69.1.118 problem 169

Internal problem ID [14200]
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 : Monday, March 31, 2025 at 12:12:16 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 21

ode:=diff(diff(y(x),x),x)+y(x) = 1/cos(2*x)^(3/2); 
dsolve(ode,y(x), singsol=all);
 

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

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

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

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) + Derivative(y(x), (x, 2)) - 1/cos(2*x)**(3/2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out