15.11 problem 11

Internal problem ID [11518]

Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section: Chapter 3, Laplace transform. Section 3.2.1 Initial value problems. Exercises page 156
Problem number: 11.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_linear, `class A`]]

\[ \boxed {x^{\prime }+4 x-\cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right )=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = 0] \end {align*}

✗ Solution by Maple

dsolve([diff(x(t),t)+4*x(t)=cos(2*t)*Heaviside(2*Pi-t),x(0) = 0, D(x)(0) = 0],x(t), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.168 (sec). Leaf size: 28

DSolve[{x''[t]+4*x[t]==Cos[2*t]*UnitStep[2*Pi-t],{x[0]==0,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

\[ x(t)\to \begin {array}{cc} \{ & \begin {array}{cc} \pi \cos (t) \sin (t) & t>2 \pi \\ \frac {1}{2} t \cos (t) \sin (t) & \text {True} \\ \end {array} \\ \end {array} \]