75.20.16 problem 655

Internal problem ID [17150]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.5 Linear equations with variable coefficients. The Lagrange method. Exercises page 148
Problem number : 655
Date solved : Tuesday, January 28, 2025 at 09:54:20 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=\frac {1}{\cos \left (x \right )^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)+y(x)=1/cos(x)^3,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 25

DSolve[D[y[x],{x,2}]+y[x]==1/Cos[x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {\sec (x)}{2}+c_1 \cos (x)+\sin (x) (\tan (x)+c_2) \]