83.40.3 problem 3

Internal problem ID [19475]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VIII. Linear equations of second order. Excercise VIII (E) at page 140
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 01:45:47 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&=4 \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)=4*tan(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.147 (sec). Leaf size: 80

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

\[ y(x)\to 2 \sqrt {2} \sin (x) \text {arctanh}\left (\sqrt {2}-\tan \left (\frac {x}{2}\right )\right )+2 \sqrt {2} \sin (x) \text {arctanh}\left (\tan \left (\frac {x}{2}\right )+\sqrt {2}\right )-2 \sqrt {2} \cos (x) \text {arctanh}\left (\sqrt {2} \sin (x)\right )+c_1 \cos (x)+c_2 \sin (x) \]