78.14.3 problem 3 (a)

Internal problem ID [18339]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 19. The Method of Variation of Parameters. Problems at page 135
Problem number : 3 (a)
Date solved : Tuesday, January 28, 2025 at 11:47:22 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

dsolve(diff(y(x),x$2)+4*y(x)=tan(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 40

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

\[ y(x)\to -\frac {1}{4} \cos (2 x) \text {arctanh}(\sin (2 x))+c_1 \cos (2 x)+\frac {1}{4} (-1+4 c_2) \sin (2 x) \]