Internal problem ID [11049]
Book: Differential Equations, Linear, Nonlinear, Ordinary, Partial. A.C. King, J.Billingham, S.R.Otto.
Cambridge Univ. Press 2003
Section: Chapter 1 VARIABLE COEFFICIENT, SECOND ORDER DIFFERENTIAL EQUATIONS.
Problems page 28
Problem number: Problem 1.3(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y-2 \sec \left (2 x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(diff(y(x),x$2)+4*y(x)=2*sec(2*x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} \sin \left (2 x \right )+c_{1} \cos \left (2 x \right )+x \sin \left (2 x \right )-\frac {\ln \left (\sec \left (2 x \right )\right ) \cos \left (2 x \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 32
DSolve[y''[x]+4*y[x]==2*Sec[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (x+c_2) \sin (2 x)+\cos (2 x) \left (\frac {1}{2} \log (\cos (2 x))+c_1\right ) \\ \end{align*}