1^t\frac {1}{55} \cos (45 K[2]) \cos (55 K[2])dK[2]+\cos (55 t) \left (\int _1^t-\frac {1}{55} \cos (45 K[1]) \sin (55 K[1])dK[1]-\int _1^0-\frac {1}{55} \cos (45 K[1]) \sin (55 K[1])dK[1]\right ) \]