12.10.2 problem 2

Internal problem ID [1806]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.7 Variation of Parameters. Page 262
Problem number : 2
Date solved : Monday, January 27, 2025 at 05:35:30 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&=\sin \left (2 x \right ) \sec \left (2 x \right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 38

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

\[ y = \frac {\ln \left (\sec \left (2 x \right )\right ) \sin \left (2 x \right )}{4}+\frac {\left (4 c_2 -1\right ) \sin \left (2 x \right )}{4}+\frac {\cos \left (2 x \right ) \left (x +2 c_1 \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 33

DSolve[D[y[x],{x,2}]+4*y[x]==Sin[2*x]*Sec[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (-x+c_1) \cos (2 x)+\sin (x) \cos (x) (2 \log (\cos (x))-1+2 c_2) \]