3.5 problem Problem 12.5

Internal problem ID [4680]

Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section: Chapter 12. VARIATION OF PARAMETERS. page 104
Problem number: Problem 12.5.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]

Solve \begin {gather*} \boxed {x^{\prime \prime }+4 x-\left (\sin ^{2}\left (2 t \right )\right )=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 24

dsolve(diff(x(t),t$2)+4*x(t)=sin(2*t)^2,x(t), singsol=all)
 

\[ x \relax (t ) = \sin \left (2 t \right ) c_{2}+\cos \left (2 t \right ) c_{1}+\frac {1}{8}+\frac {\cos \left (4 t \right )}{24} \]

Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 30

DSolve[x''[t]+4*x[t]==Sin[2*t]^2,x[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{24} (\cos (4 t)+3)+c_1 \cos (2 t)+c_2 \sin (2 t) \\ \end{align*}