40.10.2 problem 11

Internal problem ID [6724]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 15. Linear equations with constant coefficients (Variation of parameters). Supplemetary problems. Page 98
Problem number : 11
Date solved : Monday, January 27, 2025 at 02:25:01 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 44

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

\[ y = \left (-8 \cos \left (x \right )^{2}+4\right ) \ln \left (\sec \left (x \right )\right )+2 c_1 \cos \left (x \right )^{2}+8 \left (x +\frac {c_2}{4}\right ) \sin \left (x \right ) \cos \left (x \right )-4 \sin \left (x \right )^{2}-c_1 \]

✓ Solution by Mathematica

Time used: 0.066 (sec). Leaf size: 44

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

\[ y(x)\to 2 \sin (2 x) \arctan (\tan (x))+2 x \sin (2 x)+c_2 \sin (2 x)+\cos (2 x) (4 \log (\cos (x))+2+c_1)-2 \]