69.1.118 problem 169

Internal problem ID [14271]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 169
Date solved : Tuesday, January 28, 2025 at 06:25:10 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=\frac {1}{\cos \left (2 x \right )^{{3}/{2}}} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 26

DSolve[D[y[x],{x,2}]+y[x]==1/(Cos[2*x]*Sqrt[Cos[2*x]]),y[x],x,IncludeSingularSolutions -> True]
 

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